Resistance law,effective roughness length,and deviation angle over hilly terrain

In this note, we derive from the resistance law of Rossby number similarity theory the expressions for the drag coefficient and the deviation angle for strongly unstable and strongly stable stratifications. The extension of the applicability of the resistance laws to inhomogeneous terrain is discussed. A determination of the deviation angle over inhomogeneous terrain from a numerical experiment is presented.On leave from: Institute of Limnology, Academy of Sciences of the USSR, 196199 Leningrad.     

Shear convection

The paper discusses convection in the presence of wind shear, a condition analysed previously by Zilitinkevich (1971). This region (between the forced and fully developed convective layers) was also considered by Betchov and Yaglom (1971). In the present paper the author endeavors to develop a consistent analysis from the basic hypothesis of a very weak interaction between the vertical convective motions and mechanical turbulence, employing a new similarity model of the turbulent regime. Additional experimental data are introduced. Unlike the notation used in the references quoted above, this regime is termed shear convection rather than free convection. The latter is traditionally regarded as synonymous with the terms pure or fully developed convection.     

Subject Index

Subject Index

Subject Index     

Tangling Turbulence and Semi-Organized Structures in Convective Boundary Layers

A new mean-field theory of turbulent convection is developed based on the idea that only the small-scale region of the spectrum is considered as turbulence, whereas its large-scale part, including both regular and semi-organized motions, is treated as the mean flow. In the shear-free regime, this theory predicts the convective wind instability, which causes the formation of large-scale semi-organized motions in the form of cells. In the presence of wind shear, the theory predicts another type of instability, which causes the formation of large-scale semi-organized structures in the form of rolls and the generation of convective-shear waves propagating perpendicular to the convective rolls. The spatial characteristics of these structures, such as the minimum size of the growing perturbations and the size of perturbations with the maximum growth rate, are determined. This theory might be useful for understanding the origin of large-scale cells and rolls observed in the convective boundary layer and laboratory turbulent convection     

The Effect of Stratification on the Aerodynamic Roughness Length and Displacement Height

The roughness length, z _0u , and displacement height, d _0u , characterise the resistance exerted by the roughness elements on turbulent flows and provide a conventional boundary condition for a wide range of turbulent-flow problems. Classical laboratory experiments and theories treat z _0u and d _0u as geometric parameters independent of the characteristics of the flow. In this paper, we demonstrate essential stability dependences—stronger for the roughness length (especially in stable stratification) and weaker but still pronounced for the displacement height. We develop a scaling-analysis model for these dependences and verify it against experimental data.     

Calculation Of The Height Of The Stable Boundary Layer In Practical Applications

Currently used and newly proposed calculation techniques for the heightof the stable boundary layer (SBL), including the bulk-Richardson-numbermethod, diagnostic equations for the equilibrium SBL height, and a relaxation-typeprognostic equation, are discussed from the point of view of their physical basis andrelevance to experimental data. Among diagnostic equations, the best fit to data exhibits an advanced Ekman-layer height model derived recently with due regard to the role of the free-flow stability. Its extension to non-steady regimes provides a prognostic equation recommended for use in practical applications.     

Velocity profiles,the resistance law and the dissipation rate of mean flow kinetic energy in a neutrally and stably stratified planetary boundary layer

The logarithmic + polynomial approximation is suggested for vertical profiles of velocity components in a planetary boundary layer (PBL) at neutral and stable stratification. The resistance law functions A and B are determined on the basis of this approximation, using integral relations derived from the momentum equations, the Monin-Obukhov asymptotic formula for the wind profile in a stably stratified near-surface layer and the known expressions for the PBL depth. This result gives a realistic and convenient method for calculating the surface friction velocity and direction and the total dissipation rate of mean flow kinetic energy in terms of geostrophic velocity, buoyancy flux at the surface, the roughness parameter and the Coriolis parameter. In the course of these derivations a review is given of current views on the main problems of the neutral and stable PBL.     

Comments on the Numerical Simulation of Homogeneous Stably-Stratified Turbulence

The standard design for the direct numerical simulation of homogeneous stably-stratified turbulence assumes that the simulated turbulence is fully characterised by the gradient Richardson number. This assumption is justified only in sufficiently strong stratification when the Obukhov turbulent length scale, L, is essentially smaller than the depth of the computational domain, H. Otherwise simulations are not quite realistic because they cut off the large-scale part of the turbulence spectrum, namely, the scales comparable with or larger than H but smaller than L, that is just the eddies most sensitive to the stratification.     

On evaluation of the oceanic surface drift current speed and direction

The surface drift current speed and direction are defined using the resistance laws for turbulent Ekman boundary layers. Stratification conditions that coincide in the atmospheric and oceanic boundary layers yield approximate formulas whereby the drift current and geostrophic wind directions coincide and the geostrophic wind factor k is equal to the square root of the air and water density ratio. The theoretical estimates of k are compared with available experimental data.     

Temperature distribution and current system in a convectively mixed lake

During spring and autumn, many lakes in temperate latitudes experience intensive convective mixing in the vertical, which leads to almost isothermal conditions with depth. Thus the regime of turbulence appears to be similar with that characteristic of convective boundary layers in the atmosphere. In the present paper a simple analytical approach, based on boundary-layer theory, is applied to convective conditions in lakes. The aims of the paper are firstly to analyze in detail the temperature distribution during these periods, and secondly to investigate the current system, created by the horizontal temperature gradient and wind action. For these purposes, simple analytical solutions for the current velocities are derived under the assumption of depth-constant temperatures. The density-induced current velocities are shown to be small, in the order of a few mm/sec. The analytical model of wind-driven currents is compared with field data. The solution is in good qualitative agreement with observed current velocities under the condition that the wind field is steady for a relatively long time and that residual effects from former wind events are negligible.The effect of the current system on an approximately depth-constant temperature distribution is then checked by using the obtained current velocity fields in the heat transfer equation and deriving an analytical solution for the corrected temperature field. These temperature corrections are shown to be small, which indicates that it is reasonable to describe the temperature distribution with vertical isotherms.Notation T temperature - t time - x, y, z cartesian coordinates - molecular viscosity - _h , _v horizontal and vertical turbulent viscosity - K _h ,K _v horizontal and vertical turbulent conductivity - Q heat flux through the water surface - D depth - u, v, w average current velocity components inx, y andz directions - f Coriolis parameter - p pressure - density - g gravity acceleration - a constant in the freshwater state equation - h _s deviation from the average water surface elevation - L _*,H _* length and depth scale - U _*,W _* horizontal and vertical velocity scale - T temperature difference scale - bottom slope - u _* friction velocity at the water surface - von Karman constant - L Monin-Obukhov length scale - buoyancy parameter - l turbulence length scale - C ₁,C ₂,C ₃ dimensionless constants in the expressions for the vertical turbulent viscosity - , dimensionless vertical coordinate and dimensionless local depth - angle between surface stress direction andx-axis - T _bx ,T _by bottom stress components - c bottom drag coefficient