摘要:

Numerical solutions of the Shallow-Water Equations with random, balanced initial conditions are analyzed for their persistence of balance. The standard for assessing balance is provided by the pressure and velocity potential fields determined diagnostically from the instantaneous streamfunction through the momentum divergence (i.e., gradient-wind balance) and omega relations of the Balance Equations. The amplitude, wavenumber and frequency content of both the balanced and unbalanced components are examined for a wide range of RossbyR, and FroudeF, numbers. These properties are found to be generally consistent with the estimates from a formal scaling analysis for smallRandF, and the scaling estimates are apt even when these parameters are not particularly small. The unbalanced component is dominated by higher order advective motion forR≪ 1 and by nearly linear inertia-gravity waves, whose frequencies are larger than those of the balanced component, for R ≫ l. These waves are forced by nonlinear interaction with advective terms formally of O(F2) which are neglected in the Balance Equations. These results support the hypotheses that the Balance Equations are an accurate model for the advective component of the flow (also called the slow manifold), broadly throughout the regimes of significant environmental rotation and/or stable stratification, and that the dynamical coupling is weak with the small-amplitude, fast wave component, especially so forR≪ l.

ISSN:0309-1929    

DOI:10.1080/03091929208228083

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

A primitive equation numerical model is used to examine various aspects of the formation of Taylor caps over a tall isolated seamount in a steady, rotating, nearly inviscid, stratified flow. The flow is characterized by four nondimensional parameters: the Rossby number,R0=U/fL; the Burger number,S=NH/fL; the fractional seamount height, δ = hm/H; and the aspect ratio, Δ =H/L. HereUis the uniform inflow velocity,fthe Coriolis parameter,Lthe horizontal length scale of the seamount,Nthe initial buoyancy frequency,Hthe ocean depth away from the seamount, andhmthe maximum height of the seamount above the otherwise flat bottom.

ISSN:0309-1929    

DOI:10.1080/03091929208228084

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

We impose a surface forcing on the 2D, Boussinesq, thermohaline equations in a rectangular domain, in the form of equatorially symmetric cosine distributions of salinity flux and temperature. This system may be seen as an idealization of the ocean thermohaline circulation on the global scale over intervals of centuries or millenia. Multiple steady states are found numerically. They reflect the competition between the opposite signs of the temperature and salinity-driven equatorially symmetric circulations. There are also pole-to-pole, equatorially asymmetric circulations. In the control space of the temperature and salinity-flux forcing amplitudes, these equilibria form two cusp catastrophes, and transitions between stable equilibria occur through several distinct bifurcations. These catastrophes can be reproduced in simple box models connecting stirred reservoirs through capillary pipes. This steady-state analysis may provide a framework for a better understanding of climatic transitions between different stable regimes of the ocean-atmosphere system.

ISSN:0309-1929    

DOI:10.1080/03091929208228085

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Direct numerical simulations of incompressible channel flow have been performed that explore the effects of centrifugally stable differential rotation on thermal convection (with gravity and rotation axes aligned). In order to provide greater correspondence to the interior regions of astrophysical accretion disks, especially to the convective solar nebula, we consider a gravity that varies linearly with distance from midplane and Keplerian rotation. We are restricted, however, to unrealistically low Reynolds numbers. Our findings are: (1) Statistical thermal convective properties depend almost exclusively on Peclet number and epicyclic frequency, regardless of the anisotropy induced by the shear. (2) At low Reynolds numbers, Reynolds stresses show the remarkable behavior of changing sign with increasing rotation rate, going from positive to negative shear production rates. Higher-Reynolds-number simulations tend to retain positive shear production rates to more rapid rotation. (3) At very rapid rotation, independent of Reynolds number, the flow becomes quasi-two-dimensional by losing streamwise variation in one or more of its fluctuating variables (especially the vertical velocity). At this point the simulation results become unreliable. These results suggest that convection in accretion disks is characterized by very long azimuthal wavelengths, and that, in some circumstances, Reynolds stresses can feed turbulence kinetic energy to the mean flow in contradiction to the conventional eddy-viscosity ansatz.

ISSN:0309-1929    

DOI:10.1080/03091929208228086

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The problem of magnetic field generation by a flow of electrically conducting fluid parallel to a rigid plate is considered. It is shown that growing magnetic fields occur when the plate exhibits variations of the electrical conductivity in the streamwise direction of sufficient strength. In particular the case of sinusoidal variations is studied. The magnetic Reynolds number for dynamo action increases with decreasing conductivity of the plate and with decreasing amplitude of its modulation. Possible applications to geophysical problems are discussed.

ISSN:0309-1929    

DOI:10.1080/03091929208228087

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

In a weakly ionized medium, there is diffusive transport of magnetic field relative to the neutral gas. The effective diffusion coefficient is quadratic in the magnetic field strength so that the diffusion is nonlinear. We have included this nonlinear diffusion in a simple model of an α-ω dynamo in a slab. A rich variety of solutions, including steady states and steady travelling waves, are found. Our results may be relevant to the generation of magnetic fields in galaxies and in accretion disks around young starts.

ISSN:0309-1929    

DOI:10.1080/03091929208228088

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The assumptions and approximations commonly used in thin disk kinematic dynamo theory are discussed and appraised. Here attention is restricted to those modes, which have a radial length scale long compared to the disk thickness but short compared to the disc radius, upon which the characteristics of the disc vary. One of the commonly employed approximations pivots on the assumption that the radial structure is determined by lateral diffusion in the disc, whereas on those long radial scales the role of the external potential field is more potent. Stix's (1975, 1978) α ω-galactic dynamo in an oblate spheroid with aspect ratio, ε, is adopted as an illustrative example. He reports numerical results for models with ε as small as 1/30. Our perturbation methods are applied to three distinct modes, namely the steady dipole, the steady and unsteady quadrupole. Each has very different characteristics. It is shown that the determination of the radial structure of the solutions on the long radial length scale is extremely delicate in the limit ε ↓ 0. The higher order asymptotic theory, which determines these details, appears only to be valid for extremely small values of ε; certainly far smaller than the value of 1/30 reached by Stix. Nevertheless, despite the limitations of the theory, the lowest order approximation, which determines the critical Dynamo number and the nature of the dynamo itself, gives generally reliable results, while the higher order theory predicts trends.

ISSN:0309-1929    

DOI:10.1080/03091929208228089

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

In thin disc kinematic dynamo theory there are two classes of dynamo mode. In the first class, the magnetic field generated has a radial length scale long compared with the short transverse length scale defined by the disc thickness. In the second class the radial length scale is short and comparable to the disc width. The former were investigated in Part I and Stix's (1975, 1978) α ω-galactic dynamo in an oblate spheroid with small aspect ratio, ε, was adopted as an illustrative example. Here we again investigate Stix's model but, in contrast, consider the most readily excited oscillatory dipole mode, which happens to have short radial length scale and so belongs to the latter class. It is shown that, in the limit ε ↓ 0, local theory, which ignores the radial structure of the disc, leads to a critical Dynamo number which is smaller than the actual value by about 20%. The explanation of this discrepancy is the main feature of the analysis.

ISSN:0309-1929    

DOI:10.1080/03091929208228090

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor