An analytic similarity theory for the planetary boundary layer stabilized by surface buoyancy

An analytic solution for a steady, horizontally homogeneous boundary layer with rotation, % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadAgaaaa!38AA! \[ f \] , and surface friction velocity, û_*, subjected to surface buoyancy characterized by Obukhov length L, is proposed as follows. Nondimensional variables are % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeA7a6jabg2 % da9iaadAgacaWG6bGaai4laiabeE7aOnaaBaaaleaacqGHxiIkaeqa % aOGaamyDamaaBaaaleaacqGHxiIkaeqaaOGaaiilaiqadwhagaqcai % abg2da9iabeE7aOnaaBaaaleaacqGHxiIkaeqaaOGabmyvayaajaGa % ai4laiqadwhagaqcamaaBaaaleaacqGHxiIkaeqaaOGaaiilaiqads % fagaqcaiabg2da9iqbes8a0zaajaGaai4laiaadwhadaWgaaWcbaGa % ey4fIOcabeaakiqadwhagaqcamaaBaaaleaacqGHxiIkcaGGSaaabe % aaaaa!5587! \[ \zeta = fz/\eta _ * u_ * ,\hat u = \eta _ * \hat U/\hat u_ * ,\hat T = \hat \tau /u_ * \hat u_{ * ,} \] , where carets denote complex (vector) quantities; Û is the mean velocity; % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiqbes8a0zaaja% aaaa!3994!\[\hat \tau \]is the kinematic turbulent stress; and % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeE7aOnaaBa % aaleaacqGHxiIkaeqaaOGaeyypa0JaaiikaiaaigdacqGHRaWkcqaH % +oaEdaWgaaWcbaGaamOtaaqabaGccaWG1bWaaSbaaSqaaiabgEHiQa % qabaGccaGGVaGaamOuamaaBaaaleaacaWGJbaabeaakiaadAgacaWG % mbGaaiykamaaCaaaleqabaGaeyOeI0IaaGymaiaac+cacaaIYaaaaa % aa!4B1F! \[ \eta _ * = (1 + \xi _N u_ * /R_c fL)^{ - 1/2} \]is a stability parameter. The constant % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabe67a4naaBa % aaleaacaWGobaabeaaaaa!3A81! \[\xi _N \] is the ratio of the maximum mixing length(% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaamaaBaaaleaaca% WGTbaabeaaaaa!38DD!\[_m \]) to the PBL depth, % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadwhadaWgaa % WcbaGaey4fIOcabeaakiaac+cacaWGMbaaaa!3B7C! \[ u_ * /f \] , for neutrally stable conditions; and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadkfadaWgaa% WcbaGaam4yaaqabaaaaa!39AA!\[R_c\](the critical flux Richardson number) is the ratio % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadYgadaWgaa % WcbaGaamyBaaqabaGccaGGVaGaamitaaaa!3B5C! \[ l_m /L \] under highly stable conditions. Profiles of stress and velocity in the ocean (<0) are given by % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaamaaxacabaGabm % yDayaajaGaeyypa0ZaaiqaaqaabeqaaiabgkHiTiaadMgacqaH0oaz % caWGLbWaaWbaaSqabeaacqaH0oazcqaH2oGEaaGccaqGGaGaaeiiai % aabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGa % aeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccaca % qGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaa % bccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaae % iiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqG % GaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabc % cacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeii % aiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGa % GaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabcca % caqGGaGaaeiiaiaabccacaqGGaGaeqOTdONaeyizImQaeyOeI0Iaeq % OVdG3aaSbaaSqaaiaad6eaaeqaaaGcbaGaeyOeI0IaamyAaiabes7a % KjaadwgadaahaaWcbeqaaiabes7aKjabe67a4naaBaaameaacaWGob % aabeaaaaGccqGHsisldaWcaaqaaiabeE7aOnaaBaaaleaacaGGQaaa % beaaaOqaaiaadUgaaaWaamWaaeaaciGGSbGaaiOBamaalaaabaWaaq % WaaeaacqaH2oGEaiaawEa7caGLiWoaaeaacqaH+oaEdaWgaaWcbaGa % amOtaaqabaaaaOGaey4kaSIaaiikaiabes7aKjabgkHiTiaadggaca % GGPaGaaiikaiabeA7a6jabgUcaRiabe67a4naaBaaaleaacaWGobaa % beaakiaacMcacqGHsisldaWcaaqaaiaadggaaeaacaaIYaaaaiabes % 7aKjaacIcacqaH2oGEdaahaaWcbeqaaiaaikdaaaGccqGHsislcqaH % +oaEdaqhaaWcbaGaamOtaaqaaiaaikdaaaGccaGGPaaacaGLBbGaay % zxaaGaaeiiaiaabccacaqGGaGaaeiiaiabeA7a6naaBaaaleaacaaI % WaaabeaakiabgwMiZkabeA7a6jabg6da+iabgkHiTiabe67a4naaBa % aaleaacaWGobaabeaaaaGccaGL7baaaSqabKazbaiabaGabmivayaa % jaGaeyypa0JaamyzamaaCaaajqMaacqabeaacaWGPbGaeqiTdqMaeq % OTdOhaaaaaaaa!C5AA! \[ \mathop {\hat u = \left\{ \begin{array}{l} - i\delta e^{\delta \zeta } {\rm{ }}\zeta \le - \xi _N \\ - i\delta e^{\delta \xi _N } - \frac{{\eta _* }}{k}\left[ {\ln \frac{{\left| \zeta \right|}}{{\xi _N }} + (\delta - a)(\zeta + \xi _N ) - \frac{a}{2}\delta \end{array} \right.}\limits^{\hat T = e^{i\delta \zeta } } \] where % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabes7aKjabg2 % da9maabmaabaGaamyAaiaac+cacaWGRbGaeqOVdG3aaSbaaSqaaiaa % d6eaaeqaaaGccaGLOaGaayzkaaWaaWbaaSqabeaacaaIXaGaai4lai % aaikdaaaGccaGG7aGaamyyaiabg2da9iabeE7aOnaaBaaaleaacqGH % xiIkaeqaaOGaaiikaiaaigdacaGGVaGaeqOVdG3aaSbaaSqaaiaad6 % eaaeqaaOGaey4kaSIaamyDamaaBaaaleaacqGHxiIkaeqaaOGaai4l % aiaadAgacaWGmbGaamOuamaaBaaaleaacaWGJbaabeaakiaacMcaca % GGOaGaaGymaiabgkHiTiabeE7aOnaaBaaaleaacqGHxiIkaeqaaOGa % aiykaiaacUdaaaa!5CB6! \[ \delta = \left( {i/k\xi _N } \right)^{1/2} ;a = \eta _ * (1/\xi _N + u_ * /fLR_c )(1 - \eta _ * ); \] and ₀ is the nondimensional surface roughness. The constants are% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadkfadaWgaa% WcbaGaam4yaaqabaaaaa!39AA!\[R_c \]= 0.2 and% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabe67a4naaBa% aaleaacaWGobaabeaaaaa!3A81!\[\xi _N \]= 0.052. The solutions for the atmosphere are similar except û is the nondimensional velocity The model produces satisfactory predictions of geostrophic drag and near-surface current (wind) profiles under stable stratification.     

A simple model for the adjustment of velocity spectra in unstable conditions downstream of an abrupt change in roughness and heat flux

A simple model for the equilibrium spectra of velocity fluctuations in the unstable surface layer is developed. All three component spectra are written as a sum of two spectra For the horizontal spectra, the two parts scale with % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaacIcacaWGUb% GaamOEamaaBaaaleaacaWGPbaabeaakiaac+cacaWG1bGaaiilaiaa% dQhadaWgaaWcbaGaamyAaaqabaGccaGGVaGaamitaiaacMcaaaa!4232!\[(nz_i /u,z_i /L)\]and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaad6gacaWG6b% Gaai4laiaadwhaaaa!3B5E!\[nz/u\], respectively; the vertical spectrum can be written entirely as a function of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaad6gacaWG6b% Gaai4laiaadwhaaaa!3B5E!\[nz/u\] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadQhacaGGVa% Gaamitaaaa!3A42!\[z/L\].The equilibrium spectra are utilized as part of a model describing the development of velocity spectra downwind of a change in surface roughness and heat flux.Results are shown for the streamwise component and compared with hotwire measurements from the RISØ 78 experiment. The model shows excellent agreement with the measurements.on leave of absence from RISØ National Laboratory Roskilde, Denmark.     

An examination of turbulence statistics in the surface boundary layer

Simulated data derived from random numbers are used to show that the process of relating % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaWG3baabeaakiaac+cacaWG1bWaaSbaaSqaaiabgEHiQaqa% baaaaa!3D7C!\[\sigma _w /u_ * \]and similar properties to the stability parameter % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadQhacaGGVa% Gaamitaaaa!3A42!\[z/L\]is highly susceptible to error. An alternative method, making use of Ri as a stability index, is not affected in this way and is used to re-examine the data obtained in the 1968 Kansas micrometeorological experiment. The relationship % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaWG3baabeaakiaac+cacaWG1bWaaSbaaSqaaiabgEHiQaqa% baGccqWIdjYocaaIXaGaaiOlaiaaikdacaaI1aaaaa!419F!\[\sigma _w /u_ * \simeq 1.25\] % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaamaabmaabaGaaG% ymaiabgkHiTiaaikdacaWG6bGaai4laiaadYeaaiaawIcacaGLPaaa% daahaaWcbeqaaiaaigdacaGGVaGaaG4maaaaaaa!4087!\[\left( {1 - 2z/L} \right)^{1/3} \]is found to provide a good fit to the unstable data, but it is unclear as to whether a small peak observed in stable conditions is real (perhaps associated with gravity waves) or not (possibly a consequence of measurement errors).The properties % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaWG1baabeaakiaac+cacaWG1bWaaSbaaSqaaiabgEHiQaqa% baaaaa!3D7A!\[\sigma _u /u_ * \]and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaWG1baabeaakiaac+cacaWG1bWaaSbaaSqaaiabgEHiQaqa% baaaaa!3D7A!\[\sigma _u /u_ * \] are found to attain a relatively constant value ( 3) in conditions more unstable than about Ri = -0.4. The shape ratio % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaWG1baabeaakiaac+cacqaHdpWCdaWgaaWcbaGaamODaaqa% baaaaa!3E4F!\[\sigma _u /\sigma _v \] is found to decrease to less than unity in very unstable conditions, possibly as a consequence of some undetected error in measurement of _u . In the case of temperature fluctuations, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacqaHepaDaeqaaOGaai4laiaadsfadaWgaaWcbaGaey4fIOca% beaakiabg2da9iaaicdacaGGUaGaaGyoaiaaiwdacaGGOaGaeyOeI0% IaamOEaiaac+cacaWGmbGaaiykamaaCaaaleqabaGaeyOeI0IaaGym% aiaac+cacaaIZaaaaaaa!4A30!\[\sigma _\tau /T_ * = 0.95( - z/L)^{ - 1/3} \] is found to provide an excellent fit in unstable conditions (Ri < -0.1), even though this form also agrees well with random behavior.Now With: Atmospheric Turbulence and Diffusion Laboratory, NOAA, P. O. Box E, Oak Ridge Tenn., 37830, U.S.A.     

The source area influencing a measurement in the Planetary Boundary Layer: The “footprint” and the “distribution of contact distance”

This paper considers the ground area which affects the properties of fluid parcels observed at a given spot in the Planetary Boundary Layer (PBL). We examine two source-area functions; the footprint, giving the source area for a measurement of vertical flux: and the distribution of contact distance, the distance since a particle observed aloft last made contact with the surface. We explain why the distribution of contact distance extends vastly farther upwind than the footprint, and suggest for the extent of the footprint the inequalities: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOabaeqabaGaamyvam% aalaaabaGaamiAaaqaaiabeo8aZnaaBaaaleaacaWGxbaabeaakiaa% cIcacaWGObGaaiykaaaacqGH8aapcaWG4bGaeyipaWJaamyvaKazaa% iadaGabaqaamaaDaaajqwaacqaaiaadIgacaGGVaGabmOEayaacaGa% aiilaiaabccacaGGVbGaaiiDaiaacIgacaGGLbGaaiOCaiaacEhaca% GGPbGaai4CaiaacwgaaeaacaWGubWaaSbaaKazcaiabaGaamitaaqa% baqcKfaGaiaacIcacaWGObGaaiykaiaabYcacaqGGaGaaeiAaiaabc% cacaGGHbGaaiOyaiaac+gacaGG2bGaaiyzaiaabccacaGGZbGaaiyD% aiaackhacaGGMbGaaiyyaiaacogacaGGLbGaeyOeI0IaaiiBaiaacg% gacaGG5bGaaiyzaiaackhaaaaajqgaacGaay5EaaaakeaaaeaacaGG% 8bGaamyEaiaacYhacqGH8aapcqaHdpWCdaWgaaWcbaGaamODaaqaba% GccaGGOaGaamiAaiaacMcadaWcaaqaaiaadIhaaeaacaWGvbaaaaaa% aa!7877!\[\begin{array}{l} U\frac{h}{{\sigma _W (h)}} < x < U\left\{ {_{h/\dot z,{\rm{ }}otherwise}^{T_L (h){\rm{, h }}above{\rm{ }}surface - layer} } \right. \\ \\ |y| < \sigma _v (h)\frac{x}{U} \\ \end{array}\] where U is the mean streamwise (x) velocity, h is the observation height, _L is the Lagrangian timescale, _v and _w are the standard deviations of the cross-stream horizontal (y) and vertical (z) velocity fluctuations, and is the Lagrangian Similarity prediction for the rate of rise of the centre of gravity of a puff released at ground.Simple analytical solutions for the contact-time and the footprint are derived, by treating the PBL as consisting of two sub-layers. The contact-time solutions agree very well with the predictions of a Lagrangian stochastic model, which we adopt in the absence of measurements as our best estimate of reality, but the footprint solution offers no improvement over the above inequality.     

Measurement of the vertical flux of turbulent kinetic energy with a single Doppler radar

The Doppler radar velocity azimuth display (VAD) technique for obtaining first and second moments of radial wind velocities is expanded to third-moment calculations. By scanning at an elevation angle of 50.8°, terms of the third-moment equation can be reduced to yield the vertical flux of turbulent kinetic energy, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaace% WG3bGbauaaceWGXbGbauaaaaaaaa!3807!\[\overline {w'q'} \]. The technique has been applied to summertime radar measurements of the convective boundary layer in Illinois. Resulting vertical profiles of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaace% WG3bGbauaaceWGXbGbauaaaaaaaa!3807!\[\overline {w'q'} \] follow the expected shape, and the magnitudes compare well with those of aircraft measurements in previous studies.     

Macro- and micro-scale mixing in chemical reactive plumes

The average dispersion of a plume in the atmospheric boundary layer is strongly influenced by atmospheric turbulence. Atmospheric turbulence determines also concentration fluctuations due to turbulent meandering by large scale turbulent eddies and in-plume fluctuations, due to smaller scale eddies. Conversion of NO to NO₂ in a plume is influenced by micro-scale mixing, due to the concentration fluctuation correlation % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% qGobGaae4tamaaCaaaleqabaGaaeymaaaakiaab+eadaqhaaWcbaGa% ae4maaqaaiaabgdaaaaaaaaa!3AF4!\[\overline {{\rm{NO}}^{\rm{1}} {\rm{O}}_{\rm{3}}^{\rm{1}} } \] and macro-scale mixing, the mixing in of ambient air containing O₃ into the plume.The study of turbulent meandering, in-plume fluctuations, microscale and macro-scale mixing will contribute to a better understanding of concentration fluctuations in general.     

Impact of density fluctuations on flux measurements of trace gases: Implications for the relaxed eddy accumulation technique

A simple and fast approach to determine when density fluctuations are non-negligible in the calculation of the flux of trace gases (F _c ) is proposed. The correction (F _c – F _c (raw)), when expressed as the percentage of the flux, is dependent on the ratio of background concentration of the trace gas over its flux (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeikaiabeg% 8aYnaaBaaaleaacaWGJbaabeaakiaab+cacaWGgbWaaSbaaSqaaiaa% dogaaeqaaOGaaeykaaaa!3CBC!\[{\rm{(}}\rho _c {\rm{/}}F_c {\rm{)}}\], on the partitioning of available energy between sensible (F _T ) and latent (F _v ) heat fluxes, and on the flux measuring system. An increase from 100 to 200 W m^-2 in available energy and from 0 to 20% in F _T /(F _T + F _v ) led to a threefold reduction in the required value of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaacq% aHbpGCdaWgaaWcbaGaam4yaaqabaaaaOGaai4laiaadAeadaWgaaWc% baGaam4yaaqabaaaaa!3B6D!\[\overline {\rho _c } /F_c \] to have a density correction of 10%. A trace gas with a % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqWaceaaca% WGgbWaaSbaaSqaaiaadogaaeqaaaGccaGLhWUaayjcSdGaai4lamaa% naaabaGaeqyWdi3aaSbaaSqaaiaadogaaeqaaaaaaaa!3E91!\[\left| {F_c } \right|/\overline {\rho _c } \] value above 0.014 m s^-1 has a density correction on flux of less than 10%, for even the worst case scenario. Values of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa% aaleaacaWGJbaabeaakiaac+cadaqdaaqaaiabeg8aYnaaBaaaleaa% caWGJbaabeaaaaaaaa!3B6D!\[F_c /\overline {\rho _c } \] for several trace gases computed from typical situations show that the fluxes of N₂O, NO, CO₂, CH₄ and O₃ need to be corrected, while those of pesticides and volatile organic compounds, for example, do not. The corrections required with the newly developed relaxed eddy accumulation technique are discussed and equation development is shown for two sampling systems.Land Resource Research Centre Contribution No 91-61.     

A wind tunnel study of turbulent flow over a two-dimensional ridge

We present a wind-tunnel simulation of adiabatic atmospheric flow normal to a rough, two-dimensional ridge. The data are analyzed in physical streamline coordinates, which are described in some detail. The mean velocity speed-up on the hill top is adequately predicted by existing formulae while the behaviour of the wake flow fits into a pattern that emerges from other wind-tunnel experiments. The turbulent stresses evolve in response to the extra strain rates induced by the hill, streamline curvature and acceleration: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWG1bWaaWbaaS% qabeaaceaIYaGbaebaaaaaaa!3456!\[u^{\bar 2}\]is coupled strongly to acceleration while % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaadaqdaaqaaiaadw% hacaWG3baaaaaa!3462!\[\overline {uw}\]and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWG3bWaaWbaaS% qabeaaceaIYaGbaebaaaaaaa!3458!\[w^{\bar 2}\]follow curvature. These differing responses lead to significant phase differences between the changes in the component stresses as the hill is traversed. An analogous response is seen in the components of turbulent stress divergence, which are computed as part of streamwise momentum budgets. Only very close to the surface is turbulent stress divergence comparable to the inertial and pressure terms in the momentum budget; over most of the flow regime, the mean flow response is approximately inviscid. Finally, we compare our results with data from other wind tunnel models and from real hills.     

An international turbulence comparison experiment (ITCE 1976)

Turbulence data for the International Turbulence Comparison Experiment (ITCE) held at Conargo, N.S.W. (35° 18′ S., 145° 10′ E.) during October, 1976 are analysed. The standard deviation % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiqado% hagaqbamaaCaaaleqabaGaaGOmaaaakiaacMcadaahaaWcbeqaaiaa% igdacaGGVaGaaGOmaaaaaaa!3B93!\[(s'^2 )^{1/2} \] and covariance % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaace% WG3bGbauaaceWGZbGbauaaaaaaaa!3809!\[\overline {w's'} \] measured by a number of instruments and instrument arrays have been compared to assess their field performance and calibration accuracy. Satisfactory agreement, i.e. typically 5% for % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikamaana% aabaGabm4CayaafaWaaWbaaSqabeaacaaIYaaaaaaakiaacMcadaah% aaWcbeqaaiaaigdacaGGVaGaaGOmaaaaaaa!3BA4!\[(\overline {s'^2 } )^{1/2} \] (except in humidity) and of the order of 20% for % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiqado% hagaqbamaaCaaaleqabaGaaGOmaaaakiaacMcadaahaaWcbeqaaiaa% igdacaGGVaGaaGOmaaaaaaa!3B93!\[(s'^2 )^{1/2} \], was achieved, but only after consideration of:

1. Instrumental response at high frequencies.
2. Flow distortion induced by instruments and supporting structures.
3. Spatial separation of instruments used for covariance measurements.
4. Statistical errors associated with single point measurements over a finite averaging time, and with lateral separation of two sensor arrays being compared.

     

Methoxy formation in the reaction of CH3O2 radicals with NO

Formation of methoxy (CH₃O) radicals in the reaction (1) CH₃O₂+NOCH₃O+NO₂ at 298 K has been observed directly using time resolved LIF. The branching ratio % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdyMaae% 4qaiaabIeadaWgaaWcbaGaae4maaqabaGccaqGpbGaaeiiaiaabIca% ieqacaWF9aGaa8hiaiaa-nbicaWFGaGaeuiLdqKaai4waiaaboeaca% qGibWaaSbaaSqaaiaabodaaeqaaOGaae4taiaac2facaWFVaGaeuiL% dqKaai4waiaaboeacaqGibWaaSbaaSqaaiaabodaaeqaaOGaae4tam% aaBaaaleaacaqGYaaabeaakiaac2facaqGPaaaaa!4E31!\[\phi {\rm{CH}}_{\rm{3}} {\rm{O (}} = -- \Delta [{\rm{CH}}_{\rm{3}} {\rm{O}}]/\Delta [{\rm{CH}}_{\rm{3}} {\rm{O}}_{\rm{2}} ]{\rm{)}}\] has been determined by quantitative cw-UV-laser absorption at 257 nm of CH₃O₂ and CH₃ONO, the product of the consecutive methoxy trapping reaction (2) % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4qaiaabI% eadaWgaaWcbaGaae4maaqabaGccaqGpbacbeGaa83kaiaa-bcaieaa% caGFobGaa43taiaa+bcacaGFOaGaa83kaiaa+1eacaGFPaGaa4hiai% abgkziUkaabccacaqGdbGaaeisamaaBaaaleaacaqGZaaabeaakiaa% b+eacaqGGaGaaeOtaiaab+eacaqGGaGaa4hkaiaa-TcacaGFnbGaa4% xkaiaa+5cacaGFGaGaa4hiaiabeA8aMnaaBaaajqwaacqaaiaaboea% caqGibWaaSbaaKazcaiabaGaae4maaqabaqcKfaGaiaab+eaaSqaba% aaaa!55AC!\[{\rm{CH}}_{\rm{3}} {\rm{O}} + NO ( + M) \to {\rm{ CH}}_{\rm{3}} {\rm{O NO }}( + M). \phi _{{\rm{CH}}_{\rm{3}} {\rm{O}}} \] is found to be (1.0±0.2). The rate constant k ₁ is (7±2) 10^-12 cm³/molecule · s in good agreement with previous results.     

The heterogeneous formation of N2O in air containing NO2, O3 and NH3

In a nighttime system and under relatively dry conditions (about 15 ppm H₂O), the reaction mixture of NO₂, O₃, and NH₃ in purified air turns out to result in the formation of nitrous oxide (N₂O). The experiments were performed in a continuous stirred flow reactor, in the concentration region of 0.02–2 ppm.N₂O is thought to arise through the heterogeneous reaction of gaseous N₂O₅ and absorbed NH₃ at the wall of the reaction vessel % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9sq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9pue9Fve9% Ffc8meGabaqaciGacaGaaeqabaWaaeaaeaaakeaatCvAUfKttLeary% qr1ngBPrgaiuaacqWFOaakcqWFobGtcqWFibasdaWgaaWcbaGae83m% amdabeaakiab-LcaPmaaBaaaleaacqWFHbqyaeqaaOGaey4kaSIaai% ikaiab-5eaonaaBaaaleaacqWFYaGmaeqaaOGae83ta80aaSbaaSqa% aiab-vda1aqabaGccaGGPaWaaSbaaSqaaiaadEgaaeqaaOGaeyOKH4% Qae8Nta40aaSbaaSqaaiab-jdaYaqabaGccqWFpbWtcqGHRaWkcqWF% ibascqWFobGtcqWFpbWtdaWgaaWcbaGae83mamdabeaakiabgUcaRi% ab-HeainaaBaaaleaacqWFYaGmaeqaaOGae83ta8eaaa!59AC!\[(NH_3 )_a + (N_2 O_5 )_g \to N_2 O + HNO_3 + H_2 O\]In principle, there is competition between this reaction and that of adsorbed H₂O with N₂O₅, resulting in the formation of HNO₃. At high water concentrations (RH>75%), no formation of N₂O was found. Although the rate constant of adsorbed NH₃ with gaseous N₂O₅ is much larger than that of the reaction of adsorbed H₂O with gaseous N₂O₅, the significance of the observed N₂O formation for the outside atmosphere is thought to be dependent on the adsorption properties of H₂O and NH₃ on a surface. A number of NH₃ and H₂O adsorption measurements on several materials are discussed.     

A verification of an analytical formula for estimating the height of the stable internal boundary layer

A stable thermal internal boundary layer (IBL) develops when warm air is advected from warmer land upstream to a cooler sea downstream. It is shown that the analytical model for estimating the height (h) of this stable IBL as formulated by Garratt (1987) is verified. It is also demonstrated that a simpler equation, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGObGaeyisIS% RaaGymaiaaiAdacaWGybWaaWbaaSqabeaadaWcgaqaaiaaigdaaeaa% caaIYaaaaaaaaaa!390B!\[h \approx 16X^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \] (where h is in meters and X, the fetch downwind, is in kilometers), is useful operationally as a first approximation.     

The turbulent kinetic energy budget in the atmospheric surface layer: A review and an experimental reexamination in the field

The one-dimensional equation for the turbulent kinetic energy budget in steady, horizontally-homogeneous flow near the ground is reviewed, and some of the many experimental evaluations of its stability-dependent terms obtained during the last twenty years are compared. Uncertainties attributable to instrument error and inadequate sites are discussed, and it is demonstrated that improved equipment makes it possible to evaluate contributions to the budget with comparatively simple experiments. A preliminary field study finds a von Karman constant of k=0.387±0.016 and a wind shear function for the unstable surface layer% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdy2aaS% baaSqaaiaad2gaaeqaaOGaeyypa0JaaiikaiaaigdacqGHsislcaaI% YaGaaGOmaiaac6cacaaI2aGaamOEaiaac+cacaWGmbGaaiykamaaCa% aaleqabaGaeyOeI0IaaGymaiaac+cacaaI0aaaaaaa!4587!\[\phi _m = (1 - 22.6z/L)^{ - 1/4} \]: the form % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaaig% dacqGHsislcaaIXaGaaGynaiaac6cacaaIXaGaamOEaiaac+cacaWG% mbGaaiykamaaCaaaleqabaGaeyOeI0IaaGymaiaac+cacaaIZaaaaa% aa!419C!\[(1 - 15.1z/L)^{ - 1/3} \] fits equally well over the limited range of instability observed. Turbulence dissipation is found to be 15 to 20% too small to balance the production of energy by wind shear in the neutral surface layer, and this deficit appears to remain approximately constant relative to the total rate of energy production as instability increases to% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOEaiaac+% cacaWGmbGaeyypa0JaeyOeI0IaaGimaiaac6cacaaIXaGaaGOmaaaa% !3D45!\[z/L = - 0.12\]. Renormalized dissipation rates originally measured by others are shown to exhibit similar behavior beyond this narrow range. Combining these results with those of the present study suggests a dissipation function of the form % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdy2aaS% baaSqaaiabew7aLbqabaGccqGH9aqpcqaHgpGzdaWgaaWcbaGaamyB% aaqabaGccqGHsislcaWG6bGaai4laiaadYeacqGHRaWkcaWGJbaaaa!42A3!\[\phi _\varepsilon = \phi _m - z/L + c\] in which c = -0.16 represents a near constant, net negative contribution made by the sum of the divergent transport terms.School of Earth and Atmospheric Sciences, Georgia Institute of Technology.Work sponsored by the National Science Foundation under Grant Nos. ATM-8714025 and ATM-9019682, in part through The University of Chicago.     

Absolute OH quantum yields in the laser photolysis of nitrate,nitrite and dissolved H2O2 at 308 and 351 nm in the temperature range 278–353 K

Absolute quantum yields for the formation of OH radicals in the laser photolysis of aqueous solutions of NO₃ ^-, NO₂ ^- and H₂O₂ at 308 and 351 nm and as a function of pH and temperature have been measured. A scavenging technique involving the reaction between OH and SCN^- ions and the time resolved detection by visible absorption of the (SCN)₂ ^- radical ion was used to determine the absolute OH yields. The following results were obtained:

1. NO ₃ ^- -photolysis:% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaaIWa% GaaGioaGGaaiab-bcaGiaab6gacaqGTbGaaeOoaiab-bcaGiabfA6a% gnaaBaaaleaacqWFFoWtcqWFxoasaeqaaOGaaiikaiaaikdacaaI5a% GaaGioaiab-bcaGiab-P5aljaacMcacqGH9aqpcqWFGaaicqWFWaam% cqWFUaGlcqWFWaamcqWFXaqmcqWF3aWncqWFGaaicqGHXcqScqWFGa% aicqWFWaamcqWFUaGlcqWFWaamcqWFWaamcqWFZaWmcqWFGaaicaqG% MbGaae4BaiaabkhacaqGGaGaaeinaiaabccacqGHKjYOcaqGGaGaam% iCaiaabIeacaqGGaGaeyizImQaaeiiaiaabMdaaeaacqWFGaaicqWF% GaaicqWFGaaicqWFGaaicqWFGaaicqWFGaaicqWFGaaicqWFGaaicq% WFGaaicqWFGaaicqWFGaaicqWFGaaicqWFGaaicqWFGaaicqqHMoGr% daWgaaWcbaGae83Nd8Kae83LdGeabeaakiaacIcacaWGubGaaiykai% abg2da9iabfA6agnaaBaaaleaacqWFFoWtcqWFxoasaeqaaOGaaiik% aiaaikdacaaI5aGaaGioaiab-bcaGiab-P5aljaacMcacqWFGaaica% qGLbGaaeiEaiaabchacaqGGaWaamWaaeaacaqGOaGaaeymaiaabIda% caqGWaGaaeimaiaabccacqGHXcqScaaI0aGaaGioaiaaicdacaqGPa% GaaeikamaalaaabaGaaeymaaqaaiaabkdacaqG5aGaaeioaaaacaqG% GaGaeyOeI0IaaeiiamaalaaabaGaaeymaaqaaiaadsfaaaGaaeykaa% Gaay5waiaaw2faaiaac6caaaaa!9673!\[\begin{gathered}08 {\text{nm:}} \Phi _{{\rm O}{\rm H}} (298 {\rm K}) = 0.017 \pm 0.003 {\text{for 4 }} \leqslant {\text{ }}p{\text{H }} \leqslant {\text{ 9}} \hfill \\\Phi _{{\rm O}{\rm H}} (T) = \Phi _{{\rm O}{\rm H}} (298 {\rm K}) {\text{exp }}\left[ {{\text{(1800 }} \pm 480{\text{)(}}\frac{{\text{1}}}{{{\text{298}}}}{\text{ }} - {\text{ }}\frac{{\text{1}}}{T}{\text{)}}} \right]. \hfill \\\end{gathered}\] Selected experiments at 351 nm indicate that these results are essentially unchanged.
2. NO ₂ ^- -photolysis:% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaaIWa% GaaGioaGGaaiab-bcaGiaab6gacaqGTbGaaeOoaiab-bcaGiabfA6a% gnaaBaaaleaacqWFFoWtcqWFxoasaeqaaOGaaiikaiaaikdacaaI5a% GaaGioaiab-bcaGiab-P5aljaacMcacqGH9aqpcqWFGaaicqWFOaak% cqWFWaamcqWFUaGlcqWFWaamcqWFXaqmcqWF3aWncqWFGaaicqGHXc% qScqWFGaaicqWFWaamcqWFUaGlcqWFWaamcqWFWaamcqWFXaqmcqWF% PaqkcqWFGaaicaqGMbGaae4BaiaabkhacaqGGaGaaeinaiaabccacq% GHKjYOcaqGGaGaamiCaiaabIeacaqGGaGaeyizImQaaeiiaiaabMda% caqGSaaabaGae8hiaaIae8hiaaIae8hiaaIae8hiaaIae8hiaaIae8% hiaaIae8hiaaIae8hiaaIae8hiaaIae8hiaaIae8hiaaIae8hiaaIa% e8hiaaIae8hiaaIaeuOPdy0aaSbaaSqaaiab-95apjab-D5aibqaba% GccaGGOaGaamivaiaacMcacqGH9aqpcqqHMoGrdaWgaaWcbaGae83N% d8Kae83LdGeabeaakiaacIcacaaIYaGaaGyoaiaaiIdacqWFGaaicq% WFAoWscaGGPaGae8hiaaIaaeyzaiaabIhacaqGWbGaaeiiamaadmaa% baGaaeikaiaabgdacaqG1aGaaeOnaiaabcdacaqGGaGaeyySaeRaae% iiaiaabodacaqG2aGaaeimaiaabMcacaqGOaWaaSaaaeaacaqGXaaa% baGaaeOmaiaabMdacaqG4aaaaiaabccacqGHsislcaqGGaWaaSaaae% aacaqGXaaabaGaamivaaaacaqGPaaacaGLBbGaayzxaaGaaiilaaqa% aiaaiodacaaI1aGaaGymaiaabccacaqGUbGaaeyBaiaabQdacqWFGa% aicqqHMoGrdaWgaaWcbaGae83Nd8Kae83LdGeabeaakiaacIcacaaI% YaGaaGyoaiaaiIdacqWFGaaicqWFAoWscaGGPaGaeyypa0Jae8hiaa% Iae8hkaGIae8hmaaJae8Nla4Iae8hmaaJae8hnaqJae8NnayJae8hi% aaIaeyySaeRae8hiaaIae8hmaaJae8Nla4Iae8hmaaJae8hmaaJae8% xoaKJae8xkaKIae8hiaaIaaeOzaiaab+gacaqGYbGaaeiiaiaabsda% caqGGaGaeyizImQaaeiiaiaadchacaqGibGaaeiiaiaab2dacaqGGa% GaaeioaiaabYcaaeaacqWFGaaicqWFGaaicqWFGaaicqWFGaaicqWF% GaaicqWFGaaicqWFGaaicqWFGaaicqWFGaaicqWFGaaicqWFGaaicq% WFGaaicqWFGaaicqWFGaaicqqHMoGrdaWgaaWcbaGae83Nd8Kae83L% dGeabeaakiaacIcacaWGubGaaiykaiabg2da9iabfA6agnaaBaaale% aacqWFFoWtcqWFxoasaeqaaOGaaiikaiaaikdacaaI5aGaaGioaiab% -bcaGiab-P5aljaacMcacqWFGaaicaqGLbGaaeiEaiaabchacaqGGa% WaamWaaeaacaqGOaGaaeymaiaabIdacaqGWaGaaeimaiaabccacqGH% XcqScaqGGaGaaeinaiaabcdacaqGWaGaaeykaiaabIcadaWcaaqaai% aabgdaaeaacaqGYaGaaeyoaiaabIdaaaGaaeiiaiabgkHiTiaabcca% daWcaaqaaiaabgdaaeaacaWGubaaaiaabMcaaiaawUfacaGLDbaaca% GGUaaaaaa!FC61!\[\begin{gathered}08 {\text{nm:}} \Phi _{{\rm O}{\rm H}} (298 {\rm K}) = (0.017 \pm 0.001) {\text{for 4 }} \leqslant {\text{ }}p{\text{H }} \leqslant {\text{ 9,}} \hfill \\\Phi _{{\rm O}{\rm H}} (T) = \Phi _{{\rm O}{\rm H}} (298 {\rm K}) {\text{exp }}\left[ {{\text{(1560 }} \pm {\text{ 360)(}}\frac{{\text{1}}}{{{\text{298}}}}{\text{ }} - {\text{ }}\frac{{\text{1}}}{T}{\text{)}}} \right], \hfill \\351{\text{ nm:}} \Phi _{{\rm O}{\rm H}} (298 {\rm K}) = (0.046 \pm 0.009) {\text{for 4 }} \leqslant {\text{ }}p{\text{H = 8,}} \hfill \\\Phi _{{\rm O}{\rm H}} (T) = \Phi _{{\rm O}{\rm H}} (298 {\rm K}) {\text{exp }}\left[ {{\text{(1800 }} \pm {\text{ 400)(}}\frac{{\text{1}}}{{{\text{298}}}}{\text{ }} - {\text{ }}\frac{{\text{1}}}{T}{\text{)}}} \right]. \hfill \\\end{gathered}\]
3. H₂O₂-photolysis:% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaaIWa% GaaGioaGGaaiab-bcaGiaab6gacaqGTbGaaeOoaiab-bcaGiabfA6a% gnaaBaaaleaacqWFFoWtcqWFxoasaeqaaOGaaiikaiaaikdacaaI5a% GaaGioaiab-bcaGiab-P5aljaacMcacqGH9aqpcqWFGaaicqWFOaak% cqWFWaamcqWFUaGlcqWF5aqocqWF4aaocqWFGaaicqGHXcqScqWFGa% aicqWFWaamcqWFUaGlcqWFWaamcqWFZaWmcqWFPaqkcqWFGaaicaqG% MbGaae4BaiaabkhacaqGGaGaamiCaiaabIeacaqGGaGaeyizImQaae% iiaiaabEdacaqGSaaabaGae8hiaaIae8hiaaIae8hiaaIae8hiaaIa% e8hiaaIae8hiaaIae8hiaaIae8hiaaIae8hiaaIae8hiaaIae8hiaa% Iae8hiaaIae8hiaaIae8hiaaIaeuOPdy0aaSbaaSqaaiab-95apjab% -D5aibqabaGccaGGOaGaamivaiaacMcacqGH9aqpcqqHMoGrdaWgaa% WcbaGae83Nd8Kae83LdGeabeaakiaacIcacaaIYaGaaGyoaiaaiIda% cqWFGaaicqWFAoWscaGGPaGae8hiaaIaaeyzaiaabIhacaqGWbGaae% iiamaadmaabaGaaeikaiaabAdacaqG2aGaaeimaiaabccacqGHXcqS% caqGGaGaaeymaiaabMdacaqGWaGaaeykaiaabIcadaWcaaqaaiaabg% daaeaacaqGYaGaaeyoaiaabIdaaaGaaeiiaiabgkHiTiaabccadaWc% aaqaaiaabgdaaeaacaWGubaaaiaabMcaaiaawUfacaGLDbaacaGGSa% aabaGaaG4maiaaiwdacaaIXaGaaeiiaiaab6gacaqGTbGaaeOoaiab% -bcaGiabfA6agnaaBaaaleaacqWFFoWtcqWFxoasaeqaaOGaaiikai% aaikdacaaI5aGaaGioaiab-bcaGiab-P5aljaacMcacqGH9aqpcqWF% GaaicqWFOaakcqWFWaamcqWFUaGlcqWF5aqocqWF2aGncqWFGaaicq% GHXcqScqWFGaaicqWFWaamcqWFUaGlcqWFWaamcqWF0aancqWFPaqk% cqWFGaaicaqGMbGaae4BaiaabkhacaqGGaGaaeinaiaabccacqGHKj% YOcaqGGaGaamiCaiaabIeacaqGGaGaaeypaiaabccacaqG3aGaaeil% aaqaaiab-bcaGiab-bcaGiab-bcaGiab-bcaGiab-bcaGiab-bcaGi% ab-bcaGiab-bcaGiab-bcaGiab-bcaGiab-bcaGiab-bcaGiab-bca% Giab-bcaGiabfA6agnaaBaaaleaacqWFFoWtcqWFxoasaeqaaOGaai% ikaiaadsfacaGGPaGaeyypa0JaeuOPdy0aaSbaaSqaaiab-95apjab% -D5aibqabaGccaGGOaGaaGOmaiaaiMdacaaI4aGae8hiaaIae8NMdS% Kaaiykaiab-bcaGiaabwgacaqG4bGaaeiCaiaabccadaWadaqaaiaa% bIcacaqG1aGaaeioaiaabcdacaqGGaGaeyySaeRaaeiiaiaabgdaca% qG2aGaaeimaiaabMcacaqGOaWaaSaaaeaacaqGXaaabaGaaeOmaiaa% bMdacaqG4aaaaiaabccacqGHsislcaqGGaWaaSaaaeaacaqGXaaaba% GaamivaaaacaqGPaaacaGLBbGaayzxaaGaaiOlaaaaaa!F3D0!\[\begin{gathered}08 {\text{nm:}} \Phi _{{\rm O}{\rm H}} (298 {\rm K}) = (0.98 \pm 0.03) {\text{for }}p{\text{H }} \leqslant {\text{ 7,}} \hfill \\\Phi _{{\rm O}{\rm H}} (T) = \Phi _{{\rm O}{\rm H}} (298 {\rm K}) {\text{exp }}\left[ {{\text{(660 }} \pm {\text{ 190)(}}\frac{{\text{1}}}{{{\text{298}}}}{\text{ }} - {\text{ }}\frac{{\text{1}}}{T}{\text{)}}} \right], \hfill \\351{\text{ nm:}} \Phi _{{\rm O}{\rm H}} (298 {\rm K}) = (0.96 \pm 0.04) {\text{for 4 }} \leqslant {\text{ }}p{\text{H = 7,}} \hfill \\\Phi _{{\rm O}{\rm H}} (T) = \Phi _{{\rm O}{\rm H}} (298 {\rm K}) {\text{exp }}\left[ {{\text{(580 }} \pm {\text{ 160)(}}\frac{{\text{1}}}{{{\text{298}}}}{\text{ }} - {\text{ }}\frac{{\text{1}}}{T}{\text{)}}} \right]. \hfill \\\end{gathered}\] Together with the absorption coefficients and an assumed actinic flux within atmospheric droplets of twice the clear air value, the partial photolytic lifetimes (τ_OH) of these molecules at 298 K are estimated as 10.5 d, 5.4 h and 30.3 h for NO₃ ^-, NO₂ ^- and H₂O₂, respectively. These lifetimes will increase by a factor of two (NO₃ ^-, NO₂ ^-) and by 15% (H₂O₂) at T=278 K. Using average ambient concentrations in tropospheric aqueous droplets, the photolytic OH source strengths from these species are calculated to be 2.8×10^-11, 1.3×10^-11 and 1.4×10^-11 mol 1^-1 s^-1 for NO₃ ^-, NO₂ ^- and H₂O₂ respectively.

     

Models and observations of the growth of the atmospheric boundary layer

The evolution of the mixed layer during a clear day can be described with a slab model. The model equations have to be closed by a parameterization of the turbulent kinetic energy budget. Several possibilities for this parameterization have been proposed. In order to assess the practical applicability of these models for the atmosphere, field experiments were carried out on ten clear days in 1977 and 1978. Within the accuracy of the measurements the mixed-layer height in fully convective conditions (at noon on clear days) is well predicted taking a constant heat flux ratio % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Yaa0% aaaeaacqaH4oqCcaWG3bWaaSbaaSqaaiaadIgaaeqaaaaakiabg2da% 9iaaicdacaGGUaGaaGOmamaanaaabaGaeqiUdeNaam4DamaaBaaale% aacaWGZbaabeaaaaaaaa!41D4!\[ - \overline {\theta w_h } = 0.2\overline {\theta w_s } \]. In the early morning hours mechanical entrainment is also important. Good overall results are obtained with the entrainment formulation % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Yaa0% aaaeaacqaH4oqCcaWG3bWaaSbaaSqaaiaadIgaaeqaaaaakiabg2da% 9iaaicdacaGGUaGaaGOmamaanaaabaGaeqiUdeNaam4DamaaBaaale% aacaWGZbaabeaaaaGccqGHRaWkcaaI1aGaamyDamaaDaaaleaacqGH% xiIkaeaacaaIZaaaaOGaamivaiaac+cacaWGNbGaamiAaaaa!49C1!\[ - \overline {\theta w_h } = 0.2\overline {\theta w_s } + 5u_ * ^3 T/gh\].Only large differences in the entrainment coefficients lead to significantly different results. Making the entrainment model more complex does not lead to substantial improvement.The mean potential temperature in the mixed layer is reproduced within 0.5 °C. This temperature is insensitive to the choice of a particular entrainment formulation and depends more on the surface heat input and the temperature gradient in the stable air aloft.     

Minimum friction velocity and heat transfer in the rough surface layer of a convective boundary layer

A simple model is deduced for the surface layer of a convective boundary layer for zero mean wind velocity over homogeneous rough ground. The model assumes large-scale convective circulation driven by surface heat flux with a flow pattern as it would be obtained by conditional ensemble averages. The surface layer is defined here such that in this layer horizontal motions dominate relative to vertical components. The model is derived from momentum and heat balances for the surface layer together with closures based on the Monin-Obukhov theory. The motion in the surface layer is driven by horizontal gradients of hydrostatic pressure. The balances account for turbulent fluxes at the surface and fluxes by convective motions to the mixed layer. The latter are the dominant ones. The model contains effectively two empirical coefficients which are determined such that the model's predictions agree with previous experimental results for the horizontal turbulent velocity fluctuations and the temperature fluctuations. The model quantitatively predicts the decrease of the minimum friction velocity and the increase of the temperature difference between the mixed layer and the ground with increasing values of the boundary layer/roughness height ratio. The heat transfer relationship can be expressed in terms of the common Nusselt and Rayleigh numbers, Nu and Ra, as Nu ~ Ra^{% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSGbaeaaca% aIXaaabaGaaGOmaaaaaaa!3779!\[{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}\]}. Previous results of the form Nu ~ Ra^{% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSGbaeaaca% aIXaaabaGaaG4maaaaaaa!377A!\[{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}\]} are shown to be restricted to Rayleigh-numbers less than a certain value which depends on the boundary layer/roughness height ratio.     

Characteristics of turbulent fluxes of sensible heat and momentum in the surface boundary layer during the Indian summer monsoon

Turbulent fluctuations of wind and temperature were measured using a three-component sonic anemometer at 8 m on a 30 m micro-meteorological tower erected at the Indian Institute of Technology (IIT) Kharagpur (22.3° N, 87.2° E), India, as part of the Monsoon Trough Boundary Layer Experiment (MONTBLEX). Diurnal and nocturnal variations of fluxes of sensible heat and momentum were estimated by the eddy correlation technique from 42 observations, each of 10 min duration during 6–8 July in the monsoon season of 1989. The estimated heat flux shows a diurnal trend while the momentum flux shows variability but no particular trend. The nocturnal heat flux changes sign intermittently.Fluctuations of vertical wind velocity _wand temperature when normalised with the respective scaling parameters u _*and _* are found to scale with Z/L in accordance with the Monin-Obukhov similarity hypothesis: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdy2aaS% baaSqaaiaadEhaaeqaaOGaamiEaiaacIcacaWGAbGaai4laiaadYea% caGGPaWaaWbaaSqabeaacaaIXaGaai4laiaaiodaaaaaaa!3FE8!\[\phi _w x(Z/L)^{1/3} \], % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdy2aaS% baaSqaaiabeI7aXbqabaGccaWG4bGaaiikaiaadQfacaGGVaGaamit% aiaacMcadaahaaWcbeqaaiaaigdacaGGVaGaaG4maaaaaaa!40A2!\[\phi _\theta x(Z/L)^{1/3} \] during unstable conditions and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdy2aaS% baaSqaaiaadEhaaeqaaOGaamiEaiaacIcacaWGAbGaai4laiaadYea% caGGPaaaaa!3D90!\[\phi _w x(Z/L)\], % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdy2aaS% baaSqaaiabeI7aXbqabaGccaWG4bGaaiikaiaadQfacaGGVaGaamit% aiaacMcadaahaaWcbeqaaiabgkHiTiaaigdaaaaaaa!401F!\[\phi _\theta x(Z/L)^{ - 1} \] during stable conditions. Correlation coefficients for heat and momentum flux % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdC2aaS% baaSqaaiaadEhacqaH4oqCaeqaaaaa!3A71!\[\gamma _{w\theta } \] and _uwshow stability dependence. For unstable conditions, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdC2aaS% baaSqaaiaadEhacqaH4oqCaeqaaaaa!3A71!\[\gamma _{w\theta } \] increases with increasing ¦Z/L¦ whereas _uwdecreases. During stable conditions, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdC2aaS% baaSqaaiaadEhacqaH4oqCaeqaaaaa!3A71!\[\gamma _{w\theta } \] decreases with increasing Z/L while _uwdecreases very slowly from a value -0.36 to -0.37.     

Testing of a higher-order closure model for modeling airflow within and above plant canopies

A higher-order closure model was developed to simulate airflow within and above vegetative environments. The model consists of equations for the mean wind, turbulent kinetic energy (TKE) components, tangential stress and simplified equations for the third-order transport terms that appear in the second-order equations. The model in general successfully simulated wind speed profiles within and above maize, been, soybeen, wheat, orange and spruce canopies. Profiles of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaace% WG1bGbauaadaahaaWcbeqaaiaaikdaaaaaaaaa!37EC!\[\overline {u'^2 } \] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaace% WG3bGbauaadaahaaWcbeqaaiaaikdaaaaaaaaa!37EE!\[\overline {w'^2 } \] for the maize canopy were overestimated near the top of the canopy where both shear and wake production of TKE are high. These errors are believed to be caused by incorrect parameterizations for either the dissipation rate of TKE and/or the pressure-velocity correlations in the budget equations for the second moments.     

Review of some basic characteristics of the atmospheric surface layer

Some of the fundamental issues of surface layer meteorology are critically reviewed. For the von Karman constant (k), values covering the range from 0.32 to 0.65 have been reported. Most of the data are, however, found in a rather narrow range between 0.39 and 0.41. Plotting all available atmospheric data against the so-called roughness Reynolds number, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOuaiaabw% gadaWgaaWcbaGaaeimaaqabaGccqGH9aqpcaWG1bWaaSbaaSqaaiaa% cQcaaeqaaOGaamOEamaaBaaaleaacaaIWaaabeaakiaac+cacqaH9o% GBaaa!3FD0!\[{\rm{Re}}_{\rm{0}} = u_* z_0 /\nu \] or against the surface Rossby number, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOuaiaab+% gadaWgaaWcbaGaaeimaaqabaGccqGH9aqpcaWGhbGaai4laiaadAga% caWG6bWaaSbaaSqaaiaaicdaaeqaaaaa!3DF1!\[{\rm{Ro}}_{\rm{0}} = G/fz_0 \] gives no clear indication of systematic trend. It is concluded that k is indeed constant in atmospheric surface-layer flow and that its value is the same as that found for laboratory flows, i.e. about 0.40.Various published formulae for non-dimensional wind and temperature profiles, _m and _h respectively, are compared after adjusting the fluxes so as to give % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaiabg2% da9iaaicdacaGGUaGaaGinaiaaicdaaaa!3AC6!\[k = 0.40\] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWabeaaii% GacqWFgpGzdaWgaaWcbaGaamiAaaqabaGccaGGVaGae8NXdy2aaSba% aSqaaiaad2gaaeqaaaGccaGLOaGaayzkaaWaaSbaaSqaaiaadQhaca% GGVaGaamitaiabg2da9iaaicdaaeqaaOGaeyypa0JaaGimaiaac6ca% caaI5aGaaGynaaaa!4655!\[\left( {\phi _h /\phi _m } \right)_{z/L = 0} = 0.95\]. It is found that for % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqWabeaaca% WG6bGaai4laiaadYeaaiaawEa7caGLiWoacqGHKjYOcaaIWaGaaiOl% aiaaiwdaaaa!3F72!\[\left| {z/L} \right| \le 0.5\] the various formulae agree to within 10–20%. For unstable stratification the various formulations for _h continue to agree within this degree of accuracy up to at least % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOEaiaac+% cacaWGmbGaeyisISRaeyOeI0IaaGOmaaaa!3BC9!\[z/L \approx - 2\]. For _m in very unstable conditions results are still conflicting. Several recent data sets agree that for unstable stratification % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOuaiaabM% gacqGHijYUcaaIXaGaaiOlaiaaiwdacaWG6bGaai4laiaadYeaaaa!3E0D!\[{\rm{Ri}} \approx 1.5z/L\] up to at least % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Iaam% OEaiaac+cacaWGmbGaeyypa0JaaGimaiaac6cacaaI1aaaaa!3C8D!\[ - z/L = 0.5\] and possibly well beyond.For the Kolmogorov streamwise inertial subrange constant, _u , it is concluded from an extensive data set that % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS% baaSqaaiaadwhaaeqaaOGaeyypa0JaaGimaiaac6cacaaI1aGaaGOm% aiabgglaXkaaicdacaGGUaGaaGimaiaaikdaaaa!4178!\[\alpha _u = 0.52 \pm 0.02\]. The corresponding constant for temperature is much more uncertain, its most probable value being, however, about 0.80, which is also the most likely value for the corresponding constant for humidity.The turbulence kinetic energy budget is reviewed. It is concluded that different data sets give conflicting results in important respects, particularly so in neutral conditions.It is demonstrated that the inertial-subrange method can give quite accurate estimates of the fluxes of momentum, sensible heat and water vapour from high frequency measurements of wind, temperature and specific humidity alone, provided apparent values of the corresponding Kolmogorov constants are used. For temperature and humidity, the corresponding values turn out to be equal to the true constants, so % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOSdi2aaS% baaSqaaiaadgeaaeqaaOGaeyisISRaeqOSdiMaeyisISRaaGimaiaa% c6cacaaI4aGaaGimaaaa!4074!\[\beta _A \approx \beta \approx 0.80\]. For momentum, however, the apparent constant % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS% baaSqaaiaadwhacaWGbbaabeaakiabgIKi7kaaicdacaGGUaGaaGOn% aiaaicdaaaa!3E18!\[\alpha _{uA} \approx 0.60\].Based on an invited paper presented at the EGS Workshop Instrumental and Methodical Problems of Land Surface Flux Measurements, Grenoble 22–26 April, 1994.     

A comparison between observed and predicted values for the entrainment coefficient in the planetary boundary layer

A new method is presented for determining experimentally the entrainment coefficient % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeyqaiabg2% da9iabgkHiTiaacIcadaqdaaqaaiabeI7aXjaacEcacaWG3bGaai4j% aaaacaGGPaGaamyAaiabg+caViaacIcadaqdaaqaaiabeI7aXjaacE% cacaWG3bGaai4jaaaacaGGPaWaaSbaaSqaaiaaicdaaeqaaaaa!4646!\[{\text{A}} = - (\overline {\theta 'w'} )i/(\overline {\theta 'w'} )_0 \] characteristic of a convective, planetary boundary layer. This method, which makes use of sodar records together with simultaneous meteorological observations, can be applied to morning convection situations (i.e. shallow mixed layer capped by a marked temperature inversion). Data from the Voves experiment (France, summer 1977) yield A values between 0 and 1, thus departing from the 0.2 ± 0.1 interval which is the range of commonly accepted values.A comparison between these results and theoretical predictions using models developed by Stull (1976) and Zeman and Tennekes (1977) indicates a fair amount of agreement; the importance of mechanically driven turbulence in the entrainment process, especially for the early morning hours, is therefore confirmed.

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Résumé Une méthode de détermination expérimentale du coefficient d'entraînement % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeyqaiabg2% da9iabgkHiTiaacIcadaqdaaqaaiabeI7aXjaacEcacaWG3bGaai4j% aaaacaGGPaGaamyAaiabg+caViaacIcadaqdaaqaaiabeI7aXjaacE% cacaWG3bGaai4jaaaacaGGPaWaaSbaaSqaaiaaicdaaeqaaaaa!4646!\[{\text{A}} = - (\overline {\theta 'w'} )i/(\overline {\theta 'w'} )_0 \] dans une couche limite planétaire convective est proposée. Cette méthode, qui combine les données enregistrées par un sodar à des mesures météorologiques in situ, s'applique aux cas de convection matinale (couche de mélange assez peu développée surmontée par une inversion de température marquée.) Dans le cas des observations recueillies lors de la campagne de Voves (1977) elle fournit des valeurs de A qui s'écartent parfois de 0.2 ± 0.1 (gamme des valeurs souvent adoptées) et couvrent la totalité de l'intervalle 0-1.La comparaison entre les valeurs de A déterminées par cette méthode et celles prédites à partir des modèles de Stull (1976) et Zeman (1977) conduit à un accord satisfaisant, ce qui confirme le rôle joué par la turbulence mécanique dans le processus d'entraînement durant les premières heures de la convection matinale.