摘要:

We consider nonlinear baroclinic instabilities of two-layer quasi-geostrophic flow in a rectilinear channel. The full potential vorticity equations are shown to possess a countable infinity of invariant wavenumber sets. Each set is composed of a particular pattern in wavenumber space in which many Fourier modes have zero energy. Solutions with initial conditions confined to a particular wavenumber pattern will remain forever in that pattern. There is also a general asymmetric state with non-zero energy in all wavenumbers. The final state of a long-time evolution calculation depends on initial conditions and internal stability.

ISSN:0309-1929    

DOI:10.1080/03091929008208930

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

摘要:

The propagation of solitary waves in a two-layer fluid with shear is studied in the long-wave shallow-water approximation. We show that, to the first order in the perturbation, the wave motion is described by the Korteweg-de Vries equation, whose coefficients now depend on the shear present.

ISSN:0309-1929    

DOI:10.1080/03091929008208931

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

摘要:

We provide sufficient conditions for nonlinear exponential stability of the compressible Bénard problem. In particular, by using a generalized energy analysis we prove stability whenever the Rayleigh number does not exceed a computable critical numberRc. The value ofRcis given for finite amplitude depth and for thin layers as well, and such values are compared with those already computed in the linear theory. In the limit of depth which goes to zero a necessary and sufficient condition for nonlinear stability of the Bénard problem is proved. The principle of exchange of stabilities is not required to hold.

ISSN:0309-1929    

DOI:10.1080/03091929008208932

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

摘要:

The Earth's outer core is modelled as thin layer of incompressible, inviscid, perfectly conducting fluid of constant density on a rotating plane in the presence of a variable ambient magnetic field. The fluid is bounded above by a spatially varying rigid lid. The interaction of the weak nonlinearities of the governing equations with the geometry of the model and its ambient magnetic field lead to positive feedback mechanisms for the generation of westward drift via the basic waves and the associated mean flows. The relevance of these results to the real core is discussed.

ISSN:0309-1929    

DOI:10.1080/03091929008208933

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor

摘要:

The stability of a horizontally stratified, electrically conducting fluid permeated by a uniform magnetic field aligned with the motion is investigated. The resulting linear stability problem for the special case of constant density gradient and linear shear in an unbounded fluid is reduced to the study of a third order differential equation in time. In the absence of dissipation, the linear shear eventually causes hybrid Alfvén-gravity waves to decay algebraically. The effect of the shear is to shorten the vertical length scale. So with the addition of even small diffusivity, dissipation is strongly stabilising and all modes eventually collapse exponentially, generally at a fast rate. The evolution from wave motion to exponential decay is examined for particular limiting cases. When the fluid is bounded by horizontal planes a nonlinear stability criterion is derived using the energy method.

ISSN:0309-1929    

DOI:10.1080/03091929008208934

出版商:Taylor & Francis Group    

年代:1990

数据来源: Taylor