Stratified flow over three-dimensional topography     

Y. Kadri  P. Bonneton  J. M. Chomaz  M. Perrier   《Dynamics of Atmospheres and Oceans》1996,23(1-4)

In order to investigate flows over topography in an atmospheric context, we have studied experimentally the wake structure of axi-symmetric Gaussian obstacles towed through a linearly stratified fluid. Three dimensionless parameters govern the flow dynamics: F, the Froude number based on the topography height h; Re, the Reynolds number and the aspect ratio r = h/L, where L is the topography horizontal scale. Two-dimensional (2-D), saturated lee wave (SLW) and three-dimensional (3-D) regimes, as defined in Chomaz et al. (1993), are found to be functions of F and r only (Fig. 1) as soon as Re is larger than Re_c ≈ 2000. For F < 0.7 the flow goes around the obstacle and the motion in the wake is quasi-two-dimensional. This 2-D layer is topped by a region affected by lee wave motions with amplitude increasing with r and F. For 0.7 < F < 1/r, the flow is entirely dominated by a lee wave of saturated amplitude which suppresses the separation of the boundary layer from the obstacle. Above the critical value 1/r, the lee wave amplitude decreases with F and a recirculating zone appears behind the obstacle. Simultaneously, coherent large-scale vortices start to be shed periodically from the wake at a Strouhal number which decreases as 1/F until it reaches its neutral asymptotic value.  相似文献   

Neutrally Stratified Turbulent Ekman Boundary Layer: Universal Similarity for a Transitional Rough Surface     

Noor Afzal 《Boundary-Layer Meteorology》2009,132(2):241-259

The geostrophic Ekman boundary layer for large Rossby number (Ro) has been investigated by exploring the role played by the mesolayer (intermediate layer) lying between the traditional inner and outer layers. It is shown that the velocity and Reynolds shear stress components in the inner layer (including the overlap region) are universal relations, explicitly independent of surface roughness. This universality of predictions has been supported by observations from experiment, field and direct numerical simulation (DNS) data for fully smooth, transitionally rough and fully rough surfaces. The maxima of Reynolds shear stresses have been shown to be located in the mesolayer of the Ekman boundary layer, whose scale corresponds to the inverse square root of the friction Rossby number. The composite wall-wake universal relations for geostrophic velocity profiles have been proposed, and the two wake functions of the outer layer have been estimated by an eddy viscosity closure model. The geostrophic drag and cross-isobaric angle predictions yield universal relations, which are also supported by extensive field, laboratory and DNS data. The proposed predictions for the geostrophic drag and the cross-isobaric angle compare well with data for Rossby number Ro ≥ 10⁵. The data show low Rossby number effects for Ro < 10⁵ and higher-order effects due to the mesolayer compare well with the data for Ro ≥ 10³.  相似文献   

On the structure of supercritical western boundary currents     

Sang-Ki Lee   《Dynamics of Atmospheres and Oceans》2001,33(4):219

The structure of supercritical western boundary currents is investigated using a quasi-geostrophic numerical model. The basic flow is of meridional Munk balance, and the input boundary is perturbed by the most unstable wave solution obtained from linear spatial instability calculations. Self-preserving (or equilibrium) solutions are obtained for the model runs at Re=30, 60, 90, and 120, and their energy and vorticity budgets are analyzed. In an analogy with the laboratory turbulence of wall boundary layers, the western boundary layer is divided into inner and outer layers. In the inner layer, the mean energy is dissipated via direct viscous dissipation, while in the outer layer it is converted to the eddy energy via turbulence production. The main scenario is that the mean energy is produced in the inner layer via ageostrophic pressure work divergence, and it is partly removed due to viscous action within a narrow region near the wall, defined here as viscous sub-layer. The remaining portion is converted to the eddy energy via turbulence production in the outer layer, which is in turn transported to the inner layer, then again to the viscous sub-layer where it is ultimately dissipated. In the near-wall side, the vorticity balance of the mean flow is maintained by viscous effect and Reynolds flux divergence, while in the offshore side it is maintained by beta effect and Reynolds flux divergence. The length scale of the supercritical boundary current is roughly , where L_M is the Munk length, as observed from a dimensional analysis.  相似文献   

Global Intermittency and Collapsing Turbulence in the Stratified Planetary Boundary Layer   总被引：1，自引：1，他引：0  

Cedrick Ansorge  Juan Pedro Mellado 《Boundary-Layer Meteorology》2014,153(1):89-116

Direct numerical simulation of the turbulent Ekman layer over a smooth wall is used to investigate bulk properties of a planetary boundary layer under stable stratification. Our simplified configuration depends on two non-dimensional parameters: a Richardson number characterizing the stratification and a Reynolds number characterizing the turbulence scale separation. This simplified configuration is sufficient to reproduce global intermittency, a turbulence collapse, and the decoupling of the surface from the outer region of the boundary layer. Global intermittency appears even in the absence of local perturbations at the surface; the only requirement is that large-scale structures several times wider than the boundary-layer height have enough space to develop. Analysis of the mean velocity, turbulence kinetic energy, and external intermittency is used to investigate the large-scale structures and corresponding differences between stably stratified Ekman flow and channel flow. Both configurations show a similar transition to the turbulence collapse, overshoot of turbulence kinetic energy, and spectral properties. Differences in the outer region resulting from the rotation of the system lead, however, to the generation of enstrophy in the non-turbulent patches of the Ekman flow. The coefficient of the stability correction function from Monin–Obukhov similarity theory is estimated as \(\beta \approx 5.7\) in agreement with atmospheric observations, theoretical considerations, and results from stably stratified channel flows. Our results demonstrate the applicability of this set-up to atmospheric problems despite the intermediate Reynolds number achieved in our simulations.  相似文献   

Direct numerical simulation of a vigorously heated low Reynolds number convective boundary layer     

G. N. Coleman  J. H. Ferziger 《Dynamics of Atmospheres and Oceans》1996,24(1-4)

Computations of the buoyantly unstable Ekman layer are performed at low Reynolds number. The results are obtained by directly solving the three-dimensional time-dependen Navier-Stokes equations with the Boussinesq buoyancy approximation, resolving all relevant scales of motion (no turbulence closure is needed). The flow is capped by a stable temperature inversion and heated from below at a rate that produces an inversion-height to Obukhov-length ratio −z_i/L_* = 32. Temperature and velocity variance profiles are found to agree well with those from an earlier vigorously heated under-resolved computation at higher Reynolds number, and with experimental data of Deardorff and Willis (Boundary-Layer Meteorol., 32: 205–236, 1985). Significant helicity is found in the layer, and helical convection patterns of the scale of the inversion height are observed.  相似文献   

Wind flow over ridges in simulated atmospheric boundary layers     

J. R. Pearse  D. Lindley  D. C. Stevenson 《Boundary-Layer Meteorology》1981,21(1):77-92

The flows over four two-dimensional triangular hills and three two-dimensional bell-shaped hills have been investigated in a simulated rural atmospheric boundary layer modelled to a scale of 1:300: Further measurements were made over two of the triangular hills in a simulated rural boundary layer of 1: 3000 scale and in a simulated urban boundary layer modelled to a scale of 1:400. The effect of the model hill surface roughness was also investigated. Flow measurements were restricted to the mean velocity U, RMS velocity fluctuations u and the energy spectra for the streamwise velocity component Measurements were made at a number of longitudinal positions in the approach flow, over the model hills and downstream of the model hills. For each model hill, the crest was the region of largest mean velocity and smallest velocity fluctuations. The largest mean velocities over the model hills occurred for hills of intermediate slope rather than for the steepest hills. A decrease in the scale of the simulated atmospheric boundary layer led to a reduction in the amplification factors at the hill crests, whereas an increase in the surface roughness of the approach flow resulted in increased amplification factors at the hill crests.  相似文献   

Circulation and boundary layers in differentially heated rotating stratified fluid     

J. A. Whitehead  J. Pedlosky 《Dynamics of Atmospheres and Oceans》2000,31(1-4)

Recent laboratory experiments with rotating stratified water in a cylinder have revealed many of the predictions of linearized, analytic theory. Earlier measurements of the velocity field generated in a cylinder by top heating compared well with theory. Large stratification clearly suppressed Ekman pumping so that the interior velocity field (primarily azimuthal) responded by satisfying no-slip top and bottom boundary conditions without the need for Ekman layers. This interior flow also occupied a boundary layer of greater thickness than the Ekman layer under some conditions. Theory and experiments have now been conducted for sidewall heating. As before, experiment and theory agree well over some parameter ranges. But for some parameters, the flow is unstable. The exact nature of the instability remains poorly understood. The size of one combination of both vertical and horizontal boundary layers is governed by the Rossby radius of deformation multiplied by the square root of the Prandtl number. Sidewall boundary layers and their scales will be reviewed with the present results in mind.  相似文献   

Instabilities of the tidally induced bottom boundary layer in the rotating frame and their mixing effect     

K. Sakamoto  K. Akitomo 《Dynamics of Atmospheres and Oceans》2006,41(3-4):191-211

To investigate the stability of the bottom boundary layer induced by tidal flow (oscillating flow) in a rotating frame, numerical experiments have been carried out with a two-dimensional non-hydrostatic model. Under homogeneous conditions three types of instability are found depending on the temporal Rossby number Ro_t, the ratio of the inertial and tidal periods. When Ro_t < 0.9 (subinertial range), the Ekman type I instability occurs because the effect of rotation is dominant though the flow becomes more stable than the steady Ekman flow with increasing Ro_t. When Ro_t > 1.1 (superinertial range), the Stokes layer instability is excited as in the absence of rotation. When 0.9 < Ro_t < 1.1 (near-inertial range), the Ekman type I or type II instability appears as in the steady Ekman layer. Being much thickened (100 m), the boundary layer becomes unstable even if tidal flow is weak (5 cm/s). The large vertical scale enhances the contribution of the Coriolis effect to destabilization, so that the type II instability tends to appear when Ro_t > 1.0. However, when Ro_t < 1.0, the type I instability rather than the type II instability appears because the downward phase change of tidal flow acts to suppress the latter. To evaluate the mixing effect of these instabilities, some experiments have been executed under a weak stratification peculiar to polar oceans (the buoyancy frequency N²  10⁻⁶ s⁻²). Strong mixing occurs in the subinertial and near-inertial ranges such that tracer is well mixed in the boundary layer and an apparent diffusivity there is evaluated at 150–300 cm²/s. This suggests that effective mixing due to these instabilities may play an important role in determining the properties of dense shelf water in the polar regions.  相似文献   

Ekman动量近似下中间边界层模式中的风场结构   总被引：2，自引：0，他引：2  

Tan Zhemin  Wang Yuan 《大气科学进展》2002,19(2):266-278

发展了一个准三维的、中等复杂的边界层动力学模式，该模式包含了EKman动量近似下的惯性加速度和Blackadar的非线性湍流粘性系数，它进一步改进了Tan和Wu(1993）提出的边界层理论模型。该模型在数值计算复杂性上与经典Ekman模式相类似，但由于包含了Ekman动量近似下的惯性项，使得该模式比传统Ekman模式更近于实际过程。中详细地比较了该模式与其他简化边界层模式在动力学上的差异，结果表明：在经典的Ekman模式中，由于忽略了流动的惯性项作用，导致在气旋性切变气流（反气旋性切变气流）中风速和边界层顶部的垂直速度的高估（低估），而在半地转边界层模式中，由于高估了流动惯性项的作用，结果与经典Ekman模式相反。同样，该模式可以应用于斜压边界层，对于Ekman动量下的斜压边界层风场同时具有经典斜压边界层和Ekman动量近似边界层的特征。  相似文献   

The influence of the geostrophic wind advection approximation on a well-mixed layer     

Juan?FangEmail author  Rongsheng?Wu 《Boundary-Layer Meteorology》2005,114(1):31-52

Numerical results indicate that advection of momentum in the boundary layer may significantly alter both the structure of the planetary boundary layer and its influence on the overlying free atmosphere. However, due to the nonlinearity of the inertial terms, it is always difficult to obtain the analytical solution of the boundary-layer model that retains the flow acceleration. In order to overcome this difficulty, the geostrophic momentum (hereafter GM) approximation has been introduced into boundary-layer models. By replacing the advected momentum with the geostrophic wind, the effect of the flow acceleration is partially considered and the original nonlinear partial differential equation set is converted to ordinary differential equations, the solutions of which can be obtained easily with standard techniques. However, the model employing GM fails to capture the features of the boundary layer when the spatio-temporal variation of the boundary-layer flow cannot be properly approximated by the geostrophic wind. In the present work, a modified boundary-layer model with the inertial acceleration in a different approximate form is proposed, in which the advecting wind instead of the advected momentum is approximated by the geostrophic wind (hereafter GAM).Comparing the horizontal velocity and boundary-layer pumping obtained from the classical Ekman theory, and the model incorporating (i) GM and (ii) GAM, it is found that the model with GAM describes most facets of the steady well-mixed layer beneath a north-westerly flow with embedded mesoscale perturbations that is considered in the present work. Inspection of the solution of the model with GAM shows that, within the limit of the validation of the model (i.e., the Rossby number R_O is not very large and the drag coefficient C_D is not too small), the horizontal convergence (divergence) is strengthened by the effect of the inertial acceleration in the region of maximum positive (negative) geostrophic vorticity. Consequently, the boundary-layer pumping there is intensified. It is found that the intensification is firstly strengthened and then weakened as R_O or C_D increases.  相似文献   

Comments about the drag laws used in hail growth simulations     

Nesvit E. Castellano  Olga B. Nasello 《Atmospheric Research》1997,43(4):315-323

The values of the drag coefficient (C_D), experimentally obtained by different authors for graupels and hailstones, are carefully analyzed, in order to investigate how the numerical simulations of hail trajectories, which markedly depend on the C_D values assigned to the growing particle, can be improved. It is found that new measurements of C_D should be performed in the whole range of the Reynolds number (Re) of the cloud ice particles. These measurements should be carried out applying the same criterion to define the characteristic variables (particle cross section and dimensions) used to calculate C_D and Re. Furthermore, it is found that the C_D fitting curves should be expressed as a function not only of Re but also of other parameters which represent the particle surface roughness and the departure from the spherical form. Based on this finding, a plausible definition of these variables and the way to introduce them in a hail trajectory calculation are proposed.  相似文献   

Studies on critical Reynolds number indices for wind-tunnel experiments on flow within urban areas   总被引：2，自引：2，他引：0  

Kiyoshi Uehara  Shinji Wakamatsu  Ryozo Ooka 《Boundary-Layer Meteorology》2003,107(2):353-370

Reynolds-number dependence of flow fields within a modelled urban area was studied in a wind tunnel. We measured flow around a single model building and around model city blocks at various wind speeds, and studied Reynolds number indices more appropriate than the building Reynolds number. Our results led to the following conclusions. Firstly, the flow around the models in the wind tunnel was roughly divided into three parts according to the intensities of viscous stress and Reynolds stress as follows: (1) the flow in the vicinity of the ground or the surfaces of the model, where viscous stress became dominant under certain conditions; (2) the flow detached from the surfaces of the model, where Reynolds stress was always dominant; and (3) the flow around the separation bubble at the leading edge of the building model, where the influences of both viscous stress near the wall and the Reynolds stress in the separated boundary layer were mixed.Secondly, the critical Reynolds number of the flow in the modelled urban area could be defined by using both the roughness Reynolds number Re_z0 (= z₀u_*/) and the dimensionless height z₊ (= zu_*/). Reynolds-number independence could be expected for whole flow fields in the modelled urban areas as long as the critical values of Re_z0 and z₊ were satisfied.  相似文献   

On Reynolds Averaging of Turbulence Time Series   总被引：1，自引：1，他引：0  

George Treviño  Edgar L. Andreas 《Boundary-Layer Meteorology》2008,128(2):303-311

We show that validity of Reynolds averaging for estimating the (ensemble) mean of a turbulence time series requires that the series values be both stationary and uncorrelated. In strict statistical terminology, these two conditions are jointly designated as independent identically distributed (i.i.d.). Moreover, we show that when the series values are correlated, knowledge of the correlation between the values is needed to obtain a reliable estimate of the mean. Last, we contend that a viable averaging algorithm must be Reynolds number (Re) dependent, requiring one version for low Re (Gaussian) turbulence and another for high Re (non-Gaussian) turbulence. Alternatively the median (as opposed to the mean) is recommended as a measure of the central tendency of the turbulence probability density function.  相似文献   

Analysis of Turbulence Collapse in the Stably Stratified Surface Layer Using Direct Numerical Simulation   总被引：1，自引：1，他引：0  

O. Flores  J. J. Riley 《Boundary-Layer Meteorology》2011,139(2):241-259

The nocturnal atmospheric boundary layer (ABL) poses several challenges to standard turbulence and dispersion models, since the stable stratification imposed by the radiative cooling of the ground modifies the flow turbulence in ways that are not yet completely understood. In the present work we perform direct numerical simulation of a turbulent open channel flow with a constant (cooling) heat flux imposed at the ground. This configuration provides a very simplified model for the surface layer at night. As a result of the ground cooling, the Reynolds stresses and the turbulent fluctuations near the ground re-adjust on times of the order of L/u _τ , where L is the Obukhov length scale and u _τ is the friction velocity. For relatively weak cooling turbulence survives, but when Re_L=Lu_t/n <~100{Re_L=Lu_\tau/\nu \lesssim 100} turbulence collapses, a situation that is also observed in the ABL. This criterion, which can be locally measured in the field, is justified in terms of the scale separation between the largest and smallest structures of the dynamic sublayer.  相似文献   

The wind field in the nonlinear multilayer planetary boundary layer     

Xu Yinzi  Zhao Ming 《Boundary-Layer Meteorology》1989,49(3):219-230

By use of the small parameter expansion method, the nonlinear planetary boundary layer (PBL) is studied in this paper. The PBL is divided into the surface layer and the Ekman layer, which is divided into several sublayers. In the surface-layer, the eddy coefficient K is taken as a linear function of height; in the Ekman layer, different constant K values are taken within different sublayers: these values are determined from O'Brien's formula (O'Brien, 1970) approximately. Under the upper and lower boundary conditions and the continuity conditions of the wind velocities and turbulent stresses at each boundary between sublayers, analytical expressions for wind velocity in all sublayers and the vertical velocity at the top of the PBL are obtained. A specific example of steady axisymmetrical circular high and low pressure areas is analysed, and some new conclusions are obtained. The results are in better agreement with reality than previous results. This example also shows that the vertical velocity at the top of the PBL caused by friction approaches zero near the center of a high or low pressure system for this model, but attains its maximum absolute values near the center of the high or low pressure area for Wu's (1984) model. This is due to the fact that in our model, the geostrophic wind speed near the center of this specific vortex approaches zero, which causes the wind shear and the friction effect to be very weak. Therefore the wind distribution in the PBL is very sensitive to the type of eddy coefficient.  相似文献   

A general hydrodynamic theory for mixed-phase microphysics. Part I: drag and fall speed of hydrometeors     

Johannes Peter Bhm 《Atmospheric Research》1992,27(4)

A general parameterization for solid and liquid hydrometeors is presented. hydrometeors basically are viewed as porous spheroids with the following variable parameters: diameter, axial ratio, mass, and porosity. Based on this parameterization a functional dependence on the Reynolds number of the drag of hydrometeors is derived, which is based on boundary layer theory. The basic form of this functional dependence is consistent with viscous theory and the inertial drag at low Reynolds numbers is predicted with good accuracy by matching the results from the boundary layer theory with Oseen's theory of creeping motion. Based on this solution a general semi-empirical expression for the Reynolds number and fall speed of particles is found. The results from the present theory are in remarkable agreement with experiments: The errors generally are < 5–10% for a wide variety of hydrometeors in the range of Reynolds numbers 0<N_Re<5×10⁵, including columnar and variously branched planar ice crystals, rimed and unrimed aggregates, lump, conical, and hexagonal graupel, hail, and rain drops. The present parameterisation aims far beyond the limits of the conventional methods since it is suitable for mixed-phase models of the microphysics of precipitation with continuously varying particle mass and shape characteristics and including processes such as depositional growth of ice crystals under varying environmental conditions, collisional growth of particles, and melting.  相似文献   

Characteristics of helical tip vortices in a wind turbine near wake     

Kapil Varshney 《Theoretical and Applied Climatology》2013,111(3-4):427-435

Helical tip vortices in the wake of a wind turbine have been investigated in this study. To elucidate the near-wake flow field of the wind turbine, the wake has been explored in the Reynolds number (Re) range 1000 ≤?Re?≤?5000 using qualitative dye flow visualization and quantitative digital particle-image velocimetry techniques. Flow visualization showed the dye getting trapped in the shape of spirals surrounding the helical vortex cores. It was found that the helical vortex core size was increasing with downstream distance. It was also found that the normalized stream-wise component of the wake velocity decreased with increasing tip-speed ratios. The results indicate that vorticity peaks at the center of the core and it decays as the vortex moves downstream, showing that the viscous dissipation is active even at length scales of approximately 5 diameters.  相似文献   

A numerical study of the convective boundary layer     

G. N. Coleman  J. H. Ferziger  P. R. Spalart 《Boundary-Layer Meteorology》1994,70(3):247-272

Computations of the buoyantly unstable Ekman layer are performed at low Reynolds number. The turbulent fields are obtained directly by solving the three-dimensional time-dependent Navier-Stokes equations (using the Boussinesq approximation to account for buoyancy effects), and no turbulence model is needed. Two levels of heating are considered, one quite vigorous, the other more moderate. Statistics for the vigorously heated case are found to agree reasonably well with laboratory, field, and large-eddy simulation results, when Deardorff's mixed-layer scaling is used. No indication of large-scale longitudinal roll cells is found in this convection-dominated flow, for which the inversion height to Obukhov length scale ratio –z _i /L _*=26. However, when heating is more moderate (so that –z _i /L _*=2), evidence of coherent rolls is present. About 10% of the total turbulent kinetic energy and turbulent heat flux, and 20% of the Reynolds shear stress, are estimated to be a direct consequence of the observed cells.  相似文献   

An Approximate Analytical Solution For The Baroclinic And Variable Eddy Diffusivity Semi-Geostrophic Ekman Boundary Layer     

Zhe-Min Tan 《Boundary-Layer Meteorology》2001,98(3):361-385

The WKB method has been used to develop an approximate solutionof the semi-geostrophic Ekman boundary layer with height-dependenteddy viscosity and a baroclinic pressure field. The approximate solutionretains the same simple form as the classical Ekman solution. Behavioursof the approximate solution are discussed for different eddy viscosityand the pressure systems. These features show that wind structure inthe semi-geostrophic Ekman boundary layer depends on the interactionbetween the inertial acceleration, variable eddy viscosity and baroclinicpressure gradient. Anticyclonic shear has an acceleration effect on theair motion in the boundary layer, while cyclonic shear has a decelerationeffect. Decreasing pressure gradient with height results in a super-geostrophicpeak in the wind speed profile, however the increasing pressure gradient withheight may remove the peak. Anticyclonic shear and decreasing the variableeddy viscosity with height has an enhanced effect on the peak.Variable eddy viscosity and inertial acceleration has an important role in thedivergence and vorticity in the boundary layer and the vertical motion at the top of the boundary layer that is called Ekman pumping. Compared to the constanteddy viscosity case, the variable eddy diffusivity reduces the absolute value ofEkman pumping, especially in the case of eddy viscosity initially increasing with height. The difference in the Ekman pumping produced by different eddy diffusivity assumptions is intensified in anticyclonic flow and reduced in cyclonic flow.  相似文献   

Wind profile constants in a neutral atmospheric boundary layer over complex terrain   总被引：3，自引：0，他引：3  

William P. Kustas  Wilfried Brutsaert 《Boundary-Layer Meteorology》1986,34(1-2):35-54

The roughness height z ₀ and the zero-plane displacement height d ₀ were determined for a region of complex terrain in the Pre-Alps of Switzerland. This region is characterized by hills of the order of 100 m above the valley elevations, and by distances between ridges of the order of 1 km; it lies about 20 to 30 km north from the Alps. The experimental data were obtained from radiosonde observations under near neutral conditions. The analysis was based on the assumption of a logarithmic profile for the mean horizontal wind existing over one half of the boundary layer. The resulting (z ₀/h) and (d ₀/h) (where h is the mean height of the obstacles) were found to be in reasonable agreement with available relationships in terms of placement density and shape factor of the obstacles, which were obtained in previous experiments with h-scales 2 to 4 orders of magnitude smaller than the present ones.  相似文献