摘要:

Previous descriptions of the turbulent decay of an internal soliton have been based on an adiabatic assumption in which the soliton parameters continuously change in time in response to the dissipation. A complete leading order description of a decaying internal soliton including both horizontal and vertical dissipation is given. It is shown that the adiabatic ansatz fails to fully describe a decaying internal soliton under the influence of weak dissipation. Physically, the breakdown is the consequence of the fact that an adiabatically decaying internal soliton is unable to simultaneously satisfy averaged energyandmass balance relations. An extended region with vertical momentum flux develops behind the decaying soliton in order to compensate for the additional mass lost in the adiabatically decaying internal soliton. The leading order evolution of this extended region is described as is its connection to the stream function field associated with the internal soliton. The magnitude of the vertical flux associated with this region scales linearly with the dissipation parameters. The transition of this extended region back to zero is accomplished through the formation of a spatially decaying packet of linear internal gravity waves.

ISSN:0309-1929    

DOI:10.1080/03091929708208988

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

In this paper we explore how temporal variability arises through successive bifurcations of the symmetric wind-driven double gyre circulation as lateral friction is decreased in 1.5-layer and 2-layer quasi geostrophic models. In the 1.5-layer model, the symmetric double gyre flow becomes unstable to symmetry breaking stationary instabilities, leading to asymmetric flows. These asymmetric solutions subsequently destabilize to two sets of barotropic oscillatory modes, introducing an intermonthly and interannual time scale, respectively. In the 2-layer model, the symmetric double gyre solution becomes unstable to baroclinic oscillatory instabilities, giving rise to near annual temporal variability. The asymmetric solutions which appear through symmetry breaking at smaller lateral friction, are in this case all unstable.

ISSN:0309-1929    

DOI:10.1080/03091929708208989

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

Simple attractive sets of a viscous incompressible fluid on a sphere under quasi-periodic polynomial forcing are considered. Each set is the vorticity equation (VE) quasi-periodic solution of the complex (2n+ 1)-dimensional subspaceHnof homogeneous spherical polynomials of degreen. The Hausdorff dimension of its path being an open spiral densely wound around a2n-dimensional torus inHn, equals to 2n. As the generalized Grashof numbGbecomes small enough then the basin of attraction of such spiral solution is expanded fromHnto the entire VE phase space. It is shown that for givenG, there exists an integernGsuch that each spiral solution generated by a forcing ofHnwithn≥nGis globally asymptotically stable. Thus, whereas the dimension of the fluid attractor under a stationary forcing is limited above byG, the dimension of the spiral attractive solution (equal to 2n) may, for a fixedG, become arbitrarily large as the degreenof the quasi-periodic polynomial forcing grows. Since the small scale quasi-periodic functions, unlike the stationary ones, more adequately depict the barotropic atmosphere forcing, this result is of meteorological interest and shows that the dimension of attractive sets depends not only on the forcing amplitude, but also on its spatial and temporal structure.

ISSN:0309-1929    

DOI:10.1080/03091929708208990

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

In this paper the nonlinear stability of two-dimensional Langmuir circulations in a fluid layer, stratified by vertical thermal and salinity gradients, is investigated when two distinct wavenumbers become simultaneously unstable. These instabilities take the form of O(2) symmetric Hopf-Hopf and Hopf-Steady bifurcations when the lateral boundary conditions are assumed to be periodic. In the analysis of the Hopf-Hopf bifurcation a disagreement with the group theoretic work of Chossatet al.(1986) is found. This difference is resolved by correcting the lattice of Isotropy subgroups presented by Chossatet al.(1986) and by considering the effects of the higher order terms in the amplitude evolution equations.

ISSN:0309-1929    

DOI:10.1080/03091929708208991

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

ISSN:0309-1929    

DOI:10.1080/03091929708208992

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor