摘要:

Recent numerical simulations reveal remarkably different behavior in rotating stably stratified fluids at low Froude numbers for finite Rossby numbers as compared with the behavior at both low Froude and Rossby numbers. Here the reduced low Froude number limiting dynamics in both of these situations is developed with complete mathematical rigor by applying the theory for fast wave averaging for geophysical flows developed recently by the authors. The reduced dynamical equations include all resonant triad interactions for the slow (vortical) modes, the effect of the slow (vortical) modes on the fast (inertial gravity) modes, and also the general resonant triad interactions among the fast (internal gravity) waves. The nature of the reduced dynamics in these two situations is compared and contrasted here. For example, the reduced slow dynamics for the vortical modes in the low Froude number limit at finite Rossby numbers includes vertically sheared horizontal motion while the reduced slow dynamics in the low Froude number and low Rossby number limit yields the familiar quasigeostrophic equations where such vertically sheared motion is completely absent-in fact, such vertically sheared motions participate only in the fast dynamics in this quasigeostrophic limit. The use of Ertel's theorem on conservation of potential vorticity is utilized, for example, in studying the limiting behavior of the rotating Boussinesq equations with general slanted rotation and unbalanced initial data. Other interesting physical effects such as those of varying Prandtl number on the limiting dynamics are also developed and compared here.

ISSN:0309-1929    

DOI:10.1080/03091929808208993

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

The linear stability of an idealized western boundary current is studied with the emphasis on the effect of curvature. The barotropic quasigeostrophic vorticity equation is modified to incorporate the effect of small curvature. For eastward flow, the curvature increases the growth rate of the unstable mode that has the peak of the eigenfunction on the offshore side of the flow axis, while the growth rate of the unstable mode with its peak on the onshore side of the flow decreases. The curvature is found to shift the phase of the unstable waves, resulting in a change of the Reynolds stress, and a consequent change of the growth rate. The positive curvature enhances the dependence of the critical Reynolds number on the flow orientation. For the flow that has zero velocity on the coast, the cyclonic curvature is found to decrease the critical Reynolds number when the jet is northeastward.

ISSN:0309-1929    

DOI:10.1080/03091929808208994

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

Numerical studies are conducted of symmetric flows in an infinite horizontal fluid layer with a constant horizontal temperature gradient. A modified rotating Hadley-cell flow configuration is devised by adopting the free-slip and thermally insulated upper boundary. For this model, an analytic solution is available as the basic state. A finite volume numerical procedure is utilized to integrate the fully nonlinear Navier-Stokes equations over broad parameter ranges of the thermal Rossby number,Ro, and the Richardson number,Ri. TheRo—Ridiagram illustrates several flow regimes. In the present framework, both the symmetric instability and Benard-type convective instability are found to occur. These are associated respectively with a negative potential vorticity in the interior and a gravitationally unstable vertical temperature gradient in the thermal boundary layer. The detailed flow structures are computed to reveal the characteristic features of these two instabilities. Time dependent responses are analyzed to examine the dominant mechanism for two-dimensional flow developments. The interaction of the symmetric flows with the basic-state flow field is scrutinized.

ISSN:0309-1929    

DOI:10.1080/03091929808208995

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

We present a numerical solution of the magnetic induction equation in a spherical fluid shell, with an insulator inside and outside. Prescribing an axisymmetric, time-dependent, chaotic flow, we find that the magnetic field appears to grow on the fast advective, rather than on the slow diffusive time scale. We demonstrate how this may be reconciled with the theorem of Bondi and Gold (1950), that the potential field in these insulators inside and outside the shell cannot be amplified on the fast time scale, by having the field become increasingly contained within the shell with increasing magnetic Reynolds number. Thus, as the Bondi-Gold theorem becomes more and more applicable, there is indeed less and less external field being amplified. This is in precise agreement with the conjecture of Rädler (1982) that the resolution would be to have an “invisible dynamo,” one having no external field. Finally, we consider some of the implications of this adjustment for the different symmetries of the field (dipolar versus quadrupolar) and the flow (uversus—u).

ISSN:0309-1929    

DOI:10.1080/03091929808208996

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

This paper concerns the self-excitation of large-scale flow patterns in rotating stratified spherical bodies. The Anisotropic Kinetic Alpha-effect due to the small-scale turbulence is included into the mean-field motion equation and the stability to the global flow excitations is studied by solving the linear eigenvalue problem. If the magnitude of the AKA-effect exceeds some critical value, the mean-flow instability onsets. The main finding is the preference of nonaxisymmetric flow patterns with the azimuthal wave numberm= 1. The symmetry relative to the equator depends on the rotation rate and is much less definite. For Taylor numbers up to Ta ≃ 106, the symmetric flow patterns relative to the equatorial plane are slightly preferred. For faster rotation, the antisymmetric flow has somewhat smaller critical “dynamo number” for the excitation.

ISSN:0309-1929    

DOI:10.1080/03091929808208997

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor