ISSN:0309-1929    

DOI:10.1080/03091929408203657

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

We examine the stability of two-layer geostrophic flows with large displacement of the interface. The depth of the upper layer is assumed much smaller than the total depth of the fluid. It is proven that all westward and weak eastward flows are stable with respect to disturbances whose wavelengths is of the order of, or longer than the width of the flow. It is further demonstrated that westward flows are (locally) unstable with respect to short disturbances.

ISSN:0309-1929    

DOI:10.1080/03091929408203658

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

We use numerical simulations based on the shallow water equations for a homogeneous fluid on anf-plane to study the evolution of a cyclonic eddy over a topographic slope. The results are compared with analogous simulations using the nondivergent approximation in order to determine the effect of the free-surface vortex stretching terms. The simulations use a geometry and parameters related to the experimental results of Carnevaleet al.(1991). We find that this vortex stretching produces a significant reduction in the eddy speed. Our numerical results are supported by theoretical analyses, largely set in the quasi-geostrophic context.

ISSN:0309-1929    

DOI:10.1080/03091929408203659

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

This paper uses the ‘natural’ method proposed by Valliset al.(1989) to determine stable flow configurations and investigates the inviscid dynamics of the barotropic shear-layer with a hyperbolic tangent velocity profile in a channel. The ‘modified’ dynamics provides a simplified picture of the flow transitions not marred by small scale vorticity oscillations found in the ‘actual’ dynamics. The transitions to quasi-steady or steady-states are characterized in physical space by vortex pairing and the final stable state is a single vortex occupying the entire channel length if the initial conditions allow an even wavenumber to dominate. Otherwise, when an odd wavenumber grows, the final state is constrained by higher order vorticity invariants and does not quite fill the channel. For initial conditions favoring even wavenumbers, single wave quasi-steady states tend to agree with nonlinear analytical predictions. The modified dynamics does well at capturing these states.

ISSN:0309-1929    

DOI:10.1080/03091929408203660

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

ISSN:0309-1929    

DOI:10.1080/03091929408203661

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

An analytical spectral model of the barotropic divergent equations on a sphere is developed using the potential-stream function formulation and the normal modes as basic functions. Explicit expressions of the coefficients of nonlinear interaction are obtained in the asymptotic case of a slowly rotating sphere, i.e. when the normal modes can be expressed as single spherical harmonics.

ISSN:0309-1929    

DOI:10.1080/03091929408203662

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

In this paper, two problems of quasi-resonant interactions among barotropic Rossby waves over a two-wave topography are investigated. The first one is the study of three-wave quasi-resonance (TWQR) among Rossby waves for zonal wavenumbers 1–3 in which zonal waves 1 and 3 travel westward and eastward respectively, and zonal wave 2 is a quasi-stationary wave forced by two-wave topography (TWT). It is found that, in the absence of TWT, three-wave quasi-resonance will induce a nearly 7–10 day oscillation. However, under the forcing of TWT, a remarkable 30–60 day low-frequency oscillation (LFO) can be excited through TWQR, and found to depend considerably upon the initial amplitudes of these waves and the latitude. The second is the study of four-wave quasi-resonance (FWQR) among Rossby waves for the zonal wavenumbers 1–4 and same meridional wavelength over a two-wave topography that is independent of the meridional coordinate. It is shown that for the small meridional wavelength the four-wave quasi-resonance without forcing can lead to a 30–60 day LFO, which relies equally upon the initial amplitudes and latitude. However, once the forcing of TWT is considered, such a LFO is greatly affected by the zonal basic westerly wind and remains within the 30–60 day period band under favorable conditions. Moreover, in the limit of large meridional wavelength where a quasi-biweek oscillation only appears for the case without forcing, a 30–60 day LFO can occur for zonal waves 1–3 in the presence of TWT and under a moderate zonal basic westerly wind. This indicates that a moderate setting of zonal basic westerly wind favors a 30–60 day LFO.

ISSN:0309-1929    

DOI:10.1080/03091929408203663

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

A nonlinear two-layered fluid system on a variable bottom with freely moving upper surface and abrupt density change at the interface is considered. The two stably stratified layers with constant densities are assumed to be immiscible. Starting from the continuity and the mometum equations of an incompressible inviscid fluid for each layer and associated boundary and transition conditions at the free upper surface, the interface and the bottom surface, vertically averaged equations are deduced that incorporate nonlinear advection and dispersion. The approximate equations are deduced by scaling the governing equations accordingly and by using a limit analysis for small aspect ratios (shallowness) and small amplitude disturbances. The limiting equations extend known model equations and include finite amplitude nonlinearities, dispersion and variable topography. In a second step viscous effects and wind forcing are also incorporated.

ISSN:0309-1929    

DOI:10.1080/03091929408203664

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

The depth-averaged hydraulic equations augmented with a suitable bed-load sediment transport function form a closed system which governs the one-dimensional flow in an alluvial river or channel. In this paper, it is shown that this system is hyperbolic and yields three families of shock-wave solutions. These are determined to be temporally stable in restricted regions of the (H,F0)-plane, via the Lax shock inequalities. Further, it is demonstrated that this criterion is equivalent to the energy dissipation criterion developed by Needham and Hey (1991).

ISSN:0309-1929    

DOI:10.1080/03091929408203665

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

We investigate the properties of some strongly nonlinear convection cells which may occur in a rapidly rotating fluid layer. Although the stability properties of such layers have been extensively studied, most of the theoretical work concerned with this topic has been based upon either linear or weakly nonlinear analyses. However, it is well known that weakly nonlinear theory has a limited domain of validity for if the amplitude of the convection cells becomes too large then the mean temperature profile within the layer is dramatically perturbed away from its undisturbed state and the assumptions underpinning weakly nonlinear theory break down. It is the case for most fluid stability problems that when the stage is reached that the mean flow is significantly altered by the presence of instability modes, then analytical progress becomes impossible. The problem can then only be resolved by a numerical solution of the full governing equations but we show that for the case of convection rolls within a rapidly rotating layer this sequence of events does not arise. Instead, the properties of large amplitude convection rolls (which are sufficiently strong so as to completely restructure the mean temperature profile) can be determined by analytical methods. In particular, the whole flow structure can be deduced once a single, very simple eigenproblem has been solved. This solution enables us to discuss how large amplitude cells can significantly affect the characteristics of the flow leading to greatly enhanced heat transfer across the layer.

ISSN:0309-1929    

DOI:10.1080/03091929408203666

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor