摘要:

It is shown that the inclusion of the nonlinear terms in the equations of motion of a coupled density front of zero potential vorticity results in wave solutions which merely propagate with time. The linear theory, on the other hand, predicts an exponential temporal growth. The nonlinear equation admits steady solutions representing standing waves whereas if the nonlinear terms are omitted no steady solutions exist. The general initial value problem is difficult to solve numerically since the linear problem is ill posed.

ISSN:0309-1929    

DOI:10.1080/03091928608210095

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

We study the nonlinear stability of MHD waves propagating in a two-dimensional, compressible, highly magnetized, viscous plasma. These waves are driven by a weak, shear body force which could be imposed by large scale internal fluctuations present in the solar atmosphere.

ISSN:0309-1929    

DOI:10.1080/03091928608210096

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Longuet-Higgins (1964) originally recognised that the energy flux defined by pressure work from the equations of motion was not the same as the mean energy density times the group velocity for planetary waves on a beta-plane. This paper addresses a similar paradox for linear, long period edge waves on an arbitrary shaped (in the offshore direction) straight continental shelf. The approach is to first examine a wavetrain solution to the problem and then to use a multiple scale argument which results in a solution as a group of waves modulated about a central frequency [sgrave] and wavenumberk. The paradox is resolved in both instances by noting that a divergence free quantityJcan be included in the energy conservation equation to establish an equivalence between the two definitions of mean energy flux. For the wavetrain solutionwherexis the offshore direction,h(x) is the depth,A(k,x) is the complex wave displacement, [sgrave] is the frequency andkis the wavenumber. For the modulated group, the quantity J is given bywhereB=B(Y, T) is part of the edge wave complex amplitudeA(k, x)B(Y, T) andY, Tare the long longshore and time variables respectively. We discuss which energy flux definition is preferable in a given situation.

ISSN:0309-1929    

DOI:10.1080/03091928608210097

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Generalizing an idea of Arnold, we discuss the hydrodynamic stability à la Lyapunov of solitary water-waves which are rotational solutions of the Euler equation, travelling with constant phase speed[ctilde]T. In the reference frame moving with the wave profile, the solitary wave is described by a solution ofWe show that ifas in other applications of Arnold's idea, and ifat the air sea surface, a rather realistic request, the system is stable for (a) small vertical or horizontal space scale perturbations; (b) perturbations with a very long vertical space scale and very small horizontal space scale or with a very long horizontal space scale and very small vertical space scale. Finally we show that the system is also stable for irrotational perturbations.

ISSN:0309-1929    

DOI:10.1080/03091928608210098

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor