Formulation of the thermal internal boundary layer in a mesoscale model

Mesoscale models using a non-local K-scheme for parameterization of boundary-layer processes require an estimate of the planetary boundary layer (PBL) height z _i at all times. In this paper, two-dimensional sea-breeze experiments are carried out to evaluate three different formulations for the advective contribution in the z _i prognostic equation of Deardorff (1974).Poor representation of the thermal internal boundary layer in the sea breeze is obtained when z _i is advected by the wind at level z _i . However, significantly better results are produced if the mean PBL wind is used for the advecting velocity, or if z _i is determined simply by checking for the first sufficiently stable layer above the ground.A Lagrangian particle model is used to demonstrate the effect of each formulation on plume dispersion by the sea breeze.     

A higher order closure model applied to research on the structure of the thermal internal boundary layer (TIBL)

The coastal TIBL is one of the most important and interesting atmospheric processes in shoreline areas, because it has some distinct turbulent features and because it has a major influence on atmospheric dispersion in shoreline areas. In this paper the characteristics of the TIBL, such as its growth parabolically with downwind distance and its turbulent structure are examined.     

Scaling turbulence in the planetary boundary layer

Two different approaches to scaling turbulence in the planetary boundary layer over Lake Ontario are investigated. The height up to the inversion was found to be the appropriate scaling height while u. for near‐neutral and w* for unstable conditions were the appropriate scaling velocities. The results were in general agreement with the numerical models of Deardorff (1972) and Wyngaard, Cote, and Rao (1974).     

Effect of thermal stratification on the growth of the internal boundary layer

The growth of a two-dimensional internal boundary layer (IBL), which develops when a neutral or unstably stratified flow over a uniform terrain encounters a step-change in surface roughness, is numerically investigated by a higher-order turbulence closure theory. It is found that the thickness of the IBL increases as ~ x ⁿ, where x is the downstream distance from the roughness-transition line. For a given set of upstream conditions, the value of the exponent n depends only on the Monin-Obukhov length L, and it is approximately independent of the roughness-change parameter M = In (z01/z02). At large fetches, increases markedly with increasing instability.NRC-NAS Resident Research Associate at AFCRL, 1973–74     

The nocturnal boundary layer during the passage of a mesoscale fog front

The structure of the nocturnal boundary layer affected by an advected fog mass is investigated. For this, measurements of the horizontal wind vector, the temperature, relative humidity and horizontal visibility performed on a radio mast 300 m high are used together with a monostatic SODAR recording.The shape of the cold fog mass, which roughly resembles that of a density current, is described by the shallow water equations in a first approximation. Ahead of the leading edge of the fog mass, a stream function analysis suggests an upward flow component. In addition, a local circulation pattern exists at the density interface. After the fog front has passed the measuring site, the boundary-layer flow becomes more turbulent and, from the hydrodynamical point of view, critical. In agreement with this, the friction velocity inside the growing fog mass increases with time, as shown by a simple integral method.     

Measurements of turbulence structure in the boundary layer on a rough surface

Mean products of velocity fluctuations up to fourth order have been measured in a wind tunnel at the trailing edge of a flat plate, one side of which was covered with floor-sanding paper to produce a fully rough surface. This set-up permits easy comparison of structural parameters in smooth-wall and rough-wall boundary layers. The Reynolds-stress profiles and second-order parameters are closely the same on the rough and smooth surfaces; in particular the decrease in Reynolds shear stress near the rough surface, encountered by several other laboratory workers, was not found in the present results. The triple products are spectacularly altered for a distance of up to 10 roughness heights from the rough surface, and imply a large net rate of transport of turbulent energy and shear stress towards the surface. Comparison with other published data shows that the behaviour of this modified region depends on roughness geometry as well as on the roughness height itself; for example, the mean cube of the normal-component fluctuation remains positive (energy transport away from the surface) over sand or gravel roughness but goes negative, like the other energy-transport terms, over crop canopies.     

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.     

Observation of lake breeze penetration and subsequent development of the thermal internal boundary layer for the Nanticoke II Shoreline Diffusion Experiment

The turbulent structure of the lake breeze penetration and subsequent development of the thermal internal boundary layer (TIBL) was observed using a kytoon-mounted ultrasonic anemometer-thermometer. The lake breeze penetrated with an upward rolling motion associated with the upward flow near the lake breeze front. After the lake breeze front passed, the behaviors of the velocity and temperature at the top of the lake breeze layer were similar to those found in convective boundary layers (CBL). Comparing _gq/_*, _u /w _* and _w /w _* between the present observation of TIBL development after the passage of the lake breeze front and CBL data from the literature, the /_* values showed reasonable agreement; however, _u /w _* and _w /W_* had smaller values in the TIBL than in the CBL at higher altitudes. This is due to the differences in the mean velocity profiles. While the CBL has a uniform velocity profile, the TIBL has a peak at lower elevation due to the lake breeze penetration; the velocity then decreases with height.Present address: The Institute of Behavioral Science, 1-35-7 Yoyogi, Tokyo 151, Japan.     

Thermal plumes and turbulence spectra in the atmospheric boundary layer

Experimental observations on the temperature and wind fields above flat grassy terrain have been obtained with an instrumented 92-m tower during intervals of strong insolation about midday. The turbulence characteristics of the air confirm that free convection prevailed at heights between 16 and 48 m, with some tendency for departure at higher levels. The spectra of temperature and vertical velocity contain gaps at wave numbers in the range 0.01–0.025 m^–1. These are attributed to natural thermal plumes that act as sources of extra energy input to the Kolmogorov-Obukhov-Corrsin scheme of turbulence in or at the low-wave number limit of the inertial subrange. Modified forms of the K-O-C spectral laws for thermally unstable air are derived which agree with the observed spectra over the whole range of wave numbers examined, and which contain the spectral gap at wave numbers corresponding to the thermal plume diameters.     

Observations of a multi-level turbulence structure in a very stable atmospheric boundary layer

Boundary-layer measurements conducted at the Marsta site in Sweden from a winter-time situation (23–25 Feb.) with stable stratification have been analysed. The data comprise wind and temperature profile measurements up to 30 m, turbulence measurements at 2, 6 and 30 m and Doppler acoustic sounder data up to about 150 m. The upwind fetch at the site is flat and free from obstacles to a distance of ca 5 km for the particular sector chosen for the experiment.During the night, a two-layer vertical structure developed. Analysis of power spectra, co-spectra and variances in a shallow and very stable turbulent boundary layer near the ground show that the turbulence is fully developed and follow the universal behaviour.Above, at a height of 30 m, another turbulent layer is produced by increased wind shear near a low-level jet. This turbulent upper layer can be regarded as a layer of free shear flow. At this height, there also exist wave-turbulence interactions at low frequencies which sometimes cause a countergradient heat flux.     

Second-order closure modeling of diffusion in the atmospheric boundary layer

A method for calculating turbulent diffusion in the planetary boundary layer is developed based on Donaldson's second-order closure approach. The resulting partial differential equation for the turbulent mass flux has a hyperbolic character for early times when the plume scale is small compared with the ambient turbulent scale, with a smooth transition to a parabolic, gradient-diffusion-type character when the plume scale is large. Calculations are compared with available estimates from the literature for different values of Rossby number and Richardson number in the ambient atmosphere. Comparison of model predictions with laboratory simulation of diffusion in a free convection, mixed layer is good, with the model able to predict the maximum concentration rising from the ground as observed.This project has been funded in part with Federal funds from the Environmental Protection Agency under contract number EPA 68-02-1310.     

A case study of turbulence in the stable nocturnal boundary layer

Velocity and signal intensity data during stable conditions in the nocturnal boundary layer (NBL) were obtained with a minisodar on two consecutive nights with similar mean conditions. There was little turbulence activity during the first night, but during the second night, continuous background Kelvin-Helmholtz waves and instabilities having a 2-min period grew and penetrated above the mean NBL height at approximately 60-min intervals. Enhanced ozone concentrations at the surface occurred during the active periods even though most mean meteorological parameters were unchanged. Vertical profiles of vertical velocity standard deviation, dissipation rate, and temperature variance destruction rate in the NBL were measured and analyzed separately according to levels of turbulence activity. Well-defined differences between inactive and active periods of a factor of two to four were found for each parameter. The temperature structure parameter flux was large and in opposite directions in the upper and lower part of the NBL during active periods of turbulence, but small during other periods.     

An observation of waves and turbulence in the earth's boundary layer

An account is given of an observation of a wave-like phenomenon obtained during a study of nocturnal inversions. Associated bursts of turbulent activity are also described.     

The response of the marine boundary layer to mesoscale variations in sea-surface temperature

The effects of variations in sea-surface temperature on the surface fluxes of the marine atmospheric boundary layer have been investigated. The boundary model developed by Brown and Brown and Liu has been used to estimate these effects for near neutral conditions. Data taken on September 1, 1978, during the JASIN experiment have been used to corroborate the results obtained with Brown's model. Some speculations on secondary effects of the sea-surface temperature are given.     

On generation of internal waves by turbulence in the mixed layer

Turbulent fluctuations in active mixed layers can excite internal waves in stably stratified fluid regions adjoining them. Expressions are derived for the energy and momentum fluxes radiated away by internal waves from an oceanic mixed layer, in terms of the spectrum of the static pressure fluctuations imposed at the base of the mixed layer by the turbulent eddies. The role of these internal wave fluxes in questions such as the determination of the rate of deepening of the layer due to an applied surface stress and the origin of internal waves in the deep ocean is discussed.     

Turbulent characteristics of a shallow convective internal boundary layer

Turbulent characteristics of a 50 to 100 m deep convective internal boundary layer (I.B.L.) have been studied. The data were gathered at a flat coastal site (Näsudden on the island of Gotland, Sweden) during three consecutive days in May 1980 which were characterized by a steady, very stable stratified marine approach flow. The site is situated on a flat area ca. 1500 m from the shoreline. Only daytime runs have been analysed in the present paper. The sensible heat flux at the ground was typically 200 W m^-2 and was found to decrease more or less linearly with height throughout the I.B.L., being slightly negative at greater heights. The momentum flux was also found to decrease with height, but nevertheless shear production of turbulent kinetic energy was found to be large throughout the entire I.B.L. The analysis shows that the turbulent regime has a mixed character. Certain characteristics, such as the rate of growth of the I.B.L., appear to be almost entirely controlled by mechanical turbulence, while others, notably temperature variance and the spectrum of vertical velocity, scale remarkably well with w _* and z _i, in accordance with the results found in fully convective conditions during the experiments at Minnesota and Aschurch. Other turbulent characteristics, such as spectra of the horizontal wind components measured near the top of the I.B.L. tend to adhere to mixed-layer scaling in the high frequency range, exhibiting much increased energy in the lower (reduced) frequency range. Spectra of the velocity components from 10 m are shown to be in general agreement with findings from ‘ideal’, homogeneous sites (Kansas) when properly normalized, although the low frequency part of u- and v-spectra are slightly reduced compared to the case with deep convection.     

An investigation of the turbulence balance equations in the atmospheric boundary layer

Three Cardington turbulence probes were operated at heights of 61, 91, and 152 m over a 5-h period in an unstable boundary layer. The results have been used to assess (at the middle level) the relative importance of the terms in the turbulence equations for kinetic energy, temperature variance, stress, and the vertical and total horizontal heat fluxes.Now at the Building Research Station, Garston, Watford, England.     

A model for the height of the internal boundary layer over an area with an irregular coastline

A model for the time and space variation of the internal boundary-layer height over a land area with an irregular coastline is presented. It is based on the analytical model of the boundary-layer height proposed by Gryning and Batchvarova (1990) and Batchvarova and Gryning (1991), The model accounts for the temperature jump and the mean vertical air motion at the top of the internal boundary-layer. Four cases from experiments in Nanticoke and Vancouver are used for model validation. The agreement between the calculated and measured internal boundary layer height at the observational sites is fairly good. The input information for the model consist of wind speed and direction, friction velocity and kinematic heat flux in time and space for the area, and the potential temperature gradient and the mean vertical air motion above the internal boundary layer. For the experiments used in the validation the effect of subsidence is relatively important in the afternoon under low wind speed high pressure conditions, lowering the height of the internal boundary layer by up to 10%, and it is negligible in the morning hours. The effect of the mixing height over the sea is found to be negligible.