摘要:

The stability of a finite-amplitude Rossby wave on a β-plane with respect to a small amplitude perturbation is examined. Normal modes are defined, without further approximation, by a third-order Floquet system. The parametric instability exhibited by the system is examined analytically and numerically. When the amplitude of the Rossby wave tends to zero this instability is shown to be analogous to the resonant interaction of the Rossby wave with components of the perturbation. The stability of a Rossby wave is seen to depend upon two parameters,Mand ξ. The parameterMis proportional to the amplitude of the Rossby wave and ξ is its orientation on the β-plane. Curves of marginal stability in the (M, ξ) space are found numerically.

ISSN:0309-1929    

DOI:10.1080/03091927708242314

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

The onset of instability for a self-gravitating, internally heated, fluid sphere of radius, r*0, at large Taylor number, [Ttilde] (a measure of the rotation rate), is investigated. The pioneering work of Roberts (1968) and Busse (1970) has shown that at the onset of instability convection is concentrated in a layer of thickness, r*0[Ttilde]−1/9, which forms a cylindrical surface, coaxial with the diameter parallel to the angular velocity. Inside this layer, Rossby waves of short length scale, r*0[Ttilde]−1/6, propagate eastwards. For Rayleigh numbers, [Rtilde]*, close to the critical value, [Rtilde]*c, determined by Busse (1970), a linear equation governing the evolution of the waves on the long length scale, r*0[Ttilde]−1/9, and a long lime scale is derived., When [Rtilde]* is greater than [Rtilde]*csome disturbances applied at time t* = 0 initially grow exponentially. Nevertheless the equation has the remarkable property that, as t* → ∞, all solutions decay exponentially irrespective of the value of [Rtilde]*. Therefore, since no steady or periodic solution is possible, the critical Rayleigh number in the accepted sense is not close to [Rtilde]*c.

ISSN:0309-1929    

DOI:10.1080/03091927708242315

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

The linear stability of a differentially heated cylindrical annulus, of finite length, containing a dissipationless fluid and rotating uniformly in a non-uniform toroidal magnetic field is studied.

ISSN:0309-1929    

DOI:10.1080/03091927708242316

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

A reexamination is made of Backus' (1958) strain rate criterion for dynamo action. It is shown that his bound can be strengthened by about 25% by using a sharper estimate of the strength of electromagnetic induction. The new formulation also allows treatment of an arbitrary spherically symmetric conductivity distribution outside the sphere; it is found that allowing external currents reduces the necessary strain-rate.

ISSN:0309-1929    

DOI:10.1080/03091927708242317

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

By T. G. Cowling. Adam Hilger Ltd, x + 136 pp. £10.00 (ISBN O 85274 300 9) July 1976.

ISSN:0309-1929    

DOI:10.1080/03091927708242318

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

ISSN:0309-1929    

DOI:10.1080/03091927708242319

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

A periodic wind produces an oscillating response when it blows across an ocean overlying a continental shelf. In this paper, the response of a frictionless, horizontally non-divergent ocean to a wind system which travels along the shelf is considered. It is shown that the periodic response produced by such wind systems may have a resonant non-linear interaction with shelf waves whose frequency is close to half that of the wind. The theory may have applications to east-west continental shelves (for example, the south coast of Australia) when strong weather systems move eastward along the shelf.

ISSN:0309-1929    

DOI:10.1080/03091927708242320

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

The influence of mesoscale topography on the baroclinic instability of a two-layer model of the open ocean is considered. For westward velocities in the top layer (U), and for a sinusoidal topography independent ofxor longitude (a cross-stream topography), the critical value ofU(Uc) leading to instability is the same as when there is no topography. The wavelength of the unstable perturbation corresponding to Ucis shortened. For a given wavevector (k) of the perturbation the system becomes stable (as also in the absence of topography) for large values of |U|. The minimum value of the shear leading to stability is, however, significantly reduced by the topography.

ISSN:0309-1929    

DOI:10.1080/03091927708242321

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

The long time response to an arbitrary unstable disturbance in a two layer model on anf-plane is sought. It has been found that depending on the ratio of the shear to the average speed of the mean flow two types of baroclinic instabilities exist: convective and absolute. When the system supports convective instabilities the long time response to an initial pulse excitation decreases with time at a fixed point in space. When such a system is excited by a wave maker the steady state frequency of response of the system corresponds to a spatially amplifying wave oscillating with the frequency of the wave maker. If the dispersion relation yields a saddle point of the frequency in the wave number complex plane with positive imaginary part of the frequency the system supports absolute instabilities. The response of the system at any point in space excited by an arbitrary signal grows exponentially with time at a rate determined by the properties of the system at the saddle point. This response is different from that of unstable normal modes. It is conjectured that absolute instability may be responsible for local cyclogenesis activity in certain geographical regions.

ISSN:0309-1929    

DOI:10.1080/03091927708242322

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

The form of quasigeostrophic flow past isolated topography on a beta-plane is obtained for both homogeneous and strongly stratified flows. The stratified flow patterns directly above the bottom boundary are qualitatively similar to the corresponding homogeneous patterns but do not exhibit as marked a deviation from uniform flow away from this boundary. Strong stratification limits the vertical extent of perturbations to western flows. causing them to decay within a distance of orderfL/N of the bottom wherefis the Coriolis parameter, L the horizontal length scale andNthe buoyancy frequency. Perturbations to eastward flows are virtually unattenuated by this height due to the presence of a standing Rossby-wave wake behind the obstacle propagating energy vertically upwards. The minimum height required for an axisymmetric obstacle to cause blocking in a westward current is obtained as a function of the Burger number and the beta parameter. Expressions are given for the force exerted on axisymmetric obstacles in such flows. These consist of a transverse “lift” force independent of the beta effect and stratification, and a wave drag force present only in eastward currents.

ISSN:0309-1929    

DOI:10.1080/03091927708242323

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor