摘要:

It is shown that a coastal density current in a rotating system is unstable to downstream wave disturbances when the mean potential vorticity increases towards the (vertically-walled) coast and when the mean current vanishes there. Other new instability modes are also found which do not require the potential vorticity extremum of quasi-geostrophic theory. All the instabilities in our equivalent one-layer model release mean kinetic energy and most of them release mean potential energy, but an increase of the latter can occur under certain circumstances.

ISSN:0309-1929    

DOI:10.1080/03091928208221734

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

The accuracy to which the vertical structure of tidal currents can be predicted is examined. Theoretical models for current structure are developed employing (a) a constant eddy viscosityE = ϵand (b) an eddy viscosity varying linearly with height above the sea bedz;E(z)=βz. By requiring these models to satisfy the commonly accepted quadratic friction law, the condition ϵ>½k is deduced wherekis the bed friction coefficient,Wa representative velocity andDthe depth.

ISSN:0309-1929    

DOI:10.1080/03091928208221735

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

The low Rossby number flow in a rotating cylinder with an inclined bottom, of small slope, is examined when part of the lid of the container is rotating at a slightly different rate. The resulting flow is calculated numerically by solving the governing equations for the two-dimensional geostrophic motion which approximates the flow in most of the fluid including the inertially-modifiedE¼-layers. The presence of ageostrophic regions, on the container walls and beneath the velocity discontinuity on the lid, is accounted for in the governing equations and their boundary conditions. This study supplements previous work on this configuration, in which the zero Rossby number flow was calculated and experimental results were presented, by enabling a direct comparison to be made between the results of the low Rossby number theory and the experiments. The numerical results for a range of Rossby and Ekman numbers compare well with those from the experiments despite a severe limitation on the size of the Rossby number arising from the analysis in the ageostrophic part of the detached shear layer.

ISSN:0309-1929    

DOI:10.1080/03091928208221736

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

Merilees and Warn's (1975) nonlinear interaction analysis of two-dimensional nondivergent flow is extended to examine the quasi-geostrophic two-layer model. Two sets of triads exist in this model (Salmon, 1978). The purely barotropic triads are the same as the triads examined by Merilees and Warn. Baroclinic-barotropic triads are found to exchange more energy or potential enstrophy with smaller or larger scales depending on the scale of motion as compared with the internal Rossby deformation radius and the relative wavenumber position of baroclinic and barotropic components.

ISSN:0309-1929    

DOI:10.1080/03091928208221737

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

The inertial motion of a free particle on a β-plane is studied here. Analytical solutions are found, and discussed in a phase diagram. Asymptotic cases are also given some attention. Eastward and westward drift velocities are computed analytically as a function of the parameter β and an angle of incidence. Particles which do not cross the equator always drift westward, while particles which cross the equator drift either eastward or westward or describe a stationary pattern. Trajectories are also discussed on a rotating globe. Finally, the results are related to Lagrangian studies and to the stability analysis of zonal equatorial currents.

ISSN:0309-1929    

DOI:10.1080/03091928208221738

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

Nonlinear interactions of deviatoric stress components and the velocity field occur in all dynamic flows where convected elasticity is accounted for. By incorporating a linear Maxwellian constitutive relation (Oldroyd ‘B’ type) into a finite-amplitude convection model we quantify the magnitude of some of the effects of these nonlinear interactions. For viscoelastic flows the relevant nondimensional parameter is the ratio of viscoelastic constitutive relaxation time constant, λ1, to the basic flow process time. The Rayleigh number, Ra, and the nondimensional ratio of λ1to thermal conduction time, τc, are part of the parameter space investigated. However, shorter basic flow time scales than that for thermal equilibration are of interest since most viscoelastic fluids have relatively small values of λ1The ratio of λ1to buoyant time [bcirc], or λ1/[bcirc], is, therefore, a pertinent parameter. Using both lithospheric and aesthenospheric values for λ1, the ratio appropriate to mantle convection is roughly bounded by O(1)[bcirc]>λ1/[bcirc]>O(10−6). Employing these bounds and computing low Rayleigh number time-dependent convective flows in a two-dimensional box, it is demonstrated that viscoelasticity has a negligible influence on quasi-steady heat transport even for λ1/[bcirc]∼O(1) For any time-dependent behavior with time scales as short, or shorter than, the buoyant time, [bcirc], viscoelasticity might be important to the local exchange of mechanical energy. The recoverable strain energy in the descending portion of the lithosphere is comparable to the local viscous dissipation. The magnitude of this recoverable component of shear is proportional to λ1/[bcirc].

ISSN:0309-1929    

DOI:10.1080/03091928208221739

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

Angular momentum driven instabilities in a stratified differentially rotating star are investigated. In the strong buoyancy limit axisymmetric instabilities of the Goldreich-Schubert type are the most important. A detailed discussion of the linear and small amplitude theories at an arbitrary latitude is given. The bifurcation to finite amplitude steady modes is typically transcritical, and occurs whenever the angular momentum or its gradient is neither parallel not perpendicular to local gravity. Such misalignments enhance the time scale for transport of angular momentum by the Goldreich-Schubert instability. Depending on the turbulent viscosity produced by secondary shear instabilities time scales as short as the Kelvin-Helmholtz time scale are possible.

ISSN:0309-1929    

DOI:10.1080/03091928208221740

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

The modal expansion procedure has been used to analyze penetrative convection that arises when a thin unstable layer is embedded between two stable regions. The Boussinesq approximation is applied in which the effect of compressibility and stratification are neglected. Various calculations have been made, with one and two modes, for Rayleigh numbers ranging from the critical value to more than 105times critical. The effect of decreasing the Prandtl number has also been investigated.

ISSN:0309-1929    

DOI:10.1080/03091928208221741

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor