摘要:

A series of laboratory experiments are conducted concerning an azimuthal jet of a linearly stratified rotating fluid in a cylindrical geometry. The jet is characterized by vertical and horizontal shear and the question of the stability of the flow is considered experimentally. The jet is driven by a source-sink method characterized by a volume flow rate of strengthQ. BecauseQhas no direct geophysical significance a combined external set of dimensionless parameters is introduced. These include the Rossby, Richardson and Ekman numbers, the jet aspect ratio and two geometrical parameters.

ISSN:0309-1929    

DOI:10.1080/03091929208225237

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

A quasi-geostrophic numerical model of flow in a rotating channel is integrated under conditions typical of laboratory experiments with an internally heated annulus system. Compared to a laboratory experiment, or a full Navier-Stokes simulation, the quasi geostrophic numerical model is a simple system. It includes nonlinear interactions, dissipation via conventional parameterizations of Ekman layers and internal diffusion, and a steady forcing term which represents heating near the centre of the channel and cooling near both sides. Explicit boundary layers, cylindrical geometry effects, horizontal variations in static stability and variations in conductivity and diffusivity with temperature are all absent, and ageostrophic advection is incompletely represented. Nevertheless, over a range of parameters, flows are produced which strongly resemble those seen in the laboratory thus suggesting that the most important physical processes are represented. The numerical model is used to map out a regime diagram which includes examples of steady flows, flows with periodic time dependence (wavenumber vacillations) and flows which are irregularly time dependent.

ISSN:0309-1929    

DOI:10.1080/03091929208225238

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

This paper is concerned with the nonlinear stability of two-dimensional quasigeostrophic motions in atmosphere and oceans. By using an accurate a prior estimate method, some nonlinear criteria are obtained, which can be applied to the perturbations of both the initial conditions and parameters in the models rather than those of the former only. It is also shown that the conservation of mass plays an important role in presenting some better criteria of nonlinear stability. Some steady flows are presented, which can be claimed to be nonlinear stable by only the criteria established in this paper. The method of Shepherd (1988) on bounding the finite-amplitude growth of disturbances to unstable flows is also developed by considering the perturbation of parameters.

ISSN:0309-1929    

DOI:10.1080/03091929208225239

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The change of the attractor dimension (Kaplan-Yorke dimension) with an increase in the number of modes included in the Fourier expansion is investigated for a quasi-geostrophic two-layer system with topographic forcing. A particular case has been chosen such that the attractor is represented by a single “weather regime”, consisting of weak fluctuations around a fixed flow pattern. In this respect, the large-scale flow structure isleast“chaotic”. Anticipation is that this kind of organized flow may be described by a low dimensional attractor. No convergence of the dimension is found by increasing the total number of Fourier modes up to 210. The result suggests that the quasi-geostrophic system cannot be reduced to a low-dimensional dynamical system in general. The crucial importance of a large number of small scale modes to predict the planetary scale dynamics, is suggested.

ISSN:0309-1929    

DOI:10.1080/03091929208225240

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

We study the coaxial collision between two modons by using a point vortex formulation due to Zabusky and McWilliams. This leads to a set of ordinary differential equations for the motion of two pairs of point vortices, each of which make up a finite-sized dipole. Due to the symmetry present in the coaxial system, these equations reduce to a planar Hamiltonian system which can be studied analytically. We study the nature of this system and the bifurcations which occur in order to classify the behavior of the point vortices as a function of parameters. We show all the possible types of collisions which occur and discuss their relevance to collisions between two modons which are initially far apart.

ISSN:0309-1929    

DOI:10.1080/03091929208225241

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Quadrupole modon solutions of the barotropic vorticity equation on a sphere are presented. These modons can be made stationary in a westerly solid-body rotation. The sphere is divided into an inner and outer region separated by a boundary circle. There are constraints on the wavenumbers of the solutions in the inner and outer region and on the radius of the circle. Then a quadrupole and a monopole of arbitrary strength can coexist with a dipole, and tripoles can be constructed. These solutions are compared with earlier results for the beta plane and the sphere. Also an equivalent barotropic model with imposed zonal background shear is considered.

ISSN:0309-1929    

DOI:10.1080/03091929208225242

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The theory for waves on a buoyant fluid conduit in a more viscous outer fluid is extended to include a visco-elastic outer fluid. The external fluid is treated as a linear Kelvin-type visco-elastic medium and a wave evolution equation is derived. This equation is identical to the purely viscous case with the exception of a new term representing the elastic effects. A conservation law is derived and used in an analytic treatment for a slowly-varying solitary wave (given initially by the exact solution to the purely viscous case) for the case of small, but non-zero, elasticity. The theory shows that the wave amplitude will decay and a shelf, required for the conservation of mass, will develop behind the wave. Numerical solutions of the evolution equation support the analytic approximation. Laboratory experiments show qualitative agreement with the analytic and numerical development. Geophysical applications suggest that these effects may be most important for melt migration in the asthenosphere.

ISSN:0309-1929    

DOI:10.1080/03091929208225243

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

We have studied the problem of strongly time-dependent, two-dimensional, incompressible, infinite Prandtl number thermal convection in an aspect-ratio five box for a non-Newtonian power-law rheology and a heated from below configuration, as applied to mantle dynamics. The convection equations are solved by means of a characteristics-based method with a Lagrangian formulation of the total derivative in the energy equation. Iterations are required at each time step for solving the nonlinear momentum equation. Bicubic splines are used for the spatial discretization. The transition from mildly time-dependent to the strongly chaotic or turbulent regime, in which the plumes become disconnected, occurs at much lower Nusselt numbers (Nu), between 20 and 25, than for Newtonian rheology. TheNuversus Rayleigh number(Ra)relationship displays a kink at this transition. Rising non-Newtonian plumes exhibit much greater curvature in their ascent than Newtonian ones and are strongly attracted by descending currents at the top. The viscosity field becomes strongly mixed and assumes a granular character in the turbulent regime. Horizontal spectral decomposition of the viscosity field outside the boundary layer shows that in the chaotic regime the fluctuations about the mean viscosity do not vary by more than an order of magnitude for one and a half decade in horizontal wavenumber. Vorticity fields produced by non-Newtonian convection are much more intense than Newtonian. Increasing the power law index sharpens the chaotic behavior of the flow with highRa.

ISSN:0309-1929    

DOI:10.1080/03091929208225244

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

As a model for convection in the Earth's core we study the linear stability of a rapidly rotating electrically conducting spherical fluid shell, permeated by a toroidal magnetic field B. We look at the effect of introducing a stably stratified layer into the fluid adjacent to the core-mantle boundary (CMB). For values of the Elsasser number (a non-dimensional measure of the magnetic field strength), Λ ≪ 0(1), convection can penetrate significantly into the stable layer. In this weak field case, the constraints of the Taylor-Proudman theorem cause convection to become columnar in structure. As Λ is decreased the azimuthal wave number m, corresponding to the most unstable mode, increases. For Λ = O(1), convection is still unaffected by the introduction of a stable layer, but is no longer columnar. For Λ ≫ O(1), we find that convection becomes concentrated in the unstably stratified region. Except in the low magnetic field strength regime, our findings agree with previous work of Boda (1988) and Ševčík (1989), who studied a similar problem with plane-layer geometry, and with Fearn and Richardson (1991) who considered the cylindrical case.

ISSN:0309-1929    

DOI:10.1080/03091929208225245

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

A model for homogeneous anisotropic incompressible turbulence is proposed. The model generalizes the GISS model of homogeneous isotropic turbulence; the generalization involves the solution of the GISS equations along a set of integration paths in wavenumber (k-) space. In order to make the problem tractable, these integration paths (“cascade lines”) must be chosen in such a way that the behaviour of the energy spectral function along different cascade lines should be reasonably similar. In practice this is realized by defining the cascade lines as the streamlines of a cascade flow; in the simplest case the source of this flow may be identified with the source function of the turbulence. Owing to the different approximations involved, the resulting energy spectral function is not exact but is expected to give good approximative values for thebulkquantities characterising the turbulent medium, and for the measure of the anisotropy itself in particular.

ISSN:0309-1929    

DOI:10.1080/03091929208225246

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor