摘要:

By means of a multiple-scale analysis of the shallow water equations for a uniformly rotating, stratified fluid, subject to a time-periodic advection over a small-amplitude topography, it is shown that the inclusion of quasi-nonlinear advection by the barotropic (tidal) current is a necessary ingredient of the dynamics, once the internal wave length, the barotropic tidal excursion amplitude and the topographic wave length are all of the same order of magnitude. The basic set of equations describing the generation of internal tides by the interaction of barotropic tidal currents and topography thus derived, is extended with damping both by bottom- and internal friction. The effect of bottom friction is parametrized in a Rayleigh damping term for each of the separate vertical modes, thereby allowing the vertical structure of the baroclinic tidal currents to remain expressible in terms of vertical modes. The spectral forcing equation for damped internal motions is then derived. Finally the characteristic roots (dispersion relation) of the homogeneous spectral equation are discussed and summarized in a dispersion diagram. It is shown that these consist in general of two damped gravity wave modes and a transient, the asymptotic regimes of which are discussed. The transient gives rise, among other things, to baroclinic residual currents which are the subject of a second paper, whereas the structure of the quasi-nonlinear gravity wave modes is treated in a third part.

ISSN:0309-1929    

DOI:10.1080/03091928908208891

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The generation of topographically bounded internal tides and baroclinic residual currents is discussed for a linearly stratified fluid in the limit of small-amplitude topography and weak damping. It is shown that quasi-nonlinear advection by the barotropic tide generates a residual and higher harmonics, besides the ever present fundamental driving frequency in the internal motions. At all frequencies the along-isobath currents and the cross-isobath circulation arebottom intensified, the intensification being a function of the internal Rossby deformation radius. For a step topography the weak cross-isobath residual circulation has a characteristic three-cell structure with a down-slope bottom current at the position of the steepest slope, which is also the center of the along-isobath residual jet. In contrast to barotropic currents in the quasi-nonlinear regime, the baroclinic currents are exponentially bounded to the topography, rather than extending over a finite interval, in which thee-folding distance is the internal deformation radius.

ISSN:0309-1929    

DOI:10.1080/03091928908208892

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A simple model is presented for a two-layer fluid confined to a lake consisting of an inner and an outer basin of constant depths. The equations of motion separate and simple explicit solutions exist for inner and outer basins consisting of concentric circles. No assumption is required on the relative thickness of the two fluid layers and so an assessment can be made of the accuracy in this case of scalings based on upper layers of vanishing thickness. It is shown that although the scalings are useful in wide basins the frequencies of oscillations of narrow basins are a strong function of the upper layer depth, rapidly departing from the limiting value for vanishing thickness.

ISSN:0309-1929    

DOI:10.1080/03091928908208893

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The annual mean depth-integrated steric heightPand stream function ψ of the world ocean are calculated from a Sverdrup model with Hellerman and Rosenstein's (1983) annual mean wifids. The parameterization of friction is unspecified, but friction is assumed to be important only along western boundaries. A simple rule, based on Sverdrup interior flow and geostrophy of longshore flow along western boundary currents, is used to calculatePat the inshore edge of the western boundary current. The substantial predicted longshore gradients ofPdrive the model western boundary currents against friction, independent of frictional parameterization. One corollary is an “Island Rule”–an explicit expression for circulation around an island, in terms of wind stress, again independent of frictional parameterization. The circulations around Australasia, New Zealand and Malagasy are calculated as 16±4 Sv, 29±v, and 4±3 Sverdrups respectively. Inclusion of island effects result in more accurate flow estimates in the Southern Hemisphere than have previously been obtained from Sverdrup models.

ISSN:0309-1929    

DOI:10.1080/03091928908208894

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The effects of dissipation on the weakly nonlinear interactions between a marginally unstable baroclinic wave and a resonant topographic wave are examined using multiple time scales in a quasigeostrophic, two-layer model on a midlatitude beta plane channel. The lower boundary is characterized by sinusoidal bottom topography. The dissipation is chosen as one or a combination of the following forms: Ekman dissipation at the lower and upper boundaries which may be chosen different in strength, interfacial Ekman dissipation, thickness damping, and potential vorticity damping (PVD).

ISSN:0309-1929    

DOI:10.1080/03091928908208895

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor