共查询到20条相似文献，搜索用时 46 毫秒
1.
Abstract The dynamic behavior of baroclinic point vortices in two-layer quasi-geostrophic flow provides a compact model for studying the transport of heat in a variety of geophysical flows including recent heton models for open ocean convection as a response to spatially localized intense surface cooling. In such heton models, the exchange of heat with the region external to the compact cooling region reaches a statistical equilibrium through the propagation of tilted heton clusters. Such tilted heton clusters are aggregates of cyclonic vortices in the upper layer and anti-cyclonic vortices in the lower layer which collectively propagate almost as an elementary tilted heton pair even though the individual vortices undergo shifts in their relative locations. One main result in this paper is a mathematical theorem demonstrating the existence of large families of long-lived propagating heton clusters for the two-layer model in a fashion compatible to a remarkable degree with the earlier numerical simulations. Two-layer quasi-geostrophic flow is an idealization of coupled surface/interior quasi-geostrophic flow. The second family of results in this paper involves the systematic development of Hamiltonian point vortex dynamics for coupled surface/interior QG with an emphasis on propagating solutions that transport heat. These are novel vortex systems of mixed species where surface heat particles interact with quasi-geostrophic point vortices. The variety of elementary two-vortex exact solutions that transport heat include two surface heat particles of opposite strength, tilted pairs of a surface heat particle coupled to an interior vortex of opposite strength and two interior tilted vortices of opposite strength at different depths. The propagation speeds of the tilted elementary hetons in the coupled surface/interior QG model are compared and contrasted with those in the simpler two-layer heton models. Finally, mathematical theorems are presented for the existence of large families of propagating long-lived tilted heton clusters for point vortex solutions in coupled surface/interior QG flow. 相似文献
2.
Pebble clusters are common small‐scale morphological features in gravel‐bed rivers, occupying as much as 10 per cent of the bed surface. Important links exist between the presence of pebble clusters and the development of flow structures. These links are poorly understood at the three‐dimensional level. Particularly neglected has been the effect of clusters on the lateral flow characteristics. A laboratory study was conducted using a hydraulic flume, within which simulated pebble clusters were superimposed onto a plane bed of gravel material. High‐resolution three‐dimensional flow data were collected above the bed at two different flow depths using an acoustic Doppler velocimeter. The results present evidence of the importance of lateral flow in the development of turbulent flow structure. Narrow regions of high lateral and downstream turbulence intensity exist to both sides of clusters and in a three‐dimensional separation zone in their lee. This may indicate the presence of horseshoe‐type vortical structures analogous to those identified in less hydraulically rough environments. However, it is likely that these structures are more complicated given the mutual interference of the surrounding medium. The lateral flow was also identified as a key component in the upwelling identified by other authors in the lee of pebble clusters. The results of the vertical flow analysis confirm the hypothesis that six regions with distinct vertical flow characteristics exist above clusters: flow acceleration up the stoss‐side of the cluster; recirculation behind the cluster in the wake region; vortex shedding from the pebble crest and shear layer; flow reattachment downstream of the cluster; upwelling of flow downstream of the point of reattachment; and recovery of flow. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
3.
Secondary flow deflection in the lee of transverse dunes with implications for dune morphodynamics and migration 总被引：3，自引：0，他引：3
Measurements of lee‐side airflow response from an extensive array of meteorological instruments combined with smoke and flow streamer visualization is used to examine the development and morphodynamic significance of the lee‐side separation vortex over closely spaced transverse dune ridges. A differential deflection mechanism is presented that explains the three‐dimensional pattern of lee‐side airflow structure for a variety of incident flow angles. These flow patterns produce reversed, along‐dune, and deflected surface flow vectors in the lee that are inferred to result in net ‘lateral diversion’ of sand transport over one dune wavelength for incident angles as small as 10° from crest‐transverse (i.e. 80° from the crest line). This lateral displacement increases markedly with incident flow angle when expressed as the absolute value of the total deflection in degrees. Reversed and multi‐directional flow occurs for incident angles between 90° and 50°. These results document the three‐dimensional nature of flow and sand transport over transverse dunes and provide empirical evidence for an oblique migration model. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
4.
Q. Q. Shi Z. Y. Pu H. Zhang S. Y. Fu C. J. Xiao Q. -G. Zong T. A. Fritz Z. X. Liu 《Surveys in Geophysics》2005,26(1-3):369-386
Magnetic reconnection at the high-latitude magnetopause is studied using 2–1/2-dimensional (2−1/2-D) Hall-MHD simulation. Concentric flow vortices and magnetic islands appear when both Hall effect and sheared flow are considered. Plasma mixing across the magnetopause occurs in the presence of the flow vortices. Reconnected structure generated in the vicinity of the subsolar point changes its geometry with increasing flow shear while moving to high latitudes. In the presence of flow shear, with the Hall-MHD reconnection a higher reconnection rate than with the traditional MHD is obtained. The out-of-plane components of flow and magnetic field produced by the Hall current are redistributed under the action of the flow shear, which makes the plasma transport across the boundaries more complicated. The simulation results provide some help in understanding the dynamic processes at the high-latitude magnetopause. 相似文献
5.
Wind flow has been studied in situations where it encounters porous and solid windbreaks, but there has been a lack of research exploring turbulent wind dynamics around and in the lee of real vegetation elements. In dryland contexts, sparse vegetation plays an important role in modulating both the erosivity of the wind and the erodibility of surfaces. Therefore, understanding the interactions between wind and vegetation is key for improving wind erosion modelling in desert landscapes. In this study, turbulent wind flow around three typical dryland vegetation elements (a grass clump, a shrub, and a tree) was examined in Namibia using high‐frequency (10 Hz) sonic anemometry. Spatial variations in mean wind velocity, as well as Reynolds stresses and coherent turbulent structures in the flow, were compared and related to the porosities and configurations of the study elements. A shelter parameter, originally proposed by Gandemer ( 1979 , Journal of Wind Engineering and Industrial Aerodynamic 4 : 371–389), was derived to describe the combined impact of the different elements on the energy and variability of horizontal wind flow. Wind velocity was reduced by 70% in the immediate lee of the grass and 40% in the lee of the shrub, but velocity recovered exponentially to equilibrium over the same relative distance in both cases (~9 element heights downwind). Quadrant analysis of the high‐frequency wind flow data revealed that the grass clump induced a small recirculation zone in its lee, whereas the shrub did not. Also, higher Reynolds shear stress and higher ‘flow positivity magnitude’ [ratio of Q1 (outward interaction) and Q4 (sweep) quadrants to Q2 (ejection) and Q3 (inward interaction) quadrants] was generally observed in the wake of the grass. These differences arose because the porosity of the grass clump (53%) was lower than the porosity of the shrub (69%), and thus bleed flow through the shrub was more significant. The bluff‐body behaviour of the grass resulted in a more intense and more extensive sheltering effect than the shrub, which implies that overall sediment transport potential is lower in the wake of the grass. The tree displayed a different wake structure to the grass and shrub, owing to the elevation of its crown. A ‘bottom gap’ effect was observed, whereby wind velocities increased possibly due to streamline compression in the gap between the ground and the underside of the tree crown. Differences in flow momentum between the bottom gap and the low‐pressure leeward region of the crown are a probable explanation for the formation of a large recirculation vortex. The bottom gap effect led to decreased sheltering up to three tree heights downwind, but the surface became increasingly protected by the frontal impact of the crown over a further eight tree heights downwind (~30 m). The extraction of momentum from the air by the tree therefore resulted in a far more extensive sheltering effect compared to the grass and shrub. This study represents an important investigation of the impact of different vegetation types on turbulent wind flow, and results can be integrated as parameterizations into spatial sediment transport models that explore landscape‐scale change on semi‐vegetated desert surfaces. Copyright © 2016 The Authors. Earth Surface Processes and Landforms Published by John Wiley & Sons Ltd. 相似文献
6.
W. R. Young 《地球物理与天体物理流体动力学》2013,107(1-4):35-61
Abstract Various interactions between small numbers (two and four) of baroclinic, geostrophic point vortices in a two-layer system are studied with attention to the qualitative changes in behavior which occur as size of the deformation radius is varied. A particularly interesting interaction, which illustrates the richness of baroclinic vortex dynamics, is a collision between two hetons. (A heton is a vortex pair in which the constituent vortices have opposite signs and are in opposite layers. The “breadth” of a heton is the distance between its constituent vortices. A translating heton transports heat.) When two hetons, which initially have different breadths, collide, the result is either an exchange of partners, or a “slip-through” collision in which the initial structures are preserved. It is shown here that the outcome is always an exchange, provided the deformation radius is sufficiently small. This strongly contrasts with a collision between pairs of classical, one-layer vortices in which no exchange occurs if the initial ratio of the breadths is sufficiently extreme. Finally the transport of passive fluid by a translating baroclinic pair is investigated. A pair of vortices in the top layer transports no lower layer fluid if the distance between the vortices is less than 1.72 deformation radii. By contrast, the size of the region trapped by a heton increases without bound as the spacing between the vortices increases. 相似文献
7.
In this article we address two questions: Why do freely evolving vortices weaken on average, even when the viscosity is very small? Why, in the fluid's interior, away from vertical boundaries and under the influence of Earth's rotation and stable density stratification, do anticyclonic vortices become dominant over cyclonic ones when the Rossby number and deformation radius are finite? The context for answering these questions is a rotating, conservative, Shallow-water model with Asymmetric and Gradient-wind Balance approximations. The controlling mechanisms are vortex weakening under straining deformation (with a weakening that is substantially greater for strong cyclones than strong anticyclones) followed by a partially compensating vortex strengthening during a relaxation phase dominated by Vortex Rossby Waves (VRWs) and their eddy–mean interaction with the vortex. The outcome is a net, strain-induced vortex weakening that is greater for cyclones than anticyclones when the deformation radius is not large compared to the vortex radius and the Rossby number is not small. Furthermore, when the exterior strain flow is sustained, the vortex changes also are sustained: for small Rossby number (i.e., the quasigeostrophic limit, QG), vortices continue to weaken at a relatively modest rate, but for larger Rossby number, cyclones weaken strongly and anticyclones actually strengthen systematically when the deformation radius is comparable to the vortex radius. The sustained vortex changes are associated with strain-induced VRWs on the periphery of the mean vortex. It therefore seems likely that, in a complex flow with many vortices, anticyclonic dominance develops over a sequence of transient mutual straining events due to the greater robustness of anticyclones (and occasionally their net strengthening). 相似文献
8.
Flow resistance in mountain streams is important for assessing flooding hazard and quantifying sediment transport and bedrock incision in upland landscapes. In such settings, flow resistance is sensitive to grain-scale roughness, which has traditionally been characterized by particle size distributions derived from laborious point counts of streambed sediment. Developing a general framework for rapid quantification of resistance in mountain streams is still a challenge. Here we present a semi-automated workflow that combines millimeter- to centimeter-scale structure-from-motion (SfM) photogrammetry surveys of bed topography and computational fluid dynamics (CFD) simulations to better evaluate surface roughness and rapidly quantify flow resistance in mountain streams. The workflow was applied to three field sites of gravel, cobble, and boulder-bedded channels with a wide range of grain size, sorting, and shape. Large-eddy simulations with body-fitted meshes generated from SfM photogrammetry-derived surfaces were performed to quantify flow resistance. The analysis of bed microtopography using a second-order structure function identified three scaling regimes that corresponded to important roughness length scales and surface complexity contributing to flow resistance. The standard deviation σz of detrended streambed elevation normalized by water depth, as a proxy for the vertical roughness length scale, emerges as the primary control on flow resistance and is furthermore tied to the characteristic length scale of rough surface-generated vortices. Horizontal length scales and surface complexity are secondary controls on flow resistance. A new resistance predictor linking water depth and vertical roughness scale, i.e. H/σz, is proposed based on the comparison between σz and the characteristic length scale of vortex shedding. In addition, representing streambeds using digital elevation models (DEM) is appropriate for well-sorted streambeds, but not for poorly sorted ones under shallow and medium flow depth conditions due to the missing local overhanging features captured by fully 3D meshes which modulate local pressure gradient and thus bulk flow separation and pressure distribution. An appraisal of the mesh resolution effect on flow resistance shows that the SfM photogrammetry data resolution and the optimal CFD mesh size should be about 1/7 to 1/14 of the standard deviation of bed elevation. © 2019 John Wiley & Sons, Ltd. 相似文献
9.
Interaction between a surface jet and subsurface vortices in a three-layer quasi-geostrophic model 总被引：1，自引：0，他引：1
This study focuses on the interaction between mid depth vortices and surface jets and fronts in a three-layer quasi-geostrophic model. Such vortices may be regarded as an idealisation of meddies, eddies of Mediterranean Water in the Northeastern Atlantic Ocean, interacting with the Azores j t and front. Successively, a single vortex, a vortex doublet and a vortex pair (in the middle layer) are studied. When a single vortex is considered, the jet has a critical effect of its motion, temporarily slowing down its zonal drift and accelerating it meridionally as the vortex crosses the front. On the contrary, if the vortex does not cross the front, it can drift fairly rapidly along it. The merger of a vortex doublet (two like-signed vortices) below a surface jet is possible whatever the relative position of this doublet with respect to the jet axis. Nevertheless, doublets initially located below the front, will undergo stronger shear and merger efficiency will be diminished. The merged vortex will be circled at the surface by a large meander of the jet. Finally, eastward jet-dipole interaction experiments are performed with various orientations of the vortex dipoles. Eastward propagating dipoles below the jet follow it without deformation. Southeastward drifting dipoles finally join the previous evolution. Southward and southwestward directed dipoles cross the surface jet southeastward. The presence of meanders initially on the jet does not prevent its crossing by a single vortex. Characteristics of the surface jet meanders are also described for a possible remote detection of this process. 相似文献
10.
We examine the three-dimensional, nonlinear evolution of columnar vortices in a rotating environment. As the initial vorticity distribution, a wavetrain of finite amplitude Kelvin-Helmholtz vortices in shear is employed. Through direct numerical simulation of the Navier-Stokes equations we seek to better understand the process of maturation of the various three-dimensional modes of instability to which such vortical flows are subject, especially those which exist as a consequence of the action of the Coriolis force. In the absence of rotational influence, we thereby demonstrate that the nonlinear evolution of columnar vortices is most strongly controlled by one or the other of two mechanisms. One mechanism of instability is identifiable as a so-called elliptical instability, which promotes the initial bending of vortex tubes in a sinusoidal fashion, while the other is a hyperbolic mode, which is responsible for the development of streamwise vortex streaks in the "braids" between adjacent vortex cores. In the rotating case, anticyclonic vortices are strongly destabilized by weak background rotation, while rapid rotation stabilizes both the cyclones and anticyclones. The strong anticyclones are subject to two distinct forms of instability, namely a Coriolis force modified elliptical instability and an inertial (centrifugal) instability. The former instability is very similar to the nonrotating form of the elliptical instability as it promotes bending of vortex tubes, while the latter instability grows on the edge of the vortex core and generates streaks of vorticity, which surround the vortex core itself. These results of direct numerical simulation fully verify the results of previous linear stability analyses. Taken together, they provide a simple explanation for the broken symmetry that is often observed to be characteristic of the von Karman vortex streets that develop in the atmospheric lee of oceanic islands. 相似文献
11.
Ya. D. Afanasyev 《地球物理与天体物理流体动力学》2013,107(1):31-48
We present results from a new series of experiments on the geophysically important issue of the instability of anticyclonic columnar vortices in a rotating fluid in circumstances such that the Rossby number exceeds unity. The vortex pair consisting of a cyclonic and an anticyclonic vortex is induced by a rotating flap in a fluid which is itself initially in a state of solid-body rotation. The anticyclonic vortex is then subject to either centrifugal or elliptical instability, depending on whether its initial ellipticity is small or large, while the cyclone always remains stable. The experimental results demonstrate that the perturbations due to centrifugal instability have a typical form of toroidal vortices of alternating sign (rib vortices). The perturbations due to elliptical instability are of the form of sinuous deformation of the vortex filament in the plane of maximal stretching which corresponds to the plane of symmetry for the vortex pair. The initial perturbations in both cases are characterized by a definite wave number in the vertical direction. The characteristics of the unstable anticyclone are determined by the main nondimensional parameter of the flow - the Rossby number. The appearance of both centrifugal and elliptical instabilities are in accord with the predictions of theoretical criteria for these cases. 相似文献
12.
A combined numerical and experimental study of the propagation of an internal solitary wave (ISW) over a corrugated bed is
presented, in which the amplitude and the wavelength of the corrugated bed, together with the wave amplitude and wave speed
of the ISW, have been varied parametrically. Both ISWs of elevation and depression have been considered. The wave-induced
currents over the corrugated bed cause flow separation at the apex of the corrugations and a sequence of lee vortices forms
as a result. These vortices develop fully after the main wave has passed over the topographic feature, resulting in deformation
of the overlying pycnocline and, in some instances, significant vertical mixing. It is found that the intensity of the vortex
formation is dependent on both the amplitude and wavelength of the bottom topography. In the case of an ISW of depression,
the generation of vertically (upward)-propagating vortices is seen to result in entrainment of fluid from a bottom boundary
jet (Carr and Davies, Phys Fluids 18:016601, 2006), while, in the elevation case, a second mechanism is present to induce significant turbulent mixing in the water column.
It occurs when the bottom corrugations reach into, or are very near, the pycnocline at rest. Large waves of elevation that
are stable on approach to the corrugations exhibit evidence of a spatio-temporally developing shear instability as they interact
with the bottom corrugation. The shear instability takes the form of billows that have a vertical extent that can reach 50%
of the wave amplitude. 相似文献
13.
Abstract We study the formation of lenses of the ocean's intermediate water using a 2.5-layerβ-plane primitive equation model with localized injection of water mass. For the injecting rate of 1.0 Sv, we have observed that strong vortices are shed regularly. These vortices propagate westward much faster than the second baroclinic long Rossby wave. They are totally isolated from each other and show strong baroclinicity as well. Moreover, they remain stable over a sufficiently long period of time. Regular formation of such strong vortices in the intermediate layer has not been reported previously. The translation speed is explained using the Euler's momentum integral theorem for the nonlinear baroclinic vortex on the β-plane. We have demonstrated that coupling between the primary motion in the intermediate layer and the secondary motion in the upper layer with a meridional shift is crucial to the fast westward translation of the intense vortices. A simple dispersion formula relating the zonal translation speed with the vortex radius is also derived under the assumption of quasi-geostrophy. It has turned out that the analytical relation explains the numerical results surprisingly well despite the limitation of its derivation. 相似文献
14.
The interaction of meddies with a complex distribution of seamounts is studied in a three-layer quasi-geostrophic model on the f-plane. This study aims at understanding if and how this seamount chain can represent a barrier to the propagation of these eddies and how it can be involved in their decay. The eddies are idealized as vortex patches in the middle layer, interacting with a regional cyclonic current and with ten idealized seamounts. The numerical code is based on the contour surgery technique. The initial position, radius, shape, number and polarity of the eddies are varied. The main results are the following: (1) Though they do not describe the unsteady flow, the streamlines of the regional and topographic flow provide a useful estimate of the vortex trajectories, in particular towards the major seamounts, where stronger velocity shears are expected. (2) The tallest and widest seamounts which have the largest vorticity reservoir are able to considerably erode the vortices, but also to draw anticyclones towards the seamount top. The ability of narrower seamounts to erode vortices is related to their multiplicity. (3) Only 1/3 of the anticyclones with about 30-km radius reach the southern boundary of the seamount chain, and their erosion is larger than 50 %. The other anticyclones are either completely eroded or trapped over a wide seamount top. Cyclones are less affected by seamounts because they oppose the topographic draft towards the seamount top and they drift along the side of the seamount. (4) Large vortices resist topographic erosion more efficiently. The rate of erosion grows from a few percent to about 35–50 % as the vortex radius decreases from about 60 to 30 km. Small cyclones are not eroded, contrary to small anticyclones (which completely decay), in relation with the different trajectories of these eddies in the vicinity of the seamounts. (5) The detailed vortex shape does not appear critical for their evolution, if they are close enough to the seamount chain initially. The interaction between a group of vortices initially north of the seamount chain can modify their trajectory to such an extent that they finally avoid collision with seamounts. (6) Finally, meddy trajectories across the Horseshoe Seamounts (data from the AMUSE experiment) show qualitative similarity with the vortex paths in the model. Several events of vortex decay also occur at comparable locations (in particular over the wide and tall seamounts) in the model and observations. 相似文献
15.
This work addresses the linear dynamics underlying the formation of density interfaces at the periphery of energetic vortices, well outside the vortex core, both in the radial and axial directions. We compute numerically the unstable modes of an anticyclonic Gaussian vortex lens in a continuously stratified rotating fluid. The most unstable mode is a slow mode, associated with a critical layer instability located at the vortex periphery. Although the most unstable disturbance has a characteristic vertical scale which is comparable to the vortex height, interestingly, the critical levels of the successively fastest growing modes are closely spaced at intervals along the axial direction that are much smaller than the vortex height. 相似文献
16.
17.
2000年9月30日Geotail卫星分别于17∶54∶36~18∶09∶00UT和18∶59∶00~19∶30∶00UT在磁尾晨侧等离子体片内(n≈0.4 cm-3,T≈6 keV)观测到等离子体涡流事件.本文采用Grad-Shafranov (GS)流场重构技术再现了这些涡流的二维速度场、离子数密度和离子温度的分布图像.结果显示:从地心太阳磁层坐标系(GSM)赤道面上面看, 涡流的尺度约为5000 km×1400 km , 朝地球的运动速度约为15~25 km/s.所有5个涡流的旋转方向都为顺时针方向,旋转周期约为6~11 min.相邻涡流的相互作用导致它们之间的磁场强度增强.考察观测数据发现,涡流内不仅包含等离子体片热等离子体成分,也包含较大通量的类似源自磁鞘的冷等离子体成分(T<1 keV).这与观测到涡流等离子体的平均温度(T≈4 keV)较磁尾等离子体片等离子体的典型温度(T≈6 keV)明显偏低的事实是一致的.不仅如此,离子数密度和温度在结构内的分布也不均匀,数密度在涡流内部偏离中心的位置比较低而在每个涡流的边缘位置比较高,温度的分布大体上与密度相反.分析认为观测到的磁尾等离子体涡流事件可能由发生在低纬边界层的Kelvin-Helmholtz不稳定性引起,涡流结构内的冷等离子体可能来自磁层顶外部的磁鞘. 相似文献
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19.
Giorgio Riccardi 《Ocean Dynamics》2018,68(2):273-293
A new mathematical approach to kinematics and dynamics of planar uniform vortices in an incompressible inviscid fluid is presented. It is based on an integral relation between Schwarz function of the vortex boundary and induced velocity. This relation is firstly used for investigating the kinematics of a vortex having its Schwarz function with two simple poles in a transformed plane. The vortex boundary is the image of the unit circle through the conformal map obtained by conjugating its Schwarz function. The resulting analysis is based on geometric and algebraic properties of that map. Moreover, it is shown that the steady configurations of a uniform vortex, possibly in presence of point vortices, can be also investigated by means of the integral relation. The vortex equilibria are divided in two classes, depending on the behavior of the velocity on the boundary, measured in a reference system rotating with this curve. If it vanishes, the analysis is rather simple. However, vortices having nonvanishing relative velocity are also investigated, in presence of a polygonal symmetry. In order to study the vortex dynamics, the definition of Schwarz function is then extended to a Lagrangian framework. This Lagrangian Schwarz function solves a nonlinear integrodifferential Cauchy problem, that is transformed in a singular integral equation. Its analytical solution is here approached in terms of successive approximations. The self-induced dynamics, as well as the interactions with a point vortex, or between two uniform vortices are analyzed. 相似文献
20.
P. Caillol 《地球物理与天体物理流体动力学》2015,109(2):111-144
In a previous paper, Caillol [Geophys. Astrophys. Fluid Dyn., 2014, 108] investigated the steady nonlinear vortical structure of a singular vortex Rossby mode that has survived to a strong critical-layer-like interaction with a linearly stable, columnar, axisymmetric and dry vortex. We presented a general theory for this wave/mean flow interaction through the nonlinear critical layer theory and calculated the mean azimuthal and axial winds induced at the critical radius at the end of this interaction in the final stage. We here apply that theory to rapidly rotating geophysical vortices: tropical cyclones, cold-air mesocyclones and tornadoes. We find that the numerous assumptions invoked in that paper agree well with the reality of those intense vortices. We also find that in spite of a lack of moist-convection modelling, this dry vortex is fairly well accelerated at the critical radius by such a shear wave with a magnitude of order the square root of the damped-wave amplitude. The intensification level strongly depends on the aspect ratio, height of the system: rapid vortex and parent vortex, over core radius. The thinner the vortex is, the sharper the intensification is. This result is in sharp contrast to the numerous numerical simulations on VR wave/vortex interactions that yield a much smaller intensification of order the square of the wave amplitude. This weakly nonlinear approach nevertheless fails to model small vertical wavelength VR wave/vortex interactions for their related asymptotic expansions are divergent and for they yield strongly nonlinear VR waves coupled with evolving critical layers whose extent can no longer be considered as thin. 相似文献