摘要:

The instability of a swift and narrow current flowing eastward in the mid-latitude open ocean is studied with a multi-mode quasi-geostrophic model. Linear analysis shows that there exist two groups of unstable waves: short and long. The phase velocity of the former is much larger; the growth rate of both is almost proportional to the maximum speed of the baroclinic current. As the width of the jet increases, the growth rate of the long waves increases and that of the short waves decreases.

ISSN:0309-1929    

DOI:10.1080/03091929608213633

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A finite amplitude theory is developed for the evolution of marginally unstable modes for a mesoscale gravity current on a sloping bottom. The theory is based on a nonquasigeostrophic, baroclinic model of the convective destabilization of gravity currents which allows for large amplitude isopycnal deflections while filtering out barotropic instabilities. Two calculations are presented. First, a purely temporal amplitude equation is derived for marginally unstable modes not located at the minimum of the marginal stability curve. These modes eventually equilibrate with a new finite amplitude periodic solution formed. Second, the evolution of a packet of marginally unstable modes located at the minimum of the marginal stability curve is presented. These two models are dramatically different due to fundamental physical differences. For marginally unstable modes not located at the minimum of the marginal stability curve, it is possible to determine the evolution of a single normal mode amplitude. For the marginally unstable mode located at the minimum of the marginal stability curve the entire gravity current forms a nonlinear critical layer leading to an infinity of coupled amplitude equations. If this system is truncated, on anad hocbasis, to include only the fundamental harmonic and its accompanying mean flow, there exists a steadily-travelling solitary cold-core eddy solution.

ISSN:0309-1929    

DOI:10.1080/03091929608213634

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The nesting of one ocean model inside another is a developing technique for the study of detailed local circulation which is dependent on the larger scale flow. Coupled versions of such models are often not possible because of the computational cost so we investigate the passive behaviour of a nested model forced at its open boundaries by an outer model. Our actual example is a limited area model of the Vema Channel region of the South Atlantic, forced by the Fine Resolution Antarctic Model. We show that simulations much in excess of a year are likely to fail, or drift excessively, unless all parameters in the inner and outer models are the same. The best nested simulation possible still drifts significantly from the outer model, even with identical physics, grid-sizes and bathymetry, because of the modification of the equations of motion required at the boundary and the near impossibility of using actual outer model boundary forcing at each timestep. Choosing open boundaries where flow tends to be cross-boundary rather than parallel to it is likely to reduce numerical problems.

ISSN:0309-1929    

DOI:10.1080/03091929608213635

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Linearised hydromagnetic stability problems can often be formulated as eigenvalue problems with solutions proportional to exp[-iωt] whereiω=p+isis the eigenvalue andtis time. For a hydromagnetic system in the geometry of an infinite cylindrical annulus, we have revealed the presence of double eigenvalues at various locations in the parameter (Λ,n)-space. Here, Λ is the Elsasser number, a non-dimensional inverse measure of the magnetic diffusivity, andnis the axial wavenumber of the field and flow. We have found that tracking a particular eigenvalue around a closed path in parameter space does not necessarily return the original eigenvalue. This phenomena was examined by Jones (1987), in the context of Poiseuille flow. Jones showed that such changes are due to the presence of double (and multiple) eigenvalue points lying within the closed path. Thus, care must be taken when following any eigenvalue in parameter space since the final result can be path dependent. In the hydromagnetic problem, we find that the most unstable mode (i.e. the mode we are most interested in) often behaves in this manner. If great care is not taken when using the methods (such as inverse iteration) that follow a single eigenvalue and the effects of double eigenvalues accounted for, it is possible to mistakenly overestimate critical parameter values. Another consequence of this phenomenon is that classifying magnetic instabilities when Λ ∼ O(1) as either ideal or resistive is not possible. This distinction only makes sense in the perfectly conducting limit Λ → ∞.

ISSN:0309-1929    

DOI:10.1080/03091929608213636

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We consider free shear layers in a rapidly rotating fluid layer defined by |z| < 1. Atz= ± 1 we impose the velocity v =Fs(x) ± Fa(x). Discontinuities inFsandFathen turn out to induce vertical shear layers throughout the fluid. A discontinuity inFsinduces two layers of thicknessesE¼andE⅓; a discontinuity inFainduces one layer of thicknessE⅓. The Ekman numberEis an inverse measure of the rotation rate. We demonstrate that these shear layers are in fact the same as the classical Stewartson layers in cylindrical geometry. We next consider the effect of imposing a magnetic field across these shear layers. In the limit of small magnetic Reynolds numberRm, we demonstrate that for Λ≥E⅓all of the previous shear layer structure is ultimately suppressed, where the modified Elsasser number Λ(≡Rm) is a measure of the strength of the imposed field. The various transitions between the non-magnetic and the fully magnetic regimes are discussed in some detail.

ISSN:0309-1929    

DOI:10.1080/03091929608213637

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

An asymptotic solution of the magnetic induction equation in a given velocity field is constructed for large magnetic Reynolds numbers. Initially localized distributions of the magnetic field are considered. The leading term of the asymptotics is found. The expansions are proved to be rigorously valid over a finite time interval. Estimates for the residuals are given. The results are illustrated by some examples: the Hubble flow with a linear dependence of the velocity on coordinates, andABCtype flows. The solutions in these cases are expressed in terms of elementary functions.

ISSN:0309-1929    

DOI:10.1080/03091929608213638

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

By W. Munk, P. Worcester and C. Wunsch, Cambridge University Press, 1995, 433pp., US$59.95, UK$45, hardbound (ISBN 0-521-47095-1).

ISSN:0309-1929    

DOI:10.1080/03091929608213639

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor