摘要:

In this paper, the non-dimensional equivalent barotropic vorticity equation with dissipation and an external vorticity source induced by diabatic heating was reduced to the generalized periodically forced nonlinear Schrödinger (NLS) equation similar to the parametrically excited NLS equation derived by Miles (1984) by means of the multiplescale method. This forced NLS equation can be reduced to a low-dimensional ordinary differential equation describing the amplitude and phase of the forced envelope Rossby soliton by the inverse-scattering perturbation method. The numerical calculations indicate that for weaker dissipation the envelope Rossby soliton, under a constant amplitude travelling diabatic heating, exhibits multi-periodic oscillations, and its phase portrait is found to be a limit cycle. However, for the forcing of one-year modulated diabatic heating, the forced envelope Rossby soliton can execute chaotic motion when the controlling parameter reaches a certain extent. In addition, the oscillatory behaviour of the forced envelope Rossby soliton is found to be able to explain the establishment and decay of vortex pair blocking usually observed in two oceans.

ISSN:0309-1929    

DOI:10.1080/03091929708208983

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

We investigate the stability of parallel shallow-water flows on an equatorial β-plane. The flow is bounded by fronts on both sides. We focus on the case of a quadratic velocity profile and quartic depth profile. Several new instability mechanisms are identified when the potential vorticity is nonzero.

ISSN:0309-1929    

DOI:10.1080/03091929708208984

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

The combination of strong density stratification and energetic forcing from tide and mean flows leads to complex circulation and exchange processes in estuaries. The present study was motivated by field results in the Valdivia Estuary, Chile, and others where a dramatic difference in salinity stratification was observed between low and high tides, believed to be attributable to the interacting roles of tidal forcing, topography and velocity shear effects. We describe results from a laboratory experiment which models an important aspect of the dynamics in such estuaries: the role of a changing cross-section on the stratified shear-generated internal mixing. Our experiments were conducted in a long, laboratory tank fitted with a contracting central section. Fresh water ran from one end of the tank, overflowing at an adjustable weir at the other end. A slower salt water flow was introduced at the base of the weir, and intruded upstream as a gravity current. The increased velocity shear which occurred as the salt water flow moved into the contraction caused significant overturn events at the salt/freshwater interface, so changing the density field in a manner similar to the field observations. Under certain conditions, this mixing was sufficient to arrest the wedge in the contraction, so allowing measurements of the mean density and velocity fields, as well as extensive turbulent microstructure records. This enabled us to describe the intensity and spatial variation of the turbulent mixing between the saline underflow and the fresh water overflow for a saline intrusion under the influence of topographic effects.

ISSN:0309-1929    

DOI:10.1080/03091929708208985

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

Thermo-poro-elastic equations describing fluid migration through fluid-saturated porous media at depth in the crust are analyzed theoretically following recent formulations of Rice and Cleary (1976), McTigue (1986) and Bonafede (1991). In this study these ideas are applied to a rather general model, namely to a deep hot and pressurized reservoir of fluid, which suddenly enters into contact with an overlaying large colder fluid-saturated layer. In a one-dimensional idealization this system can be described by two nonlinear differential heat-like equations on the matrix-fluid temperature and on the fluid overpressure over the hydrostatic value. The nonlinear couplings are due to Darcy thermal advection and to the mechanical work rate. Here we first sketch nonlinear solutions corresponding to Burgers' “solitary shock waves”, which have recently been found valid for rocks with very low fluid diffusivity. Subsequently other nonlinear transient waves are discussed, such as “thermal” and “compensated” waves, which are found to exist for every value of the parameters present in the equations involved. One interesting aspect of these mechanisms is that the resulting time-scales are particularly small. Moreover, in order to figure out the system time-evolution and the role played by the fluid diffusivity/thermal diffusivity ratio, a mechanical similitude is proposed, which we treat both analytically and numerically. Although for realistic systems these solutions are somewhat idealized, they allow one to gain fundamental insight into fluid migration mechanisms in volcanic areas and in fault regions under strong frictional heating. As already discussed by McTigue, the theory is also of interest in studying areas of nuclear waste disposal. Furthermore such a theoretical study allows one to investigate the site at depth at which such nonlinear waves are generated.

ISSN:0309-1929    

DOI:10.1080/03091929708208986

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

We investigate numerically magnetoconvection in a rapidly rotating sphere. The model consists of a fluid filled sphere, internally heated, and rapidly rotating in the presence of both a mean toroidal magnetic field and a mean poloidal field. Motivated by the geodynamo problem, we take the magnetostrophic approximation, that is to say we neglect terms proportional to the Ekman number and the Rossby number in the momentum equation. All variables are approximated spectrally in both the radial and meridional directions. A modal dependence is assumed azimuthally. The induction and temperature equations are time stepped pseudospectrally in the angular coordinate, and by collocation in the radial coordinate, while the momentum equation, now diagnostic, is solved at each time step to give the nonaxisymmetric velocity field. Critical Rayleigh numbers and corresponding frequencies are obtained at given azimuthal wavenumber, Roberts number and strengths of the imposed toroidal and poloidal magnetic fields. The results, which include purely magnetic instabilities, are discussed and compared with related studies of magnetoconvection, with and without the presence of an inner core, carried out at small but finite Ekman number or with stress-free boundary conditions.

ISSN:0309-1929    

DOI:10.1080/03091929708208987

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor