Vortex–ridge interaction in a rotating fluid

The evolution of barotropic vortices interacting with a topographic ridge on a f-plane is studied by means of laboratory experiments in a rotating tank and numerical simulations. The initial condition in all experiments is a cyclonic vortex created at a certain distance from the ridge. The results are presented in two main scenarios: (a) weak interactions, which occur at early stages of the experiments, when the vortex is far from the ridge, and thus weakly experiences the influence of the topography. In these situations, the vortex slowly drifts towards the ridge with a leftward inclination due to the ascending slope of the topography. Such a behaviour is similar to the “northwestern” motion of cyclones over a weak sloping bottom. The circular shape of the monopolar vortex is preserved. (b) Strong interactions, in which the vortex core reaches the ridge and presents a more complicated evolution. The cyclone “climbs” to the top of the topography and crosses to the other side. Once the vortex experiences the opposite slope, it moves backwards trying to return to the original side of the ridge. For strong enough vortices, this process may be repeated a number of times until the vortex is dissipated by viscous effects. During these interactions the shape of the vortex is strongly deformed and several filaments are produced. In some cases the vortex is cleaved in two parts when crossing the ridge, one at each side of it and moving in opposite directions.Weak and strong interactions are numerically simulated by using a quasi-two-dimensional model. The results confirm that the vortex behaviour is governed by stretching and squeezing effects associated with changes in depth over the ridge and, at latter stages, by Ekman damping due to the solid bottom. The main results observed during strong interactions on a f-plane are also found on preliminar topographic β-plane experiments.     

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.     

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.     

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.     

A note on circulation in differentially heated rotating stratified fluid and other elliptic problems

This note relates to the paper Circulation and boundary layers in differentially heated rotating stratified fluid by Whitehead and Pedlosky [Whitehead, J.A., Pedlosky, J., 2000. Circulation and boundary layers in differentially heated rotating stratified fluid. Dyn. Atmos. Ocean. 31, 1–21]. Here, we describe an alternative method of solution for the theoretical model developed therein, and provide a comparison with the original method used in the paper.     

On the bottom relief effect on wind-driven currents in a homogeneous ocean

The three-dimensional model of stationary wind-driven currents in a homogeneous ocean of a variable depth is investigated. The model is linear but includes horizontal and vertical turbulent mixings. Two cases of the behaviour of the isolines of the function $\text{?/H}$ are considered, namely: (1) all isolines $\text{?/H}$ start at one part of the coastline and end in another part of it, and (2) a certain isoline $\text{?/H}$ exists which is tangential to the coastline. Here ? is the Coriolis parameter, and H is the depth of the ocean. The first case is the simplest one; it arises in particular if H = constant and the coasts are meridional. The second case is marked by the boundary current separation from the coast. The paper deals with the boundary layers which arise at the surface, bottom, side boundary and inside the ocean.     

On the determination of the absolute velocity of steady flows of a baroclinic fluid with applications to ocean currents

The problem of determining the absolute velocity of marine currents, including its barotropic component, is revisited. A generalization of the classical Needler’s formula is discussed for a Boussinesq fluid and it is shown that the steady flow solution can be deduced from a variational principle that uses the constants of motion existing in the problem. A simple model of a steady flow is considered when the Bernoulli function consists of two terms. The first term is proportional to the square of Ertel’s potential vorticity and the second term is a quadratic function of the fluid buoyancy. This model is applied to mimic the circulation in the western Mediterranean Sea near the African coast. Alternatively, “potential temperature – salinity” coordinates are applied to construct the stream-tubes and infer the steady flow velocity in the simplest case of the Bernoulli function being proportional to the product of the above two variables.     

Intermittent Turbulence Associated with a Density Current Passage in the Stable Boundary Layer

Using the unprecedented observational capabilities deployed duringthe Cooperative Atmosphere-Surface Exchange Study-99 (CASES-99),we found three distinct turbulence events on the night of 18October 1999, each of which was associated with differentphenomena: a density current, solitary waves, and downwardpropagating waves from a low-level jet. In this study, we focus onthe first event, the density current and its associatedintermittent turbulence. As the cold density current propagatedthrough the CASES-99 site, eddy motions in the upper part of thedensity current led to periodic overturning of the stratifiedflow, local thermal instability and a downward diffusion ofturbulent mixing. Propagation of the density current induced asecondary circulation. The descending motion following the head ofthe density current resulted in strong stratification, a sharpreduction in the turbulence, and a sudden increase in the windspeed. As the wind surge propagated toward the surface, shearinstability generated upward diffusion of turbulent mixing. Wedemonstrate in detail that the height and sequence of the localthermal and shear instabilities associated with the dynamics ofthe density current are responsible for the apparent intermittentturbulence.     

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.     

Energy transfer in a fluid with a uniform density gradient

Energy transfer via resonance in a stratified fluid with a constant Brunt–Väisälä frequency is studied through the Manley–Rowe relation and direct numerical simulations. The objectives of this study are two-fold. One is to determine if there is a limitation on the lengthscale of small-scale waves to which primary energy can be effectively transferred. The other is to study factors affecting the growth of parametric subharmonic instability. Resonantly interacting modes are classified into three groups: local sum modes, quasi-subharmonic modes and remote parametric subharmonic instability modes (characterized by interaction with very small-scale waves). The latter two involve energy transfer from a primary wave to secondary waves with half the frequency. Most energy transfer is through local sum resonant modes and quasi-subharmonic modes. Energy cannot effectively transfer to higher wavenumber modes since dynamical systems are altered as wavenumbers of excited modes increase. In the remote modes, the solution is sinusoidal with high angular frequency and very small energy capacity. As a consequence, these modes are inactive in energy transfer despite their high energy growth rates. Effects of non-uniform white noise amplitude and primary mode propagation angle on the quasi-subharmonic modes are also investigated. Implications for energy transfer in the ocean are discussed.     

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.     

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.     

Note on the generalized thermal theory for gravity currents in the deceleration phase

The generalized thermal theory for gravitational convection, produced from instantaneous buoyancy sources on sloping boundaries, developed in Dai and Garcia (2010) is examined in this note. An assumption implicitly made therein, that detrained fluid carries no momentum, was inappropriate and the solution was not physical in special cases. The generalized thermal theory is now improved by considering the momentum carried away by detrained mixed fluid. An asymptotic velocity–distance relation for gravity currents further downslope in the deceleration phase is provided and agreement with reported experimental data is found.     

Water-tank experiment on the thermal circulation induced by the bottom heating in an asymmetric valley

Water tank experiments were carried out to investigate the thermal convection due to the bottom heating in an asymmetrical valley under neutral and stably stratified approach flows with the Particle Image Velometry (PIV) visualization technique. In the neutral stratification approach flow, the ascending draft induced by bottom heating is mainly located in the center of the valley in calm ambient wind. However~with ambient wind flow, the thermal convection is shifted leeward, and the descending draft is located on the leeward side of the valley, while the ascending draft is located on the windward side. The descending draft is minorly turbulent and organized, while the ascending draft is highly turbulent. With the increase of the towing speed, the descending and ascending drafts induced by the mechanical elevation begin to play a more dominant role in the valley flow, while the role of the thermal convection in the valley airflow becomes limited. In the stable stratification approach flow, the thermal convection is limited by the stable stratification and no distinct circulation is formed in calm ambient wind. With ambient wind, agravity wave appears in the upper layer in the valley. With the increase of the ambient wind speed, a gravity wave plays an important role in the valley flow, and the location and intensity of the thermal convection are also modulated by the gravity internal waves. The thermal convection has difficulty penetrating the upper stable layer. Its exchange is limited between the air in the upper layer and that in the lower layer in the valley, and it is adverse to the diffusion of pollutants in the valley.     

污泥/煤流化床混烧底灰中的重金属毒性研究

研究了污泥与煤按不同质量比例混烧后,底灰中的重金属形态分布与浸出毒性.结果表明:30:70的泥煤比使底灰中重金属硫化物及有机态和残渣态所占比例最大,即生物无效部分比例最大;在浸出毒性实验中,30:70的泥煤比使底灰重金属浸出量最小.由此推出,对环境毒害程度最小的泥煤质量比为30:70,即该实验条件下最优泥煤质量比为30:70.     

A study on the nonlinear stability of fronts in the ocean on a sloping continental shelf

1.IntroductionArnol'd(1965,1969)variationalprincipleandapriorestimatemethodisessentiallyageneralizationofLyapunovstabilitymethodforfinite--dimensionaldynamicalsystemsininfinite--dimensionalones,andhestudiedthenonlinearstabilityof2--dimensionalincompressibleidealfluidmotionbyuseofthismethod,andestablishedtwotheoremswhichareArnol,d'sfirsttheoremandArnol'd'ssecondtheorem.Eversincethe1980's,manyscientistshavebeenworkingonthissubject,Holmetal.(1985);MclntyreandShepherd(1987);Zeng(1989);Muetal.(1…     

雷达资料在一次大范围冰雹天气过程中的同化试验分析

基于华南区域高分辨率数值模式,采用牛顿连续松弛逼近法(nudging)同化C波段多普勒雷达反射率资料,针对2018年4月2日贵州一次大范围冰雹天气过程进行了数值模拟试验.分析结果表明:在模式中进行雷达反射率因子信息nudging同化后,调整了分析场中的水凝物信息和热力场结构,对流层中层的雨水和冰相粒子含量均增加,水凝物...