摘要:

It is shown that the symmetry properties of barotropic nonlinear wind driven ocean circulation, as presented in the numerical simulations of Veronis (1966a, b), can easily be derived analytically for large Ekman number, the so-called “small beta regime”, and for any strength of the nonlinearity, by a perturbation expansion in the inverse Ekman number. The solution is a superposition of a vorticity monopole, dipole and quadrupole, the symmetry properties of which are qualitatively the same as those of the Veronis' sequence. It is also shown that the Veronis' sequence does not lead to the inertial Fofonoff (1954) mode, but that the latter is the limit of another sequence in the parameter plane spanned by the Rossby and Ekman numbers.

ISSN:0309-1929    

DOI:10.1080/03091929308203595

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

A nonlinear Stommel model of the ocean circulation on the beta plane, driven by a time periodic wind stress, is investigated in order to study symmetry properties of the observed time-mean ocean gyres. Due to the presence of vorticity advection terms the model will have a steady or rectified response to fluctuating wind fields. In this paper a small inverse Ekman number, “the small beta regime”, is considered. It is demonstrated that for this case all qualitative features of the residual circulation, obtained numerically by Veronis (1970). are reproduced in an analytical way. They include the dipole character of the gyre, its maximum symmetry breaking around the north-south axis for intermediate Reynolds numbers, measuring the ratio of vorticity forcing and dissipation, and the maximum residual response for intermediate forcing frequencies.

ISSN:0309-1929    

DOI:10.1080/03091929308203596

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

In this paper the linear and nonlinear stability of two dimensional Langmuir circulations in a fluid layer, stratified by vertical thermal and salinity gradients, is investigated. Stability curves for the onset of steady and oscillatory convection are determined and the point of intersection between these two curves is identified as a codimension two Hopf-zero bifurcation. The amplitude evolution equations describing this bifurcation point are then derived using the method of multiple scales and a numerical procedure for calculating the coefficients of the nonlinear terms is implemented. The results of unfolding this bifurcation are then presented for the case when the convection cells have a square cross-section.

ISSN:0309-1929    

DOI:10.1080/03091929308203597

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The linear stability of a non-divergent barotropic parallel shear flow in a zonal and a non-zonal channel on the β plane was examined numerically. When the channel is non-zonal, the governing equation is slightly modified from the Orr-Sommerfeld equation. Numerical solutions were obtained by solving the discretized linear perturbation equation as an eigenvalue problem of a matrix. When the channel is zonal and lateral viscosity is neglected the problem is reduced to the ordinary barotropic instability problem described by Kuo's (1949) equation. The discrepancy between the stability properties of westward and eastward flows, which have been indicated by earlier studies, was reconfirmed. It has also been suggested that the unstable modes are closely related to the continuous modes discretized by a finite differential approximation. When the channel is non-zonal, the properties of unstable modes were quite different from those of the zonal problem in that: (1) The phase speed of the unstable modes can exceed the maximum value of the basic flow speed; (2) The unstable modes are not accompanied by their conjugate mode; and (3) The basic flow without an inflection point can be unstable. The dispersion relation and the spatial structure of the unstable modes suggested that, irrespective of the orientation of the channel, they have close relation to the neutral modes (Rossby channel modes) which are the solutions in the absence of a basic shear flow. The features mentioned above are not dependent on whether or not the flow velocity at the boundary is zero.

ISSN:0309-1929    

DOI:10.1080/03091929308203598

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The stability of a uniformly-rotating, electrically-conducting, stratified fluid is discussed under conditions of slight tidal straining. The ensuing steady flow consisting of elliptical streamlines and magnetic field lines is linearly unstable through the resonant coupling of two free waves of the system. New families of linear waves consisting of modified Poincare, “slow” hydromagnetic and, in the case of axial stratification, internal evanescent waves are isolated upon a rotating fluid bearing an axial current. All possible resonant couplings between these waves are examined. Stable radial stratification is found to be a destabilizing influence on some elliptical couplings and always so for slow hydromagnetic waves. Internal evanescent waves can be stimulated elliptically in the case of axial stratification and typically possess boundary-layer structure. In all cases studied, including in the presence of a central core, the preferred mode of disturbance is a tipping over, or spinover, of the basic vorticity and current into the plane of elliptical distortion. The elliptical instability preferentially excites westward-propagating waves but growth rates for the slow hydromagnetic waves appropriate to the geomagnetic secular variation are found to be too small to be significant.

ISSN:0309-1929    

DOI:10.1080/03091929308203599

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The influence of the boundary conditions on convective instability in rapidly (10−5<E< 10−3) rotating spherical shells is investigated. For the purpose of comparison, both stress-free and rigid boundaries are studied at exactly the same parameter range of the problem. In the rigid boundary case an Ekman boundary layer is formed in middle latitudes where columnar convective rolls meet the outer spherical surface. There is also a boundary layer at the equatorial region of the inner sphere where the rolls are attached. When the Prandtl numberPr≥ O(1), the Ekman boundary layer produced by the rigid boundaries has a destabilizing effect, the critical Reyleigh number being substantially reduced. The value of the critical azimuthal wavenumber and the drifting rate of the convection rolls are also significantly lower compared wilh the free boundary case. When the Prandtl numberPr< O(1), so thermal dissipation dominates over the viscous dissipation, the Ekman boundary layers exhibit a stabilizing effect. Convection in a rotating annulus including the effect of the Ekman layers is investigated analytically, and shows similar behaviour to that of the spherical shells. The influence of varying aspect ratio is also discussed.

ISSN:0309-1929    

DOI:10.1080/03091929308203600

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The observed westward drift of some patches of the Earth's magnetic field suggests that the geodynamo is of the αω kind. However solutions of the αω dynamo equations tend to oscillate on a very rapid time scale, in disagreement with the observed long times between reversals. It is suggested that the problem can be cured by taking into account the generation of toroidal field by the α effect. The resulting α2ω dynamo equations are solved in the geometry of a spherical shell in both the linear and the nonlinear regime. Steady and oscillatory Taylor state solutions are found. The slow time dependence of the oscillatory solutions compares well with the observed frequency of geomagnetic reversals.

ISSN:0309-1929    

DOI:10.1080/03091929308203601

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

In this paper a method for solving the equation for the mean magnetic energy <BB> of a solar type dynamo with an axisymmetric convection zone geometry is developed and the main features of the method are described. This method is referred to as the finite magnetic energy method since it is based on the idea that the real magnetic fieldBof the dynamo remains finite only if <BB> remains finite. Ensemble averaging is used, which implies that fields of all spatial scales are included, small-scale as well as large-scale fields. The method yields an energy balance for the mean energy density ϵ ≡B2/8π of the dynamo, from which the relative energy production rates by the different dynamo processes can be inferred. An estimate for the r.m.s. field strength at the surface and at the base of the convection zone can be found by comparing the magnetic energy density and the outgoing flux at the surface with the observed values. We neglect resistive effects and present arguments indicating that this is a fair assumption for the solar convection zone. The model considerations and examples presented indicate that (1) the energy loss at the solar surface is almost instantaneous; (2) the convection in the convection zone takes place in the form of giant cells; (3) the r.m.s. field strength at the base of the solar convection zone is no more than a few hundred gauss; (4) the turbulent diffusion coefficient within the bulk of the convection zone is about 1014cm2s−1, which is an order of magnitude larger than usually adopted in solar mean field models.

ISSN:0309-1929    

DOI:10.1080/03091929308203602

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

An αomega-dynamo operating in the solar convection zone is considered as a possible explanation for the 22-year magnetic cycle of the Sun. The finite magnetic energy method of Van Geffen and Hoyng (1993) is used to find the stationary distribution of the mean magnetic energyBB, where <·> is an ensemble average. This method is based on the idea that the magnetic fieldBremains finite only ifBBremains finite. To ensure the latter, a fairly large value for the turbulent diffusion coefficient inside the convection zone is needed: β = 1014cm2s−1. Stationarity ofBBdetermines a combination of parameters, which is then used in the dynamo equation for the mean fieldB. For various profiles for the solar differential rotation we find thatBis very quickly damped: in about 14 days, a minute fraction of the solar cycle. It follows that the dynamo field in the convection zone is rapidly fluctuating and very unstable, that it has no clear period and no well-defined large-scale field: it is a small-scale field dynamo.

ISSN:0309-1929    

DOI:10.1080/03091929308203603

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The nonlinear evolution of perturbations in a magnetized plasma subject to the radiation-driven thermal instability (RDTI) is investigated analytically in a simplified model. The perturbed plasma motions are assumed to be one-dimensional and perpendicular to the magnetic field. The intermediate- and long-wavelength limits of the RDTI are considered. In the former limit, the force balance sets in rapidly, on the magneto-acoustic time scale and we assume the total (thermal-magnetic) pressure remains constant. By transforming to Lagrangian variables, the problem is reduced to a single generalized reaction-diffusion equation, which is employed to analyze the two following stages of the RDTI. The first develops on the radiative time scale, when the heat conduction is insignificant, while the second usually occurs on a much longer, heat conduction-related time scale. For the first stage, a simple analytical solution is found, which describes the development of a strong plasma stratification (coexisting hot rarefied phase and cool dense phase) across the magnetic field. Slow erosion of the stratification in the form of almost uniform motion, collision and “annihilation” of the inter-phase boundaries generally occurs at the second stage.

ISSN:0309-1929    

DOI:10.1080/03091929308203604

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor