摘要:

The stability of quasi-geostrophic β-plane flow over topography is examined. The approach is to first calculate the stationary, asymmetric response to a uniform zonal current flowing over topography, and then calculate the stability properties of the total, zonally asymmetric, field. Under many circumstances this flow is unstable, barotropically and or baroclinically particularly if the asymmetric flow is of large amplitude. This is demonstrated first using a long-wave approximation, which examines the stability with respect to perturbations of large meridional scale. So-called form-drag instability then ensues. This may be thought of as a special, nonlocal, form of isosceles triad interaction involving the zonal flow interacting with the topography and another “free” mode of topographic scale. For topography consisting of a single Fourier mode, instability then arises only if the zonal current is eastward and exceeds that required for resonance. However, in general other triads exist in which the asymmetric flow, if its amplitude is large enough, is always unstable, for any value of the zonal current. In particular, flow with the zonal current slightly below the resonant value can be unstable. This implies that resonantly amplified stationary waves, sometimes cited as possible mechanisms for blocks, will decay rapidly through their interaction with other modes, unless further nonlinear equilibration occurs. Certain integral constraints prove useful in ascertaining necessary conditions for instability, both for topographic instability and the zonally symmetric (but continuously stratified) baroclinic instability problem.

ISSN:0309-1929    

DOI:10.1080/03091928508245436

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

This paper investigates the generation of linear baroclinic Rossby waves by meridional oscillations of a climatological zonal wind stress in a reduced gravity ocean bounded by an eastern coastline. Using a power series technique an analytical solution is derived for the interfacial displacement. It is found that for a given period of oscillation of the zonal winds, a finite number of propagating Rossby waves will be generated with frequencies equal to a harmonic of the forcing frequency. The number of propagating modes increases with increasing period of the wind stress. In addition to the propagating waves the complete solution for the interfacial displacement consists of a rapidly convergent infinite sum of evanescent terms. The displacement field is calculated for atmospheric forcing parameters typical of those found at mid-latitudes. Further, it is shown that a near resonant response can be generated using atmospheric parameter values typical of those found over the North Pacific.

ISSN:0309-1929    

DOI:10.1080/03091928508245437

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

The effect of fluctuations in a periodically forced climate model involving the coupling between sea ice and mean ocean temperature is considered. The transitions between phase-locked (periodic) and quasi-periodic solutions are studied by a singular perturbation method of solution of the stochastic differential equations, as well as by numerical simulations. The variances and covariances of the principal climatic variables are computed.

ISSN:0309-1929    

DOI:10.1080/03091928508245438

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

An investigation is made of steady thermal convection of a Boussinesq fluid confined in a vertically-mounted rotating cylinder. The top and bottom endwall disks are thermal conductors at temperaturesTtandTbwith δT=Tt−Tb>0. The vertical sidewall has a finite thermal conductance. A Newtonian heat flux condition is adopted at the sidewall. The Rayleigh number of the fluid system is large to render a boundary layer-type flow. Finite-difference numerical solutions to the full Navier-Stokes equations are obtained. The vertical motions within the buoyancy layer along the sidewall induce weak meridional flows in the interior. Because of the Coriolis acceleration, the meridional flows give rise to azimuthal flows relative to the rotating container. Strong vertical gradients of azimuthal flows exist in the regions near the endwalls. As the stratification effect increases, concentration of flow gradients in thin endwall boundary layers becomes more pronounced. The azimuthal flow field exhibits considerable horizontal gradients. The temperature field develops horizontal variations superposed on the dominant vertical distribution. As either the sidewall thermal conductance or the stratification effect decreases, the temperature distribution tends to the profile varying linearly with height. Comparisons of the sizes of the dynamic effects demonstrate that, in the bulk of flow field, the vertical shear of azimuthal velocity is supported by the horizontal temperature gradient, resulting in a thermal-wind relation.

ISSN:0309-1929    

DOI:10.1080/03091928508245439

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

Recent calculations suggest that the bulk of the solar toroidal field may be stored in a thin, convectively stable region situated between the convection zone proper and the radiative zone. Determining the stability properties of such a field is therefore important with implications for both the generation and escape of magnetic flux. The plane layer, linear stability analysis of Hughes (1985) is extended to incorporate the effects of uniform rotation. Detailed studies are made of interchange, or “axisymmetric” modes and of undular, or wavelike, motions, considering modes of both low and high frequency. The force due to rotation acts to constrain the fluid motions, a feature which is strongly stabilizing for direct modes, but can, in certain circumstances, be destabilizing for oscillatory motions.

ISSN:0309-1929    

DOI:10.1080/03091928508245440

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

Two distributions of the α-effect in a sphere are considered. The inviscid limit is approached both by direct numerical solution and by solution of a simpler nonlinear eigenvalue problem deriving from asymptotic boundary layer analysis for the case of stress-free boundaries. The inviscid limit in both cases is dominated by the need to satisfy the Taylor constraint which states that the integral of the Lorentz force over cylindrical (geostrophic) contours in a homogeneous fluid must tend to zero. For a small supercritical range in α, this condition can only be met by magnetic fields which vanish as the viscosity goes to zero. In this range, the agreement of the two approaches is excellent. In a portion of this range, the method of finite amplitude perturbation expansion is useful, and serves as a guide for understanding the numerical results. For larger α, evidence from the nonlinear eigenvalue problem suggests both that the Taylor state exists, and that the transition from small to large amplitude can require a finite amplitude (oscillatory) instability in accord with the findings of Soward and Jones (1983). However, solutions of the full equations have not been found which are independent of viscosity at larger values of α.

ISSN:0309-1929    

DOI:10.1080/03091928508245441

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

Experiments have been made using shadowgraphs to examine the development of secondary structures in Kelvin-Helmhoitz billows at the diffuse interface between two layers of different densities moving in shear at moderate Reynolds numbers and high Prandtl number. The onset of turbulence in billows reported in earlier work resulted from an interaction between the billows and the side walls of the apparatus. Secondary structure within the billows remote from the side walls occurs later and is, in its early stages, well organised. Regular longitudinal bands lying parallel to the mean flow develop near the vertical boundaries of the billows and extend across their widths. The initial development and scale of the spanwise bands are similar to that of the convective rolls predicted to occur in billows by Klaassen and Peltier (1985a) using a numerical model. No longitudinal instability is observed to occur at the same time in the braids between the billows. Fine scale “turbulence” occurs in the billows about one stability period (for the original interface) after the secondaries first appear, so that the transition is not, as previously thought, “explosive” but is relatively slow. Two other “transitional” structures are reported. One has a tube-like appearance extending from one billow to its neighbour. Disturbances are transmitted down the tube and these ultimately initiate turbulence in the second billow. The second structure is a “knot” due to the spanwise amalgamation of two-billows into one.

ISSN:0309-1929    

DOI:10.1080/03091928508245442

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

Edge waves are known to give rise to beach cusps. This paper investigates the topographic feed-back upon the waves. For edge waves generated by subharmonic resonance with incident waves, the topography acts to decrease the edge wave response. As well as causing frequency detuning (Guza and Bowen, 1981) the topography can cause the scattering of edge wave energy. For synchronous waves the topographic irregularities have the opposite effect, and there can be a feed of energy into the edge waves by scattering from the incident waves.

ISSN:0309-1929    

DOI:10.1080/03091928508245443

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

A nonlinear energy stability analysis is presented for the penetrative convection model of Veronis (1963). For top temperatures between 4°C and 8°C the nonlinear stability boundary obtained is very close to the linear one of Veronis and enables a region of possible sub-critical instabilities to be determined.

ISSN:0309-1929    

DOI:10.1080/03091928508245444

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

This paper considers the static force-free equilibriumV×B=αBof a magnetic field in which all of the lines of force connect without knotting between parallel planes. The field is formed by continuous deformation from an initial uniform field, and is conveniently described in terms of the scalar function ψ, which is effectively the stream function for the incompressible wrapping and interweaving of the lines of force, and the scalar function θ, which describes the local compression and expansion. Equilibrium requires satisfaction of two independent equations (the third equation defines α), which cannot be accomplished without the full freedom of both functions ψ and θ. It is shown by integration along the characteristics of the equilibrium equations that, when ψ is predetermined by an arbitrary winding pattern, there appear discontinuities in α. Discontinuities in α have discontinuities in the field (i.e. current sheets) associated with them.

ISSN:0309-1929    

DOI:10.1080/03091928508245445

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor