共查询到20条相似文献，搜索用时 15 毫秒
1.
Jean N. Reinaud 《地球物理与天体物理流体动力学》2018,112(2):130-155
In this paper, we investigate the interaction between two like-signed quasi-geostrophic uniform potential vorticity internal vortices in the vicinity of a surface buoyancy anomaly filament in a three dimensional, stably stratified and rapidly rotating fluid. The surface buoyancy distribution locally modifies the pressure fields and generates a shear flow. We start the study by first considering the effects of a uniform linear horizontal shear on the binary vortex interaction. We confirm that a cooperative shear facilitates the merger of a pair of vortices while an adverse shear has the opposite effect. We next investigate the binary vortex interaction in the vicinity of the surface buoyancy filament explicitly. Here, not only the filament generates a shear flow, but it also responds dynamically to the forcing by the vortex pair. The filament destabilises and forms buoyancy billows at the surface. These billows interact with the internal vortices. In particular, a surface billow may pair with one of the internal vortices. In such cases, the like-signed internal vortex pair may separate if they are initially moderately distant from each other. 相似文献
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H. L. Kuo 《Pure and Applied Geophysics》1972,96(1):171-175
Summary It is shown that the general nonlinear potential vorticity equation for viscous and conductive fluid in a rotating system can be expressed in terms of the geostrophic stream function for the horizontal velocity alone, provided that the motions are hydrostatic and quasi-geostrophic and the Richardson number is much larger than unity. The form of this equation is identical with that obtained from an asymptotic expansion for a small Rossby number. 相似文献
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Lee-Or Merkine 《地球物理与天体物理流体动力学》2013,107(1-2):25-37
Abstract The mutual interaction of fields induced by spatially separated potential vorticity sources in a quasi-geostrophic barotropic flow is investigated using the weakly nonlinear approach. It is found that a powerful nonlinear response can be triggered by Rossby lee waves. This resonance phenomenon which dominates all other nonlinear corrections depends on certain global resonance conditions and on the change in the phase of the Rossby lee wave across the distance separating the sources. The response is particularly strong for topographic forcing possessing δ-function characterisitics. 相似文献
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Abstract Supercritically unstable density fronts near a vertical wall in a rotating, two-layer fluid were created on a laboratory turntable by withdrawing the outer wall of an annulus with a narrow gap, and allowing buoyant fluid from within the annulus to collapse toward a state of quasi-geostrophic balance. The resulting “coastal” current has a nearly uniform potential vorticity and is bounded by a front on which ageostrophic, wave-like disturbances grow. If the current width is comparable to the Rossby radius of deformation, the dominant length scale of disturbances is proportional to the width of the current. On the other hand, if the upper layer is much wider than the Rossby radius, then the observed length scale is a constant multiple of the Rossby radius. If the vertical boundary is omitted in the experiments, so that we are left with a circular anticyclonic vortex, the observed length scales and large-amplitude behaviour of disturbances are identical to those for the boundary currents, indicating that the wall has no significant influence on the flow. At very large amplitude the growing waves lead to the formation of cyclone-anticyclone vortex pairs. For very wide currents, both the mean flow and the disturbances are first confined to a region within a few Rossby radii of the front. However, both the mean flow and the turbulent eddy motions slowly propagate into the previously stationary upper layer until, eventually, the whole of the upper layer is turbulent. 相似文献
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Anthony Kay 《地球物理与天体物理流体动力学》2013,107(4):297-323
We consider inviscid rotating flow driven by a horizontally quadratic density variation in a horizontally unbounded slab. This configuration permits a similarity solution, removing the dependence on the horizontal coordinate from the vorticity and temperature equations, which are then solved by numerical integration along characteristics. At large values of Rossby number, the flow proceeds to a singularity in a similar manner to the non-rotating flow with the same initial conditions. At small values of Rossby number there are inertial oscillations of growing amplitude, which have been analysed using the method of multiple scales. The oscillations become desynchronised between the upper and lower parts of the domain, and static instability appears for a small fraction of each oscillation period. Eventually the oscillations give way to the rapid formation of a singularity, in contrast to geostrophic adjustment theory which predicts that a singularity will form only if the Rossby number is sufficiently large. 相似文献
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建立了求解准地转相当正压涡度方程的格子Boltzmann (LB)模型. 该模型将准地转相当正压涡度方程作为一个平流-扩散-反应方程来加以处理，在整体二阶精度下，通过Chapman_Enskog多尺度分析法，可将格子Boltzmann方程还原到相当正压涡度方程. 在不同Reynolds数、不同边界条件以及不同风应力驱动下的数值解表明，该模型正确反映了风生环流的基本结构和不同边界的耗散特征，并得到风生环流的多平衡态解等非线性特征. 此外，不同Rossby变形半径下的实验证明，小Rossby变形半径更容易激发环流的非线性模态. 通过与同等类型有限差方案的比较，表明本文的LB模型具有稳定性好、精度高等优点. 相似文献
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Rossby wave propagation in the presence of a nonseparable Brunt-Väisälä frequency,N(y,z), and the associated geostrophic zonal flow,U(y,z), is examined in this paper. The usual quasi-geostrophic potential vorticity equation only includes vertical variations in Brunt-Väisälä frequency (i.e.N(z)). We derive a linearised quasi-geostrophic potential vorticity equation which explicitly includesN(y, z), where variations inN may occur on the internal Rossby radius length scale. A mixed layer distribution that monotonically deepens in the poleward direction leads to a nonseparableN(y,z). The resulting meridional pressure gradient is balanced by an eastward zonal geostrophic flow.By assuming mixed layer depth changes occur slowly, relative to a typical horizontal wavelength of a Rossby wave, a local analysis is presented. The Rossby wave is found to have a strongly modulated meridional wavenumber,l, with amplitude proportional to |l|–1/2. To elucidate whether the modulations of the Rossby wave are caused by the horizontal variations inN orU we also consider the cases where eitherN orU vary horizontally. Mixed layer depth changes lead to largestl where the mixed layer is deepest, whereasl is reduced in magnitude whereU is nonzero. When bothU(y,z) andN(y,z) are present, the two effects compete with one another, the outcome determined by the size of |c|/U
max, wherec is the Rossby wave phase speed. Finally, the slowly varying assumption required for the analytical approach is removed by employing a numerical model. The numerical model is suitable for studying Rossby wave propagation in a rectangular zonal channel with generalN(y, z) andU(y, z). 相似文献
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Abstract Merilees and Warn's (1975) nonlinear interaction analysis of two-dimensional nondivergent flow is extended to examine the quasi-geostrophic two-layer model. Two sets of triads exist in this model (Salmon, 1978). The purely barotropic triads are the same as the triads examined by Merilees and Warn. Baroclinic-barotropic triads are found to exchange more energy or potential enstrophy with smaller or larger scales depending on the scale of motion as compared with the internal Rossby deformation radius and the relative wavenumber position of baroclinic and barotropic components. 相似文献
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Peter D. Killworth 《地球物理与天体物理流体动力学》2013,107(4):235-258
Abstract The stability of an isolated one-layer reduced gravity front is examined. It is shown that the system is unstable to long-wave disturbances provided merely that a simple condition on the depth profile is satisfied far from the front. The instability does not require the extremum of potential vorticity needed by quasi-geostrophic theory. The instability releases mean kinetic and mean potential energy from the system, but lacking a second layer cannot truly be termed baroclinic instability. 相似文献
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This paper focuses on the nonlinear interaction between a surface quasi-geostrophic buoyancy filament and an internal vortex. We first revisit the stability of an isolated buoyancy filament. The buoyancy profile considered is continuous and leads to a continuous velocity field, albeit one with infinite shear just outside its edge. The stability properties of an isolated filament help to interpret the unsteady interaction with a sub-surface (internal) vortex studied next. We find that, in all cases, the filament breaks into billows, analogous in form to those occurring in Kelvin–Helmholtz shear instability. For intense buoyancy filaments, the vortex itself may undergo strong deformations, including being split into several pieces. Generally, the nonlinear interaction causes both the filament and the vortex to lose their respective “self”-energies to the energy of interaction. The flow evolution depends sensitively on whether the vertical vorticity of the filament and the vortex have the same or opposite signs – termed “cooperative” and “adverse” shear respectively. In cooperative shear, the filament rolls up into a coherent surface eddy above a vortex initially placed below it, whereas in adverse shear, buoyancy is expelled above the vortex. Although sufficiently great shear induced by the buoyancy filament may split the vortex in both cases, adverse shear is significantly more destructive. 相似文献
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Wind-induced subduction at the South Atlantic subtropical front 总被引：1，自引：1，他引：0
Paulo H. R. Calil 《Ocean Dynamics》2017,67(10):1351-1365
The South Atlantic Subtropical Front, associated with the eastward-flowing South Atlantic Current, separates the colder, nutrient-rich waters of the subpolar gyre from the warmer, nutrient-poor waters of the subtropical gyre. Perturbations to the quasi-geostrophic, eastward flow generate meanders and filaments which induce cross-frontal exchange of water properties. Down-front winds transport denser waters from the South over warm waters from the North, inducing convective instability and subduction. Such processes occur over spatial scales of the order of 1 km and thus require high horizontal spatial resolution. In this modeling study, a high-resolution (4 km) regional grid is embedded in a basin-wide configuration (12 km) of the South Atlantic Ocean in order to test the importance of submesoscale processes in water mass subduction along the subtropical front. Stronger and more numerous eddies obtained in the high-resolution run yield more intense zonal jets along the frontal zone. Such stronger jets are more susceptible to instabilities, frontogenesis, and the generation of submesoscale meanders and filaments with \(\mathcal {O}(1)\) Rossby number. As a consequence, vertical velocities larger than 100 md 1 are obtained in the high-resolution run, one order of magnitude larger than in the low-resolution run. Wind-driven subduction occurs along the frontal region, associated with negative Ertel potential vorticity in the surface layer. Such processes are not observed in the low-resolution run. A passive tracer experiment shows that waters with density characteristics similar to subtropical mode waters are preferentially subducted along the frontal region. The wind-driven buoyancy flux is shown to be much larger than thermal or haline fluxes during the wintertime, which highlights the importance of the frictional component in extracting PV from the surface ocean and inducing subduction, a process that has been overlooked in subtropical mode water formation in the region. 相似文献
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The spatio-temporal variability of submesoscale eddies off southern San Diego is investigated with two-year observations of subinertial surface currents [O(1) m depth] derived from shore-based high-frequency radars. The kinematic and dynamic quantities — velocity potential, stream function, divergence, vorticity, and deformation rates — are directly estimated from radial velocity maps using optimal interpolation. For eddy detection, the winding-angle approach based on flow geometry is applied to the calculated stream function. A cluster of nearly enclosed streamlines with persistent vorticity in time is identified as an eddy. About 700 eddies were detected for each rotation (clockwise and counter-clockwise). The two rotations show similar statistics with diameters in the range of 5–25 km and Rossby number of 0.2–2. They persist for 1–7 days with weak seasonality and migrate with a translation speed of 4–15 cm s−1 advected by background currents. The horizontal structure of eddies exhibits nearly symmetric tangential velocity with a maximum at the defined radius of the eddy, non-zero radial velocity due to background flows, and Gaussian vorticity with the highest value at the center. In contrast divergence has no consistent spatial shape. Two episodic events are presented with other in situ data (subsurface current and temperature profiles, and local winds) as an example of frontal-scale secondary circulation associated with drifting submesoscale eddies. 相似文献
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Abstract The generation of stationary Rossby waves by sources of potential vorticity in a westerly flow is examined here in the context of a two-layer, quasi-geostrophic, β-plane model. The response in each layer consists of a combination of a barotropic Rossby wave disturbance that extends far downstream of the source, and a baroclinic disturbance which is evanescent or wave-like in character, depending on the shear and degree of stratification. Contributions from each of these modes in each layer are strongly dependent on the basic flows in each layer; the degree of stratification; and the depths of the two layers. The lower layer response is dominated by an evanescent baroclinic mode when the upper layer westerlies are much larger than those in the lower layer. In this case, weak stationary Rossby waves of large wavelengths are confined to the upper layer and the disturbance in the lower layer is confined to the source region. Increasing the upper layer flow (with the lower layer flow fixed) increases the Rossby wavelength and decreases the amplitude. Decreasing the lower layer flow (with the upper layer flow fixed) decreases the wavelength and increases the amplitude. Stratification increases the contribution from the barotropic wave-like mode and causes the response to be confined to the lower layer. The finite amplitude response to westerly flow over two sources of potential vorticity is also considered. In this case stationary Rossby waves induced by both sources interact to reinforce or diminish the downstream wave pattern depending on the separation distance of the sources relative to the Rossby wavelength. For fixed separation distance, enhancement of the downstreatm Rossby waves will only occur for a narrow range of flow variables and stratification. 相似文献
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M. M. Jalali 《地球物理与天体物理流体动力学》2013,107(6):375-401
ABSTRACTHerein we study the general interaction of two vortex patches in a single-layer quasi-geostrophic shallow-water flow. Steadily-rotating equilibrium states are found over a wide parameter space spanning the Rossby deformation length, vortex area ratio, potential vorticity ratio, and gap between their innermost edges. A linear stability analysis is then used to identify the critical gap separating stable and unstable solutions, over the entire range of area and potential vorticity ratios, and for selected values of the Rossby deformation length. A representative set of marginally unstable equilibrium states are then slightly perturbed and evolved by an accurate contour dynamics numerical algorithm to understand the long-term fate of the instabilities. Not all instabilities lead to vortex merger; many in fact are characterised by weak filamentation and a small adjustment of the vortex shapes, without merger. Stronger instabilities lead to material being torn from one vortex and either wrapped around the other or reduced to ever thinning filamentary debris. A portion of the vortex may survive, or it may be completely strained out by the other. 相似文献
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This work attempts to express and analyze the challenges, induced by stratification, affecting the Rossby-topographic eigenmodes of a closed domain with a general uneven bottom of arbitrary shape filled with a uniform fluid in the unperturbed configuration. The modified eigenmodes have been computed analytically: stratification is introduced in the mathematical form of a perturbation of a homogeneous fluid over a non-flat bottom. The eigenmodes lose their barotropic character and differences appear in the dynamical fields (velocity and pressure) from upper to lower layer, as expected. Expressions for the baroclinic and ageostrophic velocity components due to the perturbation are given. The analysis is carried out in the frame of linear shallow water approximation. All terms have been retained apart from nonlinear advection in the governing equations. We find that the frequencies of the eigenmodes change; an analytical expression of frequency correction as a function of layer density difference and interface depth is found. Initial results for some elementary geometrical settings with a waveguide bottom are determined and expressed in a concise, easily readable closed form. The results obtained in the shallow water approximation are expanded in series with respect to the Rossby number. Next, they are compared with the frequency correction obtained in an alternative framework in which the quasi-geostrophic approximation is used, and a purely baroclinic perturbation is imposed from the outset as the result of the introduction of stratification in the otherwise homogeneous fluid. In this scenario, reduced gravity and the ratio of upper to lower layer depth are, in turn, used as the expansion parameters in lieu of the Rossby number. 相似文献
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根据对卫星观测的海平面高度资料的分析，进一步证实了在北太平洋副热带两支向东的流（副热带逆流和夏威夷背风逆流）所在的区域内，海平面高度的70～210天周期振荡是主要的低频变化.发现在这两支向东的逆流区Rossby波的特性不同：副热带逆流区70～210天周期振荡对应的Rossby波西传过程中增幅，在台湾以东振幅达到最大；而在夏威夷背风逆流区，70～210天周期Rossby波在西传过程中不出现增幅现象.依据25层海洋模式得到的关于Rossby波振幅、频率与海洋层结之间的关系，揭示了周期为70～210天的Rossby波为不稳定波，这是由于副热带逆流海域模态水存在使得密度的垂直梯度变小的缘故；而在夏威夷背风逆流区位于表层逆流下的北赤道流西深东浅，70～210天周期Rossby长波在逆流的东部有可能不稳定，但其在逆流的西部是稳定的，因此不出现在西传过程中增幅现象；发现在北太平洋副热带两个向东流的海域，年周期Rossby波是稳定的，因此，在该海域海平面周期为70～210天的振荡的振幅要比年周期振荡的振幅大. 相似文献
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Research Note: A simple method of image solution for a sphere of constant electrical potential in a conducting half‐space: implications for the applied potential method 
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下载免费PDF全文 S.L. Butler 《Geophysical Prospecting》2017,65(6):1680-1686
The applied potential, or mise‐à‐la‐masse, method is used in mineral exploration and environmental applications to constrain the shape and extent of conductive anomalies. However, few simple calculations exist to help gain understanding and intuition regarding the pattern of measured electrical potential at the ground surface. While it makes intuitive sense that the conductor must come close to the ground surface in order for the lateral extent of the potential anomaly to be affected by the dimensions of the conductor rather than simply by the depth, no simple calculation exists to quantify this effect. In this contribution, a simple method of images solution for the case of a sphere of constant electrical potential in a conducting half‐space is presented. The solution consists of an infinite series where the first term is the same as the method of images solution for a point current source in an infinite half‐space. The higher order terms result from the interaction of the constant potential sphere with the no‐flux boundary condition representing the ground surface and cause the change in the shape of the potential anomaly that is of interest in the applied potential method. The calculation is relevant to applied potentials when the conductive anomaly is limited in all three space dimensions and is highly conductive. Using the derived formula, it is shown that, while the electrical potential at the ground surface caused by the sphere is affected even when the sphere is quite deep, the ratio of the potential to the current, a quantity that is more relevant to the applied potential method, is not affected until the centre of the sphere is within two radii of the ground surface. An expression for the contact resistance of the sphere as a function of depth is also given, and the contact resistance is shown to increase by roughly 45% as the sphere is moved from great depth to the ground surface. 相似文献