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

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.     

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

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.     

Topographic and stratification effects on shelf edge flows

Results are presented from two sets of laboratory model experiments on the effects of an isolated seamount upon the flow of an intermediate-water slope current along a continental shelf. The experimental results for initial ambient conditions of respectively two-layer and linearly stratified fluids show that the structure of such a boundary current depends primarily on the values of the appropriate set of dimensionless dynamical parameters (namely the Burger (Bu), Ekman (Ek) and Rossby (Ro) numbers), as well as the dimensionless lateral separation of the seamount and shelf and the proportional height of the seamount relative to the distance from the bottom at which the intermediate-water flows. Comparisons of the present results with those from a previous two-layer fluid study with no obstacle present reveals that the presence of the obstacle does not alter significantly the stability of the current even when situated close to the shelf. However, for such configurations, the density, velocity and vorticity fields in the local zone of interaction between the current and the obstacle are distorted significantly by the presence of the obstacle, provided that the summit of the obstacle penetrates the level of current flow. Measurements of density, velocity and vorticity fields show no significant dependence of the flow interaction upon the detailed bathymetry of the shelf-slope. For stable intermediate-water slope currents, the nature of the interaction with the obstacle is determined primarily by (i) the lateral separation of the obstacle and the shelf edge and (ii) the Ro of the flow. For sufficiently low values of the former and high values of the latter, the interaction results in a splitting of the incident flow around the obstacle, with cyclonic and anticyclonic eddy pairs being generated in the lee. Geostrophic equilibrium is seen to be maintained in the current, even in the near wake of the obstacle. For cases in which the summit of the seamount is below the initially-undisturbed intermediate water level, no Taylor column-like division of the slope current occurs and no significant distortion of the current structure (velocity and density) occurs for the parameter ranges investigated. For linearly stratified cases, measurements show that no significant local elevation or depression of the density interfaces is observed in the interaction zone. The distributions of the local buoyancy frequencies calculated from the density profiles reveal that the minimum value of the frequency upstream of the obstacle is smaller than that downstream, indicating that the flow interactions generate local mixing downstream, with consequent erosion of the density interfaces.     

On the instability of a planetary boundary layer with Rossby-number similarity

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.     

ALPEX-Simulation

Summary In a project ALPEX-Simulation, sponsored by the Österreichischer Fond zur Förderung der wissenschaftlichen Forschung (FWF), all eight cases of ALPEX-SOP cyclones were numerically simulated with a fine mesh isentropic model of the atmosphere. These numerical simulations in six-hourly intervals allow a deeper insight into the synoptics and dynamics of the cyclogeneses in the Western Mediterranean, especially into the genesis of the two basic types of cyclones: the so-called Überströmungs-type and Vorderseiten-type. In the first phase of cyclogenesis of the Überströmungs-type, the blocking and flow splitting of the cold air due to the Alps and the canalization between the Alps and the Massif Central are important. Cold air flows cyclonically around the western part of the Alps, creating a vorticity maximum at the south western edge of the Alpine, bow and leads also to an enhanced PV. In connection with warm air in the Mediterranean, a strong baroclinic zone is generated. The interaction between the arriving PV maximum in the upper troposphere and the enhanced PV at the bottom leads to cyclogenesis in the Western Mediterranean. In the case of the Vorderseiten-type warm air advection dominates with the exception of a shallow layer of cold air in the inner Po-Valley, which is shielded by the Alpine ridge. A well-pronounced PV maximum builds up and couples with the PV maximum arriving at upper levels, even before the cold air, coming from the north-west, has surrounded the Alps. The cold air only intensifies the development by raising the baroclinity. Therefore, the Vorderseiten-cyclogenesis is an orographically modified cyclogenesis, in the course of which the cyclonic development is triggered by the Alps, whereas the Überströmungs-cyclogenesis is an orographically induced cyclogenesis i.e. a true lee cyclogenesis.With 14 FiguresDied in a tragic traffic accident on June 6, 1993.     

Synoptic diagnosis of frontogenetic and cyclogenetic processes

Summary In the paper it is shown that theQ-vector defined by Hoskins et al. is a suitable aid for the diagnosis of frontogenetic and cyclogenetic processes. It allows a direct estimation of frontogenetic (or frontolytic) effects within the geostrophic wind field and of the macro-scale forcing of vertical motions. A partitioning of the forcing is possible into one part depending on divergences along the frontal zone and working in short baroclinic waves, and another part connected with frontogenesis (or frontolysis) and causing circulatory motions around the frontal zone. Thus the intercorrelation between both processes can be easily studied.With the described cases it is demonstrated that frontogenetic circulations often lead to the first stages of cyclogenesis but that a further forcing of ascent predominantly ahead of an upper trough is necessary for a deepening of the low. Also during the mature and occlusion stage of cyclogenesis and within the downstream development of baroclinic waves frontogenetic (or frontolytic) circulations play an important role in the regime of vertical motions.With 11 Figures     

A Quantitative Method of Detecting Transient Rossby Wave Phase Speed: No Evidence of Slowing Down with Global Warming

Based on the Complex Empirical Orthogonal Functions(CEOFs) of bandpass-filtered daily streamfunction fields, a quantitative method of detecting transient(synoptic) Rossby wave phase speed(RWPhS) is presented. The transient RWPhS can be objectively calculated by the distance between a high(or low) center in the real part of a CEOF mode and its counterpart in the imaginary part of the same CEOF mode divided by the time span between two adjacent peaks(or bottoms) of two principal component curves f...     

A fluid experiment of large-scale topography effect on baroclinic wave flows

The effects of topography on baroclinic wave flows are studied experimentally in a thermally driven rotating annulus of fluid.Fourier analysis and complex principal component (CPC) analysis of the experimental data show that, due to topographic forcing, the flow is bimodal rather than a single mode. Under suitable imposed experimental parameters, near thermal Rossby number ROT = 0.1 and Taylor number Ta = 2.2 × 107, the large-scale topography produces low-frequency oscillation in the flow and rather long-lived flow pattern resembling blocking in the atmospheric cir-culation. The ‘blocking’ phenomenon is caused by the resonance of travelling waves and the quasi-stationary waves forced by topography.The large-scale topography transforms wavenumber-homogeneous flows into wavenumber-dispersed flows, and the dispersed flows possess lower wavenumbers.     

The temporal evolution of a geostrophic flow in a rotating stratified basin

A laboratory study in a rotating stratified basin examines the instability and long time evolution of the geostrophic double gyre introduced by the baroclinic adjustment to an initial basin-scale step height discontinuity in the density interface of a two-layer fluid. The dimensionless parameters that are important in determining the observed response are the Burger number S=R/R₀ (where R is the baroclinic Rossby radius of deformation and R₀ is the basin radius) and the initial forcing amplitude (H₁ is the upper layer depth). Experimental observations and a numerical approach, using contour dynamics, are used to identify the mechanisms that result in the dominance of nonlinear behaviour in the long time evolution, τ>2⁻¹ (where τ is time scaled by the inertial period T_I=2π/f). When the influence of rotation is moderate (0.25≤S≤1), the instability mechanism is associated with the finite amplitude potential vorticity (PV) perturbation introduced when the double gyre is established. On the other hand, when the influence of rotation is strong (S≤0.1), baroclinic instability contributes to the nonlinear behaviour. Regardless of the mechanism, nonlinearity acts to transfer energy from the geostrophic double gyre to smaller scales associated with an eddy field. In the lower layer, Ekman damping is pronounced, resulting in the dissipation of the eddy field after only 40T_I. In the upper layer, where dissipative effects are weak, the eddy field evolves until it reaches a symmetric distribution of potential vorticity within the domain consisting of cyclonic and anticyclonic eddy pairs, after approximately 100T_I. The functional dependence of the characteristic eddy lengthscale L_E on S is consistent with previous laboratory studies on continuously forced geostrophic turbulence. The cyclonic and anticyclonic eddy pairs are maintained until viscous effects eventually dissipate all motion in the upper layer after approximately 800T_I. The outcomes of this study are considered in terms of their contribution to the understanding of the energy pathways and transport processes associated with basin-scale motions in large stratified lakes.     

Rectified flow along a vertical coastline

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, δ_y, of the rectified current is shown to scale as , where Ro is the Rossby number Ro_t is the temporal Rossby number and E is the Ekman number. Experiments are presented which support this scaling.     

Density fronts in the vicinity of a long ridge

Laboratory experiments concerning the nature of density fronts in a two-layer fluid in the vicinity of a continuous ridge were conducted. The experiments were carried out in a circular rotating test cell containing an annular ridge of uniform cross-section. The density fronts were established by releasing a lighter fluid contained in a bottomless cylinder in the interior of the region defined by the topography into a heavier fluid occupying the rest of the test cell. The system was also equipped with an oscillating plunger located along the test cell axis to produce simulated tidal currents impinging in the normal direction on the ridge; experiments without and with tidal forcing were conducted. The governing parameters for the physical system considered are the Rossby, temporal Rossby, Burger and Ekman numbers and geometrical parameters. It is found that for both the non-forced and tidally forced experiments the fronts were stabilized by the ridge. The fronts in the simulated tidal currents experiments were found to advect radially outward more rapidly at early times than their non-forced counterparts; at large times, the temporal evolution of the front for these forced experiments approached that of the non-forced experiments. In the region interior to the annular ridge, the motion field is highly baroclinic, while outside this region, the flow response at the forcing frequency is barotropic. Scaling arguments regarding frontal position, viscous decay and barotropic oscillatory flow responses are advanced and supported by experimental observations.     

Diagnosis of mesoscale structures in cases of lee cyclogenesis during ALPEX

Summary Several cases of lee cyclogenesis that occurred during ALPEX-SOP have been analyzed, with the aim of separating the large scale structures from the subsynoptic/meso-a scale features that are characteristic of this meteorological phenomenon. The results presented here are mainly based on composites of the analyzed cases. We assume that the deformation caused by the orography can be, at least to a reasonable extent, isolated from the undisturbed state using scale separation. The analysis technique we employ provides the scale separation as built-in in the interpolation algorithm. The scale separation error due to the large inhomogeneities of the data density distribution is partly corrected using a method described in the text. The orographic disturbance appears in different mesoscale fields as a quasiantisymmetric dipolar structure. For example, high/low pressure, cold/warm temperature and anticyclonic/cyclonic couplets characterize the mesoscale fields near the Alps. A qualitative agreement is found with the structure of the orographically induced perturbations predicted by the normal mode theory of lee cyclogenesis.With 7 Figures     

A mechanism of Alpine lee cyclogenesis as revealed by a quasigeostrophic variational filter

Summary Mechanisms associated with Alpine lee cyclogenesis during the early phase of their generation are investigated using a variational quasigeostrophic filter technique. It was possible to extract the quasigeostrophic signal from the available analyzed real data set.The results presented here are for the 11–12 March 1982, an example of so-called orographically induced lee cyclogenesis. Non-quasigeostrophic fields, calculated as a difference between observations and the quasigeostrophic fields, show significant magnitudes indicating the possible importance of non-quasigeostrophic processes. A dipole structure in the residual geopotential field was observed, similar to the results of numerical model experiments. Also, a strong upper-level non-quasigeostrophic divergence was found in the Alpine region 24 hours prior to lee cyclogenesis, lasting for 6–12 hours. On the other hand, quasigeostrophic results indicate only a local effect of mountain slopes, suggesting possibly a dominant role of the low-level blocking. A hypothetical scenario of Alpine lee cyclogenesis is proposed, based on results obtained here.With 14 Figures     

Some Effects of Rotation Rate on Planetary-Scale Wave Flows

A series of experiments were performed in a rotating annulus of fluid to study effects of rotation rate on planeta-ry-scale baroclinic wave flows. The experiments reveal that change in rotation rate of fluid container causes variation in Rossby number and Taylor number in flows and leads to change in flow patterns and in phase and amplitude of quasi-stationary waves. For instance, with increasing rotation rate, amplitude of quasi-stationary waves increases and phase shifts upstream. On the contrary, with decreasing rotation rate, amplitude of quasi-stationary waves decreases and phase shifts downstream. In the case of the earth’s atmosphere, although magnitude of variation in earth’s rotation rate is very small, yet it causes a very big change in zonal velocity component of wind in the atmosphere and of currents in the ocean, and therefore causes a remarkable change in Rossby number and Taylor number deter-mining regimes in planetary-scale geophysical flows. The observation reveals that intensity and geographic location of subtropic anticyclones in both of the Northern and Southern Hemispheres change consistently with the variation in earth’s rotation rale. The results of fluid experiments are consistent, qualitatively, with observed phenomena in the atmospheric circulation.     

One-Equation Turbulence Modelling for Atmospheric and Engineering Applications

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.     

Some effects of rotation rate on planetary — scale wave flows

Summary A series of experiments was performed in a rotating annulus of fluid to study effects of rotation rate on planetary-scale baroclinic wave flows. The experiments reveal that change in rotation rate of fluid container causes variation in Rossby number and Taylor number in flows and leads to change in flow patterns and in phase and amplitude of quasi-stationary Waves. For instance, with increasing rotation rate, amplitude of quasi-stationary waves increases and phase shifts upstream. On the contrary, with decreasing rotation rate, amplitude of quasi-stationary waves decreases and phase shifts downstream. In the case of the earth's atmosphere, although magnitude of variation in earth's rotation rate is very small, yet it causes a very big change in zonal velocity component of wind in the atmosphere and of currents in the ocean, and therefore causes a remarkable change in Rossby number and Taylor number determining regimes in planetary-scale geophysical flows. The observation reveals that intensity and geographic location of subtropic anticyclones in both of the Northern and Southern Hemispheres change consistently with variation in earth's rotation rate. The results of fluid experiments are consistent, qualitatively, with observed phenomena in the atmospheric circulation.With 12 Figures     

Modeling the evolution of the family of Mediterranean cyclones using the regional model of the atmosphere

Due to the complex orography and the presence of the moisture-saturated air, the Mediterranean region is characterized by the increased baroclinic and convective instability, that leads to the sudden cyclogenesis and the formation of dangerous weather phenomena. The results are given of the investigation of formation mechanisms of Mediterranean cyclones, peculiarities of stages of their evolution and dynamical processes, which occur throughout the atmosphere, using the regional numerical ETA model of the atmosphere by the example of individual cases of the cyclogenesis over the Mediterranean Sea. It is revealed that the cold Arctic air outbreak (the intrusion of the cold Arctic air) to the south of the Western Europe, leading to the formation of the areas of the baroclinic instability and the increased moisture content of the air in the area of the vortex origin, favors the cyclogenesis. The use of the vertical coordinate η in the model enabled to compute more precisely the vertical wind speed, therefore, the influence of the orography on the moisture content and precipitation increase became pronounced. The transformation of the structure of meteorological fields in the course of the development of vortexes is considered. The computation of the helicity is made, and it is shown that this characteristic can be one of the earliest predictors of cyclogenesis.     

1991年江淮梅雨暴雨与亚洲季风的关系

利用实际大气参数取值进行尺度分析，求得斜压半地转模式中非线性斜压Ｒｏｓｓｂｙ波的非频散周期解的存在条件与解。给出了能够描述非线性特性波动的无量纲拟能效ε，由此推导了非线性特征波动的波速公式及波参数间的一些诊断关系。     

Submesoscale fronts observed by satellites over the Northern South China Sea shelf

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.