The long-time decay of rotating homogeneous flows over variable topography

The long-time decay of rotating, homogeneous flows over variable topography is analyzed by means of laboratory experiments and numerical simulations. The influence of the topography on the flow evolution is associated with stretching and squeezing effects on fluid columns as they experience changes in depth, and with viscous effects produced by the boundary condition at the solid bottom of the tank. In particular, experiments with a sine-shaped topography in one of the horizontal directions are analyzed by using two different basic flows. First, the evolution of dipolar vortices drifting across the topography while slowly decaying, is examined. The second set of experiments considers the evolution and decay of an initially circular vortex transforming into a tripolar structure. The experiments are well represented by numerical simulations based on a quasi-two-dimensional formulation with variable topography.     

Laboratory experiments on along-slope flows in homogeneous and stratified rotating fluids

Laboratory experiments have been carried out for the flow along isobaths of simulated shelf-continental slope geometry. Cases of both homogeneous and linearly stratified fluids are considered and the background flows are sufficiently strong to have the flow near the bottom boundary range from transitional to fully turbulent. The background motions are impulsively started and flows with a coast on the right (spin-down) and on the left (spin-up) are considered. The homogeneous spin-down and spin-up processes are smooth in the sense that no vortical structures were found to be of the order of the slope width or larger. Flows reach equilibrium more quickly for spin-down cases, and this is attributed to secondary flows forced by the basin geometry. All of the stratified experiments exhibited large-scale instabilities as evidenced by the generation of slope and basin scale eddy structures and a much slower decay than their homogeneous counterparts.     

Experiments with density currents on a sloping bottom in a rotating fluid

The behaviour of a density current on a sloping bottom in a rotating system is investigated by laboratory experiments. The main result is that the dense bottom outflow induces cyclonic vortices in the upper fluid layer, which are formed periodically and move to the west parallel to coast. Two regimes of vortex formation have been identified. For strong density currents and weak rotation, vortices are formed by stretching of the upper layer near the source as found also in the experiments by Lane-Serff and Baines (1998) [Lane-Serff, G.F., Baines, P.G., 1998. Eddy formation by dense flows on slopes in a rotating fluid. J. Fluid Mech. 363, 229–253]. For weak density currents and strong rotation vortices are due to instability of the bottom plume itself as found in the numerical simulations of Jiang and Garwood (1996) [Jiang, L., Garwood, W. Jr., 1996. Three-dimensional simulations of overflows on continental slopes. J. Phys. Oceanogr. 26, 1224–1233].     

Laboratory studies of the effects of interrupted, sloping topography on intermediate depth boundary currents in linearly stratified fluids

Laboratory experiments are described which provide insight into the interaction of intermediate depth boundary currents (IDBCs) with interrupted sloping topography. Specifically, they contribute to the debate over meddy formation on the Iberian continental slope. The experiments were performed in a rectilinear rotating tank filled initially with a linearly-stratified fluid. A false bottom sloped away from the side-wall along which the current flowed, and was interrupted by a gap of variable length. The effects of varying gap length and rotation rate on the boundary current were observed.In the first of two sets of experiments, the current flowed above the slope, along the vertical sidewall. In the second, the current flowed along the sloping bottom. In the former, current nose speed was consistent with geostrophic predictions, but decreased in the presence of a gap in the topography. Kelvin wave radiation is postulated as a reason for this. The IDBCs exhibited vortical lateral intrusions at values of the Burger number Bu=(N₀/Ω)² at which counterpart flat-bottom studies had been stable, implying that the sloping topography had a de-stabilising effect. Energy measurements and qualitative observations suggest the intrusions were due to mixed barotropic/baroclinic instabilities, the latter dominating at higher rotation rates.In the second configuration, four distinct flows were observed, distinguished by the deformation radius:gap width ratio R_D/G^*. For a range of values of R_D/G^*, attached eddies formed at the upstream end of the gap. They remained at this position, unlike those in similar studies of surface boundary currents (Klinger, 1993). Their persistence and ability to move downstream – salient factors for meddy – formation were greater for a finite gap size than a permanent change from sloping to flat bottom.     

Interaction between an eddy and a zonal jet : Part II. Two-and-a-half-layer model

In a two-and-a-half-layer quasi-geostrophic model, a process study is conducted on the interaction between a vortex and a zonal jet, both with constant potential vorticity. The vortex is a stable anticyclone, initially located north of the eastward jet. The potential vorticity of the jet is allowed to have various vertical structures, while the vortex is concentrated in only one layer. The flow parameters are set to values characteristic of the Azores region.First, the jet is stable. Weak vortices steadily drift north of the jet without crossing it while strong vortices can cross the jet and tear off a cyclone with which they pair as a heton (baroclinic dipole). This heton often breaks later in the shear exerted by the jet; the two vortices finally drift apart. When crossed by deep anticyclones, the jet develops meanders with 375 km wavelength. These results exhibit a noticeable similarity with the one-and-a-half-layer case studied in Part I.Secondly, the jet is allowed to be linearly unstable. In the absence of the vortex, it develops meanders with 175 km wavelength and 25-day e-folding time on the β-plane. For various vertical structures of the jet, baroclinic instability is shown to barely affect jet–vortex interaction if the linear growth rate of unstable waves is smaller than 1/(14 days). Further simulations with a linearly unstable, nonlinearly equilibrated jet evidence its strong temporal variability when crossed by a deep vortex on the β-plane. In particular, long waves can dominate the spectrum for a few months after jet crossing by the vortex. Again in this process, the deep vortex couples with a surface cyclone and both drift southwestward.     

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.     

Numerical modeling of flow characteristics in a rotating annular flume

A rotating annular flume (RALF) has been constructed at the Center of Coastal and Land-Margin Research (CCALMR) to study the biogeochemistry of sediment–water interfaces. The flume was designed to allow for evolving, integrated measurements of physical, chemical, and biological parameters, as often as possible in a real-time, computer-controlled mode. Several numerical models have or are being developed/applied to provide a virtual representation of the flume, with the dual objective of assisting the design of experiments and of assessing our level of understanding of processes and process interactions. We will concentrate here on the characterization of the flow in the flume, a basic but interestingly complex problem. The operational challenge is to minimize secondary circulation and lateral variability of shear stress, factors that prevent the flume flow to match the idealized concept of an endless channel flow. Satisfactory minimization of these factors can be achieved by allowing both the top and the bottom rings of the flume to rotate in contrary directions, a concept introduced by earlier research efforts and verified in RALF via Acoustic Doppler Velocimeter (ADV) measurements and 3D numerical modeling. Once logistics (e.g., in the form of the size of the ADV's sampling volume and of the vertical discretization of the numerical grids) are appropriately handled, observations and model results show good agreement. This agreement legitimates the use of the model as a design and investigative tool, in particular to define optimal rotation ratios of the top and bottom rings. The ratios that minimize secondary flow and lateral variability of shear stress are distinct. This is a logical (generating mechanisms are different) but often not recognized aspect of the operation of annular flumes.     

Rossby waves in a rotating fluid of spheroidal configuration

The ray method is used to study quasi-geostrophic waves in a thin layer of incompressible, inviscid fluid of constant density both in a rotating spheroidal shell and on a rotating spheroid bounded above by a free surface. Asymptotic approximations to solutions of both the time-dependent and time-reduced problems are found; the dispersion relation obtained has the form of the Rossby-Haurwitz formula when the shell is spherical, and is asymptotically equivalent to that found by Longuet-Higgins (1965) for the free surface problem on a sphere. The approximation is first applied to free oscillations in a rotating spherical shell and Longuet-Higgins' (1964) results are rederived. Spheroidal shells in which the shell thickness depends only upon the latitude are studied next and a necessary and sufficient condition for oscillations to occur is obtained.     

Measurements in a turbulent patch in a rotating,linearly-stratified fluid

A series of experiments is described in which a turbulent patch is generated locally by an oscillating grid positioned at one end and mid-depth of a rotating channel filled initially with a linearly-stratified fluid. Measurements have been made of vertical density profiles through the patch both during sustained oscillations and following cessation of grid forcing. Temporal variations in patch size and structure, Thorpe scales, mixedness parameter and available potential energy are deduced from these measurements, and the effects thereon of varying the background rotation rate, initial buoyancy frequency and grid action are investigated. For the growth phase of the patch, previous results obtained by other workers are confirmed and extended. Because the rapid turbulent motions implied a large Rossby number, rotation was not important during this phase. During the decay phase, rotational effects are shown to become important, and the presence of rotation is found to retard the decay of both the mixedness and the Thorpe scales of the density overturns within the patch. The work is novel in that measurements of the patch parameters listed above have not previously been carried out in the presence of rotation. The results are relevant to studies of such patches that have been observed in the ocean and atmosphere.     

Weakly non-linear Rossby waves in a rotating fluid of spheriodal configuration

A modified ray method is used to study weakly non-linear Rossby waves in a thin layer of incompressible inviscid fluid of constant density both in a rotating spheroidal shell and on a rotating spheroid bounded above by a free surface. This method yields the same dispersion relation and conservation law as in the linear case (London) but gives an equation for a new, second order mean term. This mean term is shown to be unstable for all free oscillations on any axisymmetric bottom topography in the free surface problem. This contrasts with the analogous problem on the Beta-plane where the corresponding mean term is stable.     

Wind Measurements in a Square Plot Enclosed by a Shelter Fence

Wind statistics were measured within a square plot (sidelengthD = 20 m) that was sheltered on all four sides by a porous plasticwindbreak fence (height h=1.25 m, resistance coefficient k_r0 = 2.4, porosity p = 0.45), standing on otherwise uniform land (sparse stubble, roughness length z₀ 0.015 m). At any given point within the plot, short term wind statistics were extremely sensitive to the mean wind direction relative to thefences. Whereas the entire plot was sheltered from a wind blowingnormal to any side of the plot, whenever the wind was oriented soas to blow over a corner, wind reduction was observed onlyover a small fraction of the plot, in the near lee of the upwindfences.     

Onset of convection in a rotating semi‐infinite fluid: Theory and experiment

Abstract

We look at the development of the first plumes that emerge from a convectively unstable boundary layer by modelling the process as the instability of a fluid with a time‐dependent mean density field. The fluid is semi‐infinite, rotating, dissipative ‐ characterized by the ratio of its viscosity to thermal diffusivity (Prandtl number Pr = ν/κ) ‐ and initially homogeneous. A constant destabilizing heat flux is applied at the boundary and the stability of the evolving density field is investigated both mathematically and in laboratory experiments.

Using a “natural convective” scaling, we show that the behaviour of the non‐dimensional governing equations depends on Pr and the parameter γ = f(ν/B)^1/2, where f is the Coriolis parameter, and B is the applied buoyancy flux. For the ocean, γ ≈ 0.1, whilst for the atmosphere γ ≈ 0.01. In the absence of rotation, the behaviour of the differential equations is independent of B, depending only on Pr. The boundary‐layer Rayleigh number (Ra_bl) is also independent of B. We show that Ra_bl, evaluated at the onset of rapid vertical motion, depends on the form of the perturbation.

Due to the time‐dependence of the mean density field, analytic instability analysis is difficult, so we use a numerical technique. The governing equations are transformed to a stretched vertical coordinate and their stability investigated for a particular form of perturbation function. The model predictions are, for the ocean: instability time ～2–4 h, density difference ～0.002–0.013 kg m^‐3, boundary‐layer thickness ～50–75 m and horizontal scale ～200–300 m; and for the atmosphere: instability time ～10 min, temperature difference ～2.0–3.0°C, boundary‐layer thickness ～400–500 m and horizontal scale ～1.5–2.0 km.

Laboratory experiments are performed to compare with the numerical predictions. The time development of the mean field closely matches the assumed analytic form. Furthermore, the model predictions of the instability timescale agree well with the laboratory measurements. This supports the other predictions of the model, such as the lengthscales and buoyancy anomaly.     

2013年“苏力”台风西行登陆引发闽南大暴雨成因的模拟研究

利用中尺度数值模式对2013 年7 月13~14 日“苏力”台风引发福建南部大暴雨的天气过程进行了数值模拟、诊断分析和敏感性试验。结果发现：台风环流内强的正差动涡度平流和强的低层暖平流叠置是台风对流暴雨形成的有利大尺度强迫环境。台风登陆后移动旋转过程中,其风场、假相当位温场（θ_se）、水汽场、对流有效位能（CAPE）、对流不稳定度的空间结构及其正相对涡度、辐合区随着台风旋转在不断发生变化,台风环流内高θ_se 和高比湿气团的影响、带有CAPE 气流的输入、低层气流汇合或风速辐合、对流不稳定以及局地地形强迫等共同作用是闽南大暴雨发生的主要原因,强降水区主要位于环境风垂直切变的下游和左侧。此西移经台湾北侧的台风个例中,台湾地形可能主要通过改变台风环流内降水及其非绝热加热分布,进而影响台风的结构和移动路径,最终影响台风暴雨的强度和落区。闽南局地地形在台风大暴雨的形成中起到了一定的增幅作用,海陆摩擦差异造成的风速辐合在台风移近到登陆阶段对台风北侧偏东气流内降水具有不可忽视的增幅作用。     

Circulation and boundary layers in differentially heated rotating stratified fluid

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.     

Air–sea interaction over ocean fronts and eddies

Air–sea interaction at ocean fronts and eddies exhibits positive correlation between sea surface temperature (SST), wind speed, and heat fluxes out of the ocean, indicating that the ocean is forcing the atmosphere. This contrasts with larger scale climate modes where the negative correlations suggest that the atmosphere is driving the system. This paper examines the physical processes that lie behind the interaction of sharp SST gradients and the overlying marine atmospheric boundary layer and deeper atmosphere, using high resolution satellite data, field data and numerical models. The importance of different physical mechanisms of atmospheric response to SST gradients, such as the effect of surface stability variations on momentum transfer, pressure gradients, secondary circulations and cloud cover will be assessed. The atmospheric response is known to create small-scale wind stress curl and divergence anomalies, and a discussion of the feedback of these features onto the ocean will also be presented. These processes will be compared and contrasted for different regions such as the Equatorial Front in the Eastern Pacific, and oceanic fronts in mid-latitudes such as the Gulf Stream, Kuroshio, and Agulhas Return Current.     

Wave/wave interaction producing horizontal mean flows in stably stratified fluids

We show that internal wave/wave interactions in stratified fluids are able to produce strong horizontal mean currents. A simple analytical model allows us to estimate the amplitude of the time-periodic horizontal mean flow induced by the interaction of two monochromatic waves. This model shows that in some cases, the mean flow velocity can overgo a threshold beyond which critical layers and intense energy transfers from the waves to the mean flow are expected. This prediction is confirmed by direct pseudo-spectral simulations of the Navier–Stokes equations under the Boussinesq approximation. Such interactions may help to further understand the presence of strong vertical shear observed in the final stage of stratified flows in oceans and atmospheres.     

北方一次强降雪过程的中尺度数值模拟

利用中尺度数值模式MM5对2003年3月14~16日发生在内蒙古中部偏南地区的一次强降雪过程进行了二重嵌套的48 h数值模拟研究。结果表明:模式较好地模拟了本次过程强降雪中心的强度、位置以及强降雪的时间变化。导致本次过程降雪产生的主要影响系统是地面倒槽和700 hPa中α尺度低涡,其影响时间相对持久。强降雪的出现则是由于高空短波槽产生的高层强辐散强迫与低层增强的辐合相互耦合所致。高低层系统这一适宜配置的维持时间相对短暂,却导致了本次过程降雪强度的两个峰值的出现。同时,中α尺度低涡的形成和加强及其与低空暖湿急流的适宜配置也是强降雪产生的一个有利因素。阴山山脉对本次过程强降雪的强度和位置具有重要影响:山脉使降雪在其南麓增强,北麓减弱。山地强迫抬升是导致这一结果的直接原因。另外,山地在其迎风坡使上升运动增强的同时也使正涡度减小和低层辐散增强。