Effect of atmospheric stability on the growth of surface gravity waves

In this paper we study the effect of atmospheric stability on the growth of surface gravity waves. To that end we numerically solved the Taylor-Goldstein equation for wind profiles which deviate from a logarithmic form because stratification affects the turbulent momentum transport. Using Charnock's relation for the roughness height z ₀ of the wind profile, it is argued that the growth rate of the wave depends on the dimensionless phase velocity c/u _* (where u _* is the friction velocity) and a measure of the effect of atmospheric stability, namely the dimensionless Obukhov length gL/u _* ², whereas it only depends weakly on gz _t /u _* ² (where z _t is the roughness height of the temperature profile). Remarkably for a given value of u _* /c, the growth rate is larger for a stable stratification (L > 0) than for an unstable one (L < 0). We explain why this is the case. If, on the other hand, one considers the growth rate as a function of c/U ₁₀ (where U ₁₀ is the windspeed at 10 m), the situation reverses for c/U ₁₀ < 1. For practical application in wave prediction models, we propose a new parameterization of the growth rate of the waves which is an improvement of the Snyder et al. (1981) proposal because the effect of stability is taken into account.     

On the impact of thermal stability on some rough flow effects over mobile surfaces

Calculations are made of the effects of thermal stability under a range of conditions, over the sea and land, on the physical factors (including the critical wind speed) affecting dust-storm generation, snow drift, and rough sea conditions. The computational procedure involves the surface friction velocity, u _*, and its relation with the aerodynamic roughness over aerodynamically rough, mobile surfaces. The results indicated that even at relatively high wind speeds, thermal effects under extreme advection situations may be significant, particularly for those properties of the agitated surface dependent on u _* ³ and u _* ⁴.     

Effects of Topographical Slope Angle and Atmospheric Stratification on Surface-Layer Turbulence

The effect of topographical slope angle and atmospheric stratification on turbulence intensities in the unstably stratified surface layer have been parameterized using observations obtained from a three-dimensional sonic anemometer installed at 8 m height above the ground at the Seoul National University (SNU) campus site in Korea for the years 1999–2001. Winds obtained from the sonic anemometer are analyzed according to the mean wind direction, since the topographical slope angle changes significantly along the azimuthal direction. The effects of the topographical slope angle and atmospheric stratification on surface-layer turbulence intensity are examined with these data. It is found that both the friction velocity and the variance for each component of wind normalized by the mean wind speed decrease with increase of the topographical slope angle, having a maximum decreasing rate at very unstable stratification. The decreasing rate of the normalized friction velocity (u _* /U) is found to be much larger than that of the turbulence intensity of each wind component due to the reduction of wind shear with increase in slope angle under unstable stratification. The decreasing rate of the w component of turbulence intensity (σ _w /U) is the smallest over the downslope surface whereas that of the u component (σ _u /U) has a minimum over the upslope surface. Consequently, σ _w /u _* has a maximum increasing rate with increase in slope angle for the downslope wind, whereas σ _u /u _* has its maximum for the upslope wind. The sloping terrain is found to reduce both the friction velocity and turbulence intensity compared with those on a flat surface. However, the reduction of the friction velocity over the sloping terrain is larger than that of the turbulence intensity, thereby enhancing the turbulence intensity normalized by the friction velocity over sloping terrain compared with that over a flat surface.     

The impact of soil moisture on dispersion-related characteristics

This study investigates the impact of soil moisture availability on dispersion-related characteristics: surface fric-tion velocity (u*), characteristic scales of temperature and humidity (T* and q*), the planetary boundary layer height (h) and atmospheric stability classified by Monin-Obukhov length (L), Kazanski-Monin parameter (μ) and convective velocity scale (w*) during daytime convective condition using a one-dimensional primitive equation with a refined soil model.     

A Richardson Number criterion for the air-sea interface

It is shown that the observationally determined roughness relation z ₀ = u _* ²/g in which g is the acceleration of gravity, u _*, is the friction velocity in air, and = 0.0185 (Wu, 1982) for the wind profile over the sea surface relative to the surface current, is consistent with the existence of a Richardson Number criterion at the air-sea interface in which the critical Richardson Number, Ri_c = 1, such that all the shear energy is converted into potential energy.     

The characteristics of turbulent velocity components in the surface layer under convective conditions

It is proposed that the ratios of the standard deviations of the horizontal velocity components to the friction velocity in the surface layer under convective conditions depend only onz _i /L wherez _i is the height of the lowest inversion andL is the Monin-Obukhov length. This hypothesis is tested by using observations from several data sets over uniform surfaces and appears to fit the data well. Empirical curves are fitted to the observations which have the property that at largez _i /-L, the standard deviations become proportional tow _*, the convective scaling velocity.Fluctuations of vertical velocity obtained from the same experiments scale withz/L, wherez is the height above the surface, in good agreement with Monin-Obukhov theory.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The Fallacy of Drifting Snow

A common parametrization over snow-covered surfaces that are undergoing saltation is that the aerodynamic roughness length for wind speed (z ₀) scales as au_*²/g{\alpha u_\ast^2/g}, where u _* is the friction velocity, g is the acceleration of gravity, and α is an empirical constant. Data analyses seem to support this scaling: many published plots of z ₀ measured over snow demonstrate proportionality to u_*²{u_\ast^2 }. In fact, I show similar plots here that are based on two large eddy-covariance datasets: one collected over snow-covered Arctic sea ice; another collected over snow-covered Antarctic sea ice. But in these and in most such plots from the literature, the independent variable, u _*, was used to compute z ₀ in the first place; the plots thus suffer from fictitious correlation that causes z ₀ to unavoidably increase with u _* without any intervening physics. For these two datasets, when I plot z ₀ against u _* derived from a bulk flux algorithm—and thus minimize the fictitious correlation—z ₀ is independent of u _* in the drifting snow region, u _* ≥ 0.30 ms⁻¹. I conclude that the relation z₀ = au_*²/g{z_0 = \alpha u_\ast^2/g} when snow is drifting is a fallacy fostered by analyses that suffer from fictitious correlation.     

光滑海面上风、温、湿廓线的层结订正模式及海气整体交换系数

详细介绍了光滑面标量粗糙度ＺＴ,Ｚｑ与风速粗糙度Ｚ０的相似表达式,论述了把Ｍｏｎｉｎ－Ｏｂｕｋｈｏｖ相似理论推广到光滑面上湍流气层的合理性,从而得到光滑面风、温、湿层结订正廓线与粗糙面廓线相统一的形式。总结了用该模式处理的三个海上梯度观测资料的计算结果,揭示出了微风时通过光滑海面的海气通量及整体交换系数受层结影响远大于风速影响的特征。并给出光滑界面上不同层结的整体交换系数随风速变化的拟合公式。     

Note on turbulent scaling parameters for the convective planetary boundary layer

Scaling velocities relevant for turbulent flows in the planetary boundary layer are discussed. It is suggested that the scaling parameters should be determined by integrated bulk properties of the respective turbulent production terms. According to this concept, a new velocity scale, replacing the friction velocityu*, is proposed depending on bothu* and the geostrophic windu _g . The convective velocity scalew* can be determined by the integral of the buoyancy production term and is therefore an appropriate velocity scale. Examination of Minnesota and Kansas data shows that these data do not give the possibility of verifying whether the new scaling velocity is more appropriate thanu*. This is because the range of variability of atmospheric stability during the field measurements is too small. However, theoretical considerations based on integrated properties of the turbulence, through the depth of the planetary boundary layer, are given in support of the new scaling velocity.     

Standard deviation of vertical two-point longitudinal velocity differences in the atmospheric boundary layer

The standard deviation of vertical two-point longitudinal velocity fluctuation differences is analyzed experimentally with eleven sets of turbulence measurements obtained at the NASA 150-m ground-winds tower site at Cape Kennedy, Florida. It is concluded that /u _*0 is proportional to (fz/u _*0)^0.22, where the coefficient of proportionality is a function of fz/u _*0 and u _*0/fL ₀. The quantities f and L₀ denote the Coriolis parameter and the surface Monin-Obukhov stability length, respectively; u _*0 is the surface friction velocity; z is the vertical distance between the two points over which the velocity difference is calculated; and zz is the mean height of the mid-point of the interval z above natural grade. The results of the analysis are valid for 20<-u _*0/fL ₀<2000.     

Aircraft estimates of the geostrophic drag coefficient and the rossby similarity functions A and B over the sea

Estimates of the geostrophic drag coefficient and the Rossby similarity functions, A and B obtained from data collected by an instrumented aircraft over the sea are presented. The average value of the geostrophic drag coefficient is 0.027 and is independent of the geostrophic windspeed. The dependence of the similarity functions A and B on boundary-layer parameters is investigated. The function A is found to depend on baroclinicity parameters, while B depends on the parameter u _*/fh (where u _* is the surface friction velocity, f is the Coriolis parameter, and h is the boundary-layer depth). Using the geostrophic drag coefficient found here and the results of surface drag coefficient studies, a relationship between geostrophic windspeed and surface windspeed is obtained which shows good agreement with empirical data.     

Notes on an Internal Boundary-Layer Height Formula

The derivation of the Panofsky–Dutton internal boundary-layer(IBL) height formula has been revisited. We propose that the upwindroughness length (rather than downwind) should be used in theformula and that a turbulent vertical velocity (_w) ratherthan the surface friction velocity (u_*) should be considered asthe appropriate scaling for the rate of propagation ofdisturbances into the turbulent flow. A published set ofwind-tunnel and atmospheric data for neutral stratification hasbeen used to investigate the influence of the magnitude ofroughness change on the IBL height.     

Monin-Obukhov Functions for Standard Deviations of Velocity

The origins of Monin-Obukhov similarity theory (MOST) are briefly reviewed, as a context for the analysis of signals from sonic anemometers operating in the surface layer over a Utah salt flat. At this site (over the interval of these measurements) the neutral limit for the normalized vertical velocity standard deviation (σ _w /u _*) deviates markedly from what has generally been regarded as the standard value (i.e. about 1.3), suggesting (since others have also reported such deviations) that this Monin-Obukhov constant is not, in fact, universal. New (but tentative) formulae are suggested for σ _w and for the longitudinal standard deviation σ _u .     

Determination of similarity functions of the resistance laws for the planetary boundary layer using surface-layer similarity functions

Functional forms of the universal similarity functions A, B (for wind components parallel and normal to the surface stress), and C (for potential temperature difference) are determined based on the generalized theory of the resistance laws for the Planetary Boundary Layer (PBL). The similarity-profile functions for the surface layer are matched with the velocity and temperature-defect profiles that are assumed to have shapes modified by certain powers of nondimensional height z/h, where h is the PBL height. The powers of the outer-layer profile functions are determined, so that the functions become negligible in the surface layer. To close the temperature defect law, an assumption that the temperature gradient across the top of the PBL is continuous with the stratification of the overlying atmosphere is used. The result of this assumption is that nondimensional momentum and temperature profiles in the PBL can be described in terms of four basic ratios: (1) roughness ratio = /h (2) scale-height ratio =|f|h/u_*, (3) ambient stratification parameter =h/_*, and (4) stability parameter =h/L, where L is the Monin-Obukhov length, z₀ is the surface roughness, is the upper-air stratification, u _* is the friction velocity, and _* is the temperature scale at the surface. For stable conditions, the scale-height ratio can be related to the atmospheric stability and the upperair stratification, and the generalized similarity and Rossby number similarity theories become identical. Under appropriate boundary conditions, function A is explicitly dependent on the stability parameter , while B is a function of scale-height ratio , which in turn depends on the stability. Function C is shown to be dependent on the stability and the upper-air stratification, due to the closure assumption used for the temperature profile.The suggested functional forms are compared with other empirical approximations by several authors. The general framework used to determine the functional forms needs to be tested against good boundary-layer measurements.     

The limitations on stress parameterization imposed by intermittency in turbulent flow

The indirect dissipation technique is used to estimate 1-min averages of friction velocity u _*in the surface layer over the tropical ocean. These estimates are compared to estimates of u _*obtained using a drag coefficient and the relative difference between the two is examined in relation to stability and averaging time. Plumes and downdrafts are found to be responsible for an anomalous behavior of the drag coefficient estimates. Certain factors relating to plume properties, derived using conditional sampling as described in Khalsa (1980), are shown to be related to the variance between the two estimates of friction velocity. An investigation into the effects of increasing the averaging time reveals that plume spacing, which is dependent on stability, and the mean wind speed determine the minimum time for smoothing the influence of plumes and downdrafts.Department of Atmospheric Sciences contribution number 513.     

A numerical model study of the structure and similarity scaling of the nocturnal boundary layer (NBL)

A one-dimensional numerical model based on the equations of mean motion and turbulent kinetic energy (TKE), with Delage's (1974) mixing-length parameterization has been used to simulate the mean and turbulent structure of the evolving stably stratified nocturnal boundary layer (NBL). The model also includes a predictive equation for the surface temperature and longwave radiational cooling effects.In the absence of advective and gravity wave effects, it is found that the model-simulated structure, after a few hours of evolution, could be ordered fairly well by a similarity scaling (u _*0, _*0, L ₀, and h) based on surface fluxes and the NBL height. Simple expressions are suggested to describe the normalized profiles of momentum and heat fluxes, TKE, eddy-viscosity and energy dissipation. A good ordering of the same variables is also achieved by a local scaling (u _*0, _* and L) based on the height-dependent local fluxes. The normalized TKE, eddy viscosity and energy dissipation are unique functions of z/L and approach constant values as z/L , where L is the local Monin-Obukhov length. These constants are close to the values predicted for the surface layer as z/L , thus suggesting that the Monin-Obukhov similarity theory can be extended to the whole NBL, by using the local (height-dependent) scales in place of surface-layer scales. The observed NBL structure has been shown to follow local similarity (Nieuwstadt, 1984).     

Observational evidence for the Monin-Obukhov similarity under all stability conditions

Data collected in the surface layer in a northern suburban area of Nanjing from 15 November to 29 December 2007 were analyzed to examine the Monin-Obukhov similarity for describing the turbulent fluctu- ations of 3D winds under all stability conditions and to obtain the turbulence characteristics under different weather conditions. The results show that the dimensionless standard deviations of turbulent velocity com- ponents (σ u /u* , σ v /u* , σ w /u * ) and dimensionless turbulent kinetic energy (TKE) can be well described by "1/3" power law relationships under stable, neutral, and unstable conditions, with σ u /u * > σ v /u * > σ w /u* . Land use and land cover changes mainly impact dimensionless standard deviations of horizontal component fluctuations, but they have very little on those of the vertical component. The dimensionless standard devi- ations of wind components and dimensionless TKE are remarkably affected by different weather conditions; the deviations of horizontal wind component and dimensionless TKE present fog day > clear sky > overcast > cloudy; the trend of the vertical wind component is the reverse. The surface drag coefficient at a Nan- jing suburban measurement site during the observation period was obviously higher than at other reported plains and plateau areas, and was approximately one order larger in magnitude than the reported plains areas. Dimensionless standard deviation of temperature declined with increasing |z /L| with an approximate "-1/3" slope in unstable stratification and "-2/3" slope in stable stratification.     

Nighttime free convection characteristics within a plant canopy

An intensive measurement campaign within and above a maize row canopy was carried out to investigate flow characteristics within this vegetation. Attention was given to finding adequate scaling parameters of the within-canopy windspeed and air temperature profiles under above-canopy stable stratification.During clear and calm nights the within-canopy condition differs considerably from the abovecanopy state. In contrast to the daytime, the windspeed and temperature profiles do not scale with the above-canopy friction velocity,u ^* , and the scaling temperature,T ^* , respectively. A free convection flow regime is generated, forced by the soil heat flux at the canopy floor and by cooling at the top of the canopy. However, the windspeed and temperature profiles appear to scale well with the free convective velocity scale,w ^* , and the free convective temperature scale,T ^f , respectively. The free convective state within the canopy agrees well with the free convection criterion Gr>16Re²(u ^* ), where Gr is the Grashof number and Re(u ^* ) the Reynolds number, a criterion often used in technical flow problems. Also it is shown that under within-canopy free convection, there is a unique relation between the Grashof number, Gr, and the Reynolds number if the latter is based on the free convective velocity scale.Under within-canopy free convective conditions, it appears that within the canopy the fluxes of heat and water vapour can be estimated well with the relatively simple variance technique. Under these conditions, the Grashof, or Rayleigh number, represents a measure for the kinetic energy of the turbulence within the canopy.     

The turbulent structure of the internal boundary layer near the shore

The mean structure within the internal boundary layer (IBL) near the shore, which develop from the coast in the presence of a sea breeze, has been described in Part I of this study (Ogawa and Ohara, 1984). This paper presents the results of the similarity and energy budget analysis for the purpose of parameterization of the turbulent structure within the IBL. The analysis of the turbulent kinetic energy balance, turbulent intensities and spectra show that the wind is strongly affected by mechanical turbulence in comparison with the past results in a fully developed convective layer where thermal convection dominated. The standard deviations of the wind velocities normalized by the friction velocity u _* (surface-layer scaling parameter) are functions only of the normalized height z/Z _i within 160 m of the shoreline, where Z _i is the IBL. On the other hand, the standard deviations of temperature normalized by _* (mixing-layer scaling parameter) have less scatter with distance than those normalized by T _* (surface-layer scaling parameter). The data showed that both u _* (not a mixed-layer parameter), and Z _i (not a surface-layer parameter) are necessary to describe the turbulent characteristics of the IBL near the shore.Deceased March, 1984.     

A bulk similarity approach in the atmospheric boundary layer using radiometric skin temperature to determine regional surface fluxes

Profiles of wind velocity and temperature in the outer region of the atmospheric boundary layer (ABL) were used together with surface temperature measurements, to determine regional shear stress and sensible heat flux by means of transfer parameterizations on the basis of bulk similarity. The profiles were measured by means of radiosondes and the surface temperatures by infrared radiation thermometry over hilly prairie terrain in northeastern Kansas during the First ISLSCP Field Experiment (FIFE). In the analysis, the needed similarity functions were determined and tested; the main scaling variables used for the ABL were h _i , the height of the convectively mixed layer, and V _a and _a, the wind speed and potential temperature averaged over the mixed layer. Good agreement (r = 0.80) was obtained between values of friction velocity u _* determined by this ABL bulk similarity approach and those obtained by Monin-Obukhov similarity in the surface sublayer. Similarly, values of surface flux of sensible heat H determined by this method compared well (r = 0.90) with the regional means measured at six ground stations. The corresponding regional evaporation values, determined with the energy budget equation, also compared favorably (r = 0.94).