摘要:

The stability of Rossby waves in a two-layer fluid on a β-plane is examined. There are four parameters in the problem, (a)M =UK2/β whereUis the velocity amplitude of the particular wave being considered andKis its wavenumber, (b)F= (Kac)−2whereacis the baroclinic radius of deformation, (c) the depth ratio δ =H1/H2whereH1andH2are the mean thicknesses of the upper and lower layer, respectively, and (d) the wave direction.

ISSN:0309-1929    

DOI:10.1080/03091927908242674

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

The form of quasi-geostrophic flow past isolated topography on a beta plane is obtained for finite depth, linearly stratified flow. The response is shown to consist of an isotropic perturbation plus, in eastward flows, a single barotropic and a finite number of baroclinic waves. The form of the solution allows a rapid calculation of the Rossby wave drag on an axisymmetric obstacle in an eastward flow.

ISSN:0309-1929    

DOI:10.1080/03091927908242675

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

Drazin's weakly non-linear theory of baroclinic instability is recast in a framework which allows us to account more clearly for experimentally observed changes of eddy heat flux and temperature variance with wave scale and rotation. The theory deals with a single slightly unstable self interacting mode in a viscous baroclinic fluid with a continuous density stratification. Viscosity is accounted for only in Ekman layers.

ISSN:0309-1929    

DOI:10.1080/03091927908242676

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

Lee waves are considered in the framework of nonlinear motion of an inviscid perfect gas with constant specific heats and gravity taken into account. Perturbations are assumed to be confined to the troposphere with vanishing vertical velocity at the top. An asymptotic analysis is then worked out under the hypothesis that the Mach number is small and that the ratio of the horizontal scale to the height of the troposphere is of the order of the Mach number. Long’s (1953) equation and Miles’s (1968) model are recovered as an inner approximation. It is shown that the upper boundary condition belongs to an outer approximation. Such an outer asymptotic approximation is worked out and it is shown that the upper and lower boundaries of the troposphere alternately reflect internal short waves excited by the lee waves of the inner approximation. The important point is that to lowest order, there is no feedback from these waves to the inner approximate solution. It is suggested that the upper boundary condition is an artificial one and that it should be replaced by matching with a set of waves in the upper part of the atmosphere.

ISSN:0309-1929    

DOI:10.1080/03091927908242677

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

Numerical solutions have been calculated for the non-linear Rayleigh-Bénard convection problem in a cylindrical geometry, including the effect of a magnetic field. The development of the field is governed by the induction equation and its back reaction on the motion is determined via the Lorentz force in the momentum equation. If the input fieldB0is weak a thin fluxrope is formed on the axis, and whenB0is increased the amplified field reaches a maximum value as this region becomes stagnant. The equipartition valueBe≡ (μoρU2)½is easily exceeded. WhenBois stronger, heat transport is reduced and osciliations can occur; there are hysteresis effects, and erratic hehaviour is found for high magnetic Prandtl numbers. These results help to interpret ohserved flux concentrations on the Sun, and provide models for some subsidiary features of sunspots.

ISSN:0309-1929    

DOI:10.1080/03091927908242678

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

The static equilibrium of a thin vertical magnetic tube embedded in the solar atmosphere is shown to be dynamically unstable against the fundamental mode of perturbation having no nodes in the vertical displacement. The instability has its origin in the convection zone, and the eigenfunction is extended further up in the stable upper layers by the magnetic field which guides the displacement mainly in the longitudinal direction. It is suggested that the downdraft observed in the solar network structure is a finite amplitude consequence of this instability. The overtone modes are found to be stable.

ISSN:0309-1929    

DOI:10.1080/03091927908242679

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

A complete qualitative investigation of the classical model of stellar explosions has been carried out. A number of new solutions have been found in which radial oscillations of gas occur after the shock wave passes. Conditions for the formation of an expanding vacuum within the gas have been investigated.

ISSN:0309-1929    

DOI:10.1080/03091927908242680

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

The growth of linear, Boussinesq convective modes for a superadiabatic fluid in a planar geometry with negligible thermal diffusion or molecular viscosity is analysed. Small and large magnetic diffusivity limits are both considered. A finite amplitude theory is constructed by assuming that non-linearities (e.g. shear instabilities) limit the flow amplitude, and the dominant modes are assumed to he those which transport most heat. This leads to a unique prescription for the average velocity, superadiabaticity and horizontal lengthscale as a function of the imposed heat flux, rotation rate, large scale magnetic field and vertical lengthscale. Simple analytical results are provided (in terms of the relevant dimensionless numbers) which are as easy to apply as the conventional mixing length theory (MLT). The conclusions are: (i) For no rotation or magnetic field, the model reproduces MLT except that it predicts about an order of magnitude lower heat flux. (ii) Rotation alone or magnetic field alone inhibits the convection. For a given heat flux, the convective velocity and horizontal wavelength are reduced, and the temperature gradient increases. (iii) IfRo≲0.1, whereRois the nominal Rossby number, then the combined effect of rotation and magnetic field enhances the convection, and the maximum heat flux occurs at non-zero field. (iv) The rotational inhibition of convection in rapidly rotating stars does not substantially modify their static structure. (v) Convective velocities of around 0.02 cm/sec are predicted for the Earth’s core, consistent with geomagnetic secular variation timescales, provided the toroidal field is less than about three times the poloidal field. (vi) In both the Earth and Jupiter, the actual magnetic field is within an order of magnitude of the field which minimizes the temperature gradient for a given heat flux.

ISSN:0309-1929    

DOI:10.1080/03091927908242681

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

A method has recently been proposed for finding the radiusrcof the electrically-conducting fluid core of a planet of outer radiusrsfrom observations of the magnetic field B in the accessible region near or well above the surface of the planet (Hide, 1978). The method is based on the supposition that when the magnetic field is produced by hydromagnetic dynamo action in the core, implying that the magnetic Reynolds numberRthere is large, (a) fluctuations in B can occur everywhere on the comparatively short advective time-scale τAassociated with fluid motions in the core and so can fluctuations in the quantityN, defined for any closed surfaceSas the total number of intersection of magnetic lines of force withS, provided thatSlies well outside the core, but (b) at the surface of the core, where lines of magnetic force emerge from their region of origin, concomitant fluctuations inNare negligibly small, of the order of τA/τOwhere τO(= RτA) is the Ohmic decay time of the core.

ISSN:0309-1929    

DOI:10.1080/03091927908242682

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

Hide's (1979) theorem on the magnetic flux linkage of an electrically-conducting fluid is extended to the fully general relativistic case by rederiving the theorem in the elegant and succinct formalism of Cartan's exterior calculus.

ISSN:0309-1929    

DOI:10.1080/03091927908242683

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor