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1.
A new algebraic turbulent length scale model is developed, based on previous one-equation turbulence modelling experience in atmospheric flow and dispersion calculations. The model is applied to the neutral Ekman layer, as well as to fully-developed pipe and channel flows. For the pipe and channel flows examined the present model results can be considered as nearly equivalent to the results obtained using the standard k– model. For the neutral Ekman layer, the model predicts satisfactorily the near-neutral Cabauw friction velocities and a dependence of the drag coefficient versus Rossby number very close to that derived from published (G. N. Coleman) direct numerical simulations. The model underestimates the Cabauw cross-isobaric angles, but to a less degree than the cross-isobar angle versus Rossby dependence derived from the Coleman simulation. Finally, for the Cabauw data, with a geostrophic wind magnitude of 10 ms–1, the model predicts an eddy diffusivity distribution in good agreement with semi-empirical distributions used in current operational practice. 相似文献
2.
The formation of longitudinal vortex rolls in the planetary boundary layer (PBL) is investigated by means of perturbation analysis. The method is the same as that used by previous authors who have investigated the instability of a laminar Ekman layer. To study the instability of the turbulent boundary layer of the atmosphere, vertical profiles are needed of the eddy viscosity and of the two components of the basic flow. These profiles have been obtained by a numerical PBL-model; they are universal for zz
0. (However, the stability equations are not completely universal, i.e., independent of the external parameters). For each thermal stratification, expressed by the internal stratification parameter , one has a set of three consistent profiles.The numerical solution of the stability equations gives the critical values and the perturbation growth rates as functions of thermal stratification and of the surface Rossby number Ro0. This is in contrast to the case of a laminar Ekman layer, where the instability depends on a Reynolds number only, which makes atmospheric applications difficult. The most unstable perturbations are found for Ro0 = 1 × 106 approximately, which is in the range of surface Rossby numbers observed in the atmosphere. However, considering vortex rolls oriented in the direction of the surface stress, the instability is found to be universal, i.e., independent of the external parameters combined in the surface Rossby number. With respect to thermal stratification, the results show that the instability of the perturbations increases with increasing static stability. 相似文献
3.
Richard A. Dobbins 《Boundary-Layer Meteorology》1977,11(1):39-54
Data from low-level soundings over Cambridge, U.S.A. were selected on the basis of an Ekman-like variation of the wind vector with altitude combined with evidence of a barotropic atmosphere. The method of geostrophic departure was used to determine the shear-stress distribution. The analysis yields the dimensionless properties of the barotropic Ekman layer under neutral and stable stratification. Some important results include: the geostrophic drag coefficient displays no dependence on the degree of static stability; the dimensionless height of the boundary layer decreases with increasing stability in agreement with the prediction of Zilitinkevich; the properties of the urban surface layer, where the roughness elements are multistory buildings, show no dependence on atmospheric stability under the moderate wind conditions which display the Ekman-like wind profile; and the directions of the horizontal shear stress and the vertical derivative of the velocity vector usually tend to be parallel only near the surface layer. Values of the two constants of the Rossby number similarity theory are found for the neutral barotropic Ekman layer at a surface Rossby number equal to 2 × 105. The implications of the work with respect to wind-tunnel simulation of the flow over models of urban areas are discussed. 相似文献
4.
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 Rot, the ratio of the inertial and tidal periods. When Rot < 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 Rot. When Rot > 1.1 (superinertial range), the Stokes layer instability is excited as in the absence of rotation. When 0.9 < Rot < 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 Rot > 1.0. However, when Rot < 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
5.
Xiuzhang Zhang Don L. Boyer Gabriel Chabert d'Hires Denis Aelbrecht Henri Didelle 《Dynamics of Atmospheres and Oceans》1993,19(1-4)
Laboratory experiments are conducted on a physical system in which an oscillatory, along-shore, free stream flow of a homogeneous fluid occurs in the vicinity of a long coastline with vertical slope; the model sea-floor is horizontal. Particular attention is given to the resulting rectified (mean) current which is along the coastline with the shore on the right, facing downstream. In the lateral far field region defined by
(1), where y is the offshore coordinate and H is the depth of the fluid, the motion field is approximately independent of the lateral distance from the coast. The vertical structure of the cross-stream motion in this region consists of Ekman layers near the sea-floor and interior adjustment flows, both periodic in time. In the near field, defined by
(1), the motion is strongly dependent on the cross-stream coordinate as well as time, and rectified currents are observed. The mechanism responsible for the rectification is a complex nonlinear coupling between laterally directed adjustment flows driven by the transport in the bottom Ekman layers, and the free stream motion field. The rectified current is found to be substantially wider than the Stewartson layer thickness but much narrower than the Rossby deformation radius. The characteristic width, δy, of the rectified current is shown to scale as
, where Ro is the Rossby number Rot is the temporal Rossby number and E is the Ekman number. Experiments are presented which support this scaling. 相似文献
6.
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. 相似文献
7.
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 RO is not very large and the drag coefficient CD 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 RO or CD increases. 相似文献
8.
R. A. Brown 《Boundary-Layer Meteorology》1978,14(3):381-396
A two-layer, first-order closure model for the Planetary Boundary Layer (PBL) is developed with the objective of parameterizing the surface stress with respect to the synoptic scale. The model includes stability effects by considering stratification-dependent secondary flow in the outer layer and empirical corrections to the surface layer flow. It shows the compatibility of simple eddy viscosity closure solutions with similarity theory by producing the now well-known Rossby similarity equations. It allows further insight into the Rossby similarity parameters by relating them to a single similarity parameter which is the ratio of the characteristic scales of the PBL and the surface layer.The measured and derived values of the similarity parameters A and B are compared with AIDJEX data and other published values. The variation in these values in stably stratified conditions is predicted and two alternate similarity parameters are calculated, one a constant and the other with a small variation and decreasing influence on the drag coefficient in stable stratification. The result is an empirical resistance law for a geostrophic drag coefficient variation which parameterizes an observed order-of-magnitude change in surface stress with changes in roughness or PBL stratification. This variation is related to similarity parameters characteristic of the region and to measurable changes in the geostrophic departure angle. 相似文献
9.
E. Ferrero A. Longhetto L. Briatore G. Chabert d&#x;Hieres H. Didelle C. Giraud P. Gleizon 《Dynamics of Atmospheres and Oceans》2002,35(1):308
A series of laboratory experiments, aimed at the simulation of some aspects of Alpine lee cyclogenesis has been carried out in the rotating tank of the Coriolis Laboratory of LEGI-IMG in Grenoble. Dynamic and thermodynamic processes, typical of baroclinic development triggered by the orography, were simulated. The background flow simulating the basic state of the atmosphere consisted of a stream of intermediate density fluid introduced at the interface between two fluid layers. The structure of the intermediate current was established by mixing fluid obtained from the upper layer of fresh water with fluid removed from the heavier salty layer below.The dynamical similarity parameters are the Rossby (Ro), Burger (Bu) and Ekman (Ek) numbers, although this last, owing to its small values, need not be matched between model and prototype, since viscous effects are not important for small time scales. The flow in both the prototype and laboratory simulation is characterized by hydrostatics; this requires (Ro2δ2/Bu)1 (where δ=H/L is the aspect ratio of the obstacle) which is clearly satisfied, in the atmosphere and oceans, and for the laboratory experiment.A range of experiments for various Rossby and Burger numbers were conducted which delimited the region of parameter space for which background flows akin to that found to the northwest of the Alps prior to baroclinic cyclogenesis events, were observed.One such experiment was carried out by placing a model of the Alps at the appropriate place in the flow field. The subsequent motion in the laboratory was observed and dye tracer motions were used to obtain the approximate particle trajectories. The density field was also analyzed to provide the geopotential field of the simulated atmosphere. Using standard transformations from the similarity analysis, the laboratory observations were related to the prototype atmosphere. The flow and the geopotential fields gave results compatible with the particular atmospheric event presented. 相似文献
10.
Sylvain M. Joffre 《Boundary-Layer Meteorology》1985,32(3):237-255
Substitution of the geostrophic wind by the actual upper wind in the equations of motion for the boundary layer implies less sensitivity of the mean wind to inertial effects. This is confirmed by observations, although the problem of computing time or spatial derivatives from scattered data reduces the accuracy and the clarity of the results. It is found that acceleration (deceleration) increases (decreases) the cross-isobar angle whereas the geostrophic drag coefficient is a minimum (maximum) for crosswind acceleration (deceleration). On the other hand, cold air advection increases the cross-isobar angle whereas the geostrophic drag coefficient is a maximum when the thermal wind is parallel to the surface wind. The universal functions A
m and B
m based on vertically averaged winds are also rather insensitive to inertial influences. 相似文献
11.
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
12.
Data for the cross-isobaric angle 0, the geostrophic drag coefficient Cg, and the functions A and B of Rossby number similarity theory, obtained from meteorological field experiments, are used to evaluate a range of models of the neutral, barotropic planetary boundary layer. The data give well-defined relationships for 0, Cg, and the integrated dissipation rate over the boundary layer, as a function of the surface Rossby number. Lettau's first-order closure mixing-length model gives an excellent fit to the data; other simple models give reasonable agreement. However more sophisticated models, e.g., higher-order closure, large-eddy simulation, direct numerical simulation and laboratory models, give poor fits to the data. The simplemodels have (at least) one free parameter in their turbulence closure that is matched toatmospheric observations; the more sophisticated models either base their closure onmore general flows or have no free closure parameters. It is suggested that all of theatmospheric experiments that we could locate violate the strict simplifying assumptionsof steady, homogeneous, neutral, barotropic flow required by the sophisticated models.The angle 0 is more sensitive to violations of the assumptions than is Cg.The behaviour of the data varies in three latitude regimes. In middle and high latitudes the observed values of A and B exhibit little latitudinal dependence; the best estimates are A = 1.3 and B = 4.4. In lower latitudes the neutral, barotropic Rossby number theory breaks down. The value of B increases towards the Equator; the determination of A is ambiguous – the trend can increase or decrease towards the Equator. Between approximately 5° and 30° latitude, the scatter in the data is thought to be primarily due to the inherent presence of baroclinicity. The presence of the trade-wind inversion, thermal instability and the horizontal component of the Earth's rotation H also contribute.Marked changes in the values of A and B occur in the region between the Equator andapproximately 5° latitude, as the Coriolis parameter |f| approaches zero. Although the variation of A and B with latitude suggests some similarity to the results obtained from the direct numerical simulations, the presence of additional complexities in the real atmosphere that are not included in the numerical model, precludes a meaningful direct comparison. 相似文献
13.
The inertial coupling model of the surface shear stress at the sea surface (Bye, 1995) which takes account of the surface wavefield, has been applied to couple the Ekman layers of the ocean and atmosphere. We determine the surface shear stress and geostrophic drag coefficient, under barotropic conditions. The results are expressed in terms of the shear between the inertially weighted (i.e. velocity×square root of the density) relative geostrophic velocities in the two fluids, in which the reference velocity need not be specified, a priori. We find, in particular, that the deflection of the relative surface geostrophic wind to the surface shear stress in naturally occurring seastates, is about 9°. In the application of the analysis to general circulation models, it is argued that, since the inertially weighted relative geostrophic velocities in air and water are of similar magnitude, this implies that the surface shear stress can be significantly reduced by the current component of the inertially weighted geostrophic shear, with a corresponding reduction in importance of the Ekman transport. 相似文献
14.
Fronts are ubiquitous dynamic processes in the ocean, which play a significant role in the ocean dynamical and ecological environments. In this paper strong temperature fronts are investigated on the shelf of the Northern South China Sea using high resolution satellite data. These fronts have large horizontal gradients exceeding 1 °C km−1 with spatial scales around several kilometers. The fronts generate meanders and eddies due to baroclinic instability, since these instabilities have spatial scales around the local first baroclinic mode deformation radius. The estimated Rossby number of the fronts is O(0.4), suggesting that the fronts tend to be ageostrophic and show submesoscale features. The Finite Size Lyapunov Exponent analysis of the generation mechanism indicates that the fronts are tightly related to the combined flow straining of geostrophic and Ekman currents. 相似文献
15.
Summary The principle of the group-kinetic method is elucidated. This method of renormalization serves as the basis for analyzing the spectral structure of turbulence. The spectral distributions include the Kolmogoroff lawk
–5/3 for isotropic turbulence, the power lawk
–1 for shear turbulence, the spectrum for stratified turbulence not in the power law form, the power lawk
–3 for two-dimensional geostrophic turbulence, and the power lawsk
–3,k
–2 andk
–5 for two-dimensional Rossby wave turbulence with uniform and differential rotations. We discuss a spectrum-dependent modeling in reference to the problems of the universal functions and parameters in the similarity theories for the atmospheric surface layer and the planetary boundary layer. A renormalization-based modeling of atmospheric turbulence is proposed. 相似文献
16.
E. L. Deacon 《Boundary-Layer Meteorology》1973,5(3):321-340
Data on the relationship of the surface wind to the geostrophic wind at Porton Down, Salisbury Plain, are presented for various
stability conditions and analysed in the light of the Rossbynumber similarity theory. For near-neutral conditions, the geostrophic
drag coefficients for geostrophic wind speeds 5 to 15 m s-1 are close to those found by other workers but at higher speeds the values are low. Comparisons of geostrophic and radar wind
speeds for ⋍900-m height, suggest that undetectably small mean cyclonic curvatures of the trajectories of the air are responsible
for this departure.
A value of the geostrophic drag coefficient for the open sea at wind speeds around 8 m s-1 (neutral conditions) is deduced from recent observations of the drag in relation to the surface wind, combined with the ratios
of 900-mb radar wind to surface wind obtained from the North Atlantic weather ship data tabulations of Findlater et al. (1966). 相似文献
17.
The flow of water over a regular array of hills in a rotating laboratory experiment is studied as an analogue of planetary boundary layers. Gaussian-shaped hills of heighth = 1 cm andh = 1/3 cm covered the floor of a 228 cm diam rotating tank. The characteristic depth of the Ekman layer varied fromD = 0.1 cm toD = 0.3 cm and the Reynolds number for the Ekman layer varied up toRe = 150. The integrated boundary-layer stress as a function ofRe andD/h was determined by the rate of spin-up of the water after a small increase of the rotation rate.Selected functional relations were fitted to the empirical data by the method of least squares for the laminar and turbulent regimes of flow. These results indicate maximum non-linear effects of the hills and a minimum transition Reynolds number nearD/h = 0.2. The patterns of flow as indicated by dye tracers are briefly discussed. Peculiar circular bands of dye appear to be caused by the selective ejection of dye from the boundary layer when the circular flow is at a particular angle of incidence with respect to the triangular pattern of hills.The research reported herein was supported in part by the National Science Foundation under Grant NSF GA 4388. 相似文献
18.
Geostrophic drag coefficients are obtained from direct measurements of the momentum flux and from an objective analysis of the synoptic pressure field by the method of least squares. At a site in the Kiel Bight, a mean geostrophic drag coefficient c
g
= 0.0223 was obtained with near neutral/ slightly unstable conditions and a surface Rossby Number of 1.2 × 109.Contribution of the sonderforschungsbereich Meeresforschung Hamburg der Deutschen Forschungsgemeinschaft, Hamburg, F.R.G. 相似文献
19.
The steady-state, horizontally homogeneous, neutral, barotropiccase forms the foundation of our theoretical understanding of the planetary boundary layer (PBL).While simple analytical models and first-order closure models simulate atmospheric observationsof this case well, more sophisticated models, in general, do not. In this paperwe examine how well three higher-order closure models, E - - l, E - l, and LRR - l,which have been especially modified for PBL applications, perform in predicting the behaviour of thecross-isobaric angle 0, the geostrophic drag coefficient Cg, and the integral of the dissipationrate over the boundary layer, as a function of the surface Rossby number Ro. For comparison we alsoexamine the performance of three first-order closure mixing-length models, two proposed byA. K. Blackadar and one by H. H. Lettau, and the performance of the standard model forsecond-order closure and a modification of it designed to reduce the overprediction of turbulence inthe upper part of the boundary layer. 相似文献
20.
The turning of wind with height and the related cross-isobaric (ageostrophic) flow in the thermally stable stratified boundary
layer is analysed from a variety of model results acquired in the first Global Energy and Water Cycle Experiment (GEWEX) Atmospheric
Boundary Layer Study (GABLS1). From the governing equations in this particular simple case it becomes clear that the cross-isobaric
flow is solely determined by the surface turbulent stress in the direction of the geostrophic wind for the quasi-steady state
conditions under consideration. Most models indeed seem to approach this relationship but for very different absolute values.
Because turbulence closures used in operational models typically tend to give too deep a boundary layer, the integrated total
cross-isobaric mass flux is up to three times that given by research numerical models and large-eddy simulation. In addition,
the angle between the surface and the geostrophic wind is typically too low, which has important implications for the representation
of the larger-scale flow. It appears that some models provide inconsistent results for the surface angle and the momentum
flux profile, and when the results from these models are removed from the analysis, the remaining ten models do show a unique
relationship between the boundary-layer depth and the surface angle, consistent with the theory given. The present results
also imply that it is beneficial to locate the first model level rather close to the surface for a proper representation of
the turning of wind with height in the stable boundary layer. 相似文献