摘要:

The propagation of tides in the vicinity of the critical latitude, defined here as the latitude where the tidal frequency ω equals the Coriolis parameterf, is investigated using a barotropic, depth-averaged, divergent and frictionless analytical model using the standard β-plane approximationf= ω + βy. Standard techniques of ray theory are used to deduce the energy propagation path, which temporarily crosses the critical latitude in a parabolic path when — β/k<0, wherekis the eastward component of wavenumber. An expression for eccentricity and sense of rotation of the velocity vector in the horizontal current ellipse shows a complicated dependence on the wavenumberkand on the dimensionless parameter γ =gHβ2/(2ω)4, whereHis the ocean depth andgis the gravitational acceleration.

ISSN:0309-1929    

DOI:10.1080/03091929308203559

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The linear and weakly nonlinear stability characteristics of spatially growing, long, low frequency baroclinic waves are examined in a continuous atmosphere on a midlatitude β-plane channel in the presence of Ekman friction and Newtonian cooling (NC). Under the assumption that the damping mechanisms are sufficiently weak, the linear spatial instability problem is solved analytically and explicit expressions for the zonal wavenumber and spatial growth rate are obtained. The expressions show that Ekman damping is stabilizing whereas NC is destabilizing. The tendency of NC to dominate over Ekman damping increases linearly with frequency and β, and quadratically with reduction in zonal wind at the surface. The zonal wavelength of the disturbance is affected only by the flow supercriticality and NC, which always oppose each other; increasing the NC (supercriticality) increases (decreases) the zonal wavelength.

ISSN:0309-1929    

DOI:10.1080/03091929308203560

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

A one-layer quasi-geostrophic model is used to study Taylor columns on both the f-plane and the β-plane in the inviscid limit of the frictional problem. In this limit, the fluid is stagnant within the Taylor column and the velocity vanishes on its boundary. Ingersoll (1969) found an analytic solution for such a Taylor column for flow over a right circular cylinder on the f-plane. Under more general circumstances, an analytic solution is no longer possible. In this paper, solutions are found numerically by solving an integral equation for the values of the stream function on the boundary of the Taylor column, and then iteratively solving for the shape of the boundary. Ingersoll's solution is first extended by finding the shape of the Taylor column for flow over a cone on the f-plane where the Taylor column has a tear drop shape. Solutions are also found for westward and eastward flow over a cylinder on the β-plane. The Taylor column is approximately elliptical for westward flow with the major axis in thexdirection, while it is slightly elongated in theydirection for eastward flow. For eastward flow, it is located north and west of where it was on the f-plane because of the asymmetry in the solution arising from the Rossby lee waves downstream of the topography. The stagnation point of the Taylor column is located on the edge of the topography for all the solutions found.

ISSN:0309-1929    

DOI:10.1080/03091929308203561

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

This paper investigates the behavior of vorticity in a polytropic or isothermally stratified fluid under the condition that the density profile remains constant in time. An expression for the velocity field of a general vorticity distribution (analogous to the Biot-Savart law for a uniform fluid) as well as expressions for the far velocity field, vector potential, and kinetic energy, are derived. The particular cases of the infinite straight vortex filament and the vortex ring each having infinitesimal cross-section are presented. They yield the surprising result that vortex filaments in a stratified fluid are propelled transverse to the stratification axis with a velocity given by (K/4πλ)In(b/λ) whereKandb2are the magnitude and cross-sectional area of the filament respectively and λ is the density scale height. For a vortex ring, this transverse motion is manifested as an expansion or contraction of the ring radius, depending on the ring's direction. This effect is unrelated to the curvature of the vorticity; rather, it is a direct result of the expansion/contraction of fluid moving in a density gradient. The implications for the vortex-ring sunspot model and for the formation of hillocks around magnetic flux fibrils are discussed.

ISSN:0309-1929    

DOI:10.1080/03091929308203562

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

High resolution numerical simulations of thermal convection in a rapidly rotating channel with gravity perpendicular to the rotation vector are described. The convecting columns are subject to a β-effect resulting from topographic vortex stretching. The symmetries of the problem allow many invariant wavenumber sets, and this property is associated with the existence of stable multiple-equilibria at modest supercriticality. The transition to chaotic behavior involves the production of intermittent unstable orbits off a two-torus in energy space. At very high Rayleigh number (of order 106to 107) the motion can be turbulent, depending on the size of β. However, the turbulence is usually characterized by an almost-periodic formation of patches of small scale convection that cause regular pulsations in the accompanying strong zonal jets. The processes maintaining these flows may be related to those responsible for the zonal currents on Jupiter and for cyclic variability on the Sun.

ISSN:0309-1929    

DOI:10.1080/03091929308203563

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Steady, nonlinear, penetrative convection in a viscous, incompressible fluid confined between free horizontal boundaries in two dimensions is investigated numerically. For Prandtl numbers [sgrave] less than unity and for fixed imposed heat flux, the resulting Rayleigh numberRα [sgrave]−1indicating a strong dependence on the Prandtl number not realised with two-dimensional Rayleigh-Bénard calculations. At low Prandtl numbers, the convection bifurcates supercritically and less efficient heat transport and different cell geometry are exhibited, with no “flywheel” solution in existence.

ISSN:0309-1929    

DOI:10.1080/03091929308203564

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

Complicated bifurcation structures that appear in nonlinear systems governed by partial differential equations (PDEs) can be explained by studying appropriate low-order amplitude equations. We demonstrate the power of this approach by considering compressible magnetoconvection. Numerical experiments reveal a transition from a regime with a subcritical Hopf bifurcation from the static solution, to one where finite-amplitude oscillations persist although there is no Hopf bifurcation from the static solution. This transition is associated with a codimension-two bifurcation with a pair of zero eigenvalues. We show that the bifurcation pattern found for the PDEs is indeed predicted by the second-order normal form equation (with cubic nonlinearities) for a Takens—Bogdanov bifurcation with Z2symmetry. We then extend this equation by adding quintic nonlinearities and analyse the resulting system. Its predictions provide a qualitatively accurate description of solutions of the full PDEs over a wider range of parameter values. Replacing the reflecting (Z2) lateral boundary conditions with periodic [O(2)] boundaries allows stable travelling wave and modulated wave solutions to appear; they could be described by a third-order system.

ISSN:0309-1929    

DOI:10.1080/03091929308203565

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The stratification profile of the Earth's magnetofluid outer core is unknown, but there have been suggestions that its upper part may be stably stratified. Braginsky (1984) suggested that the magnetic analog of Rossby (planetary) waves in this stable layer (the ‘H’ layer) may be responsible for a portion of the short-period secular variation. In this study, we adopt a thin shell model to examine the dynamics of theHlayer. The stable stratification justifies the thin-layer approximations, which greatly simplify the analysis. The governing equations are then the Laplace's tidal equations modified by the Lorentz force terms, and the magnetic induction equation. We linearize the Lorentz force in the Laplace's tidal equations and the advection term in the magnetic induction equation, assuming a zeroth order dipole field as representative of the magnetic field near the insulating core-mantle boundary. An analytical β-plane solution shows that a magnetic field can release the equatorial trapping that non-magnetic Rossby waves exhibit. A numerical solution to the full spherical equations confirms that a sufficiently strong magnetic field can break the equatorial waveguide. Both solutions are highly dissipative, which is a consequence of our necessary neglect of the induction term in comparison with the advection and diffusion terms in the magnetic induction equation in the thin-layer limit. However, were one to relax the thin-layer approximations and allow a radial dependence of the solutions, one would find magnetic Rossby waves less damped (through the inclusion of the induction term). For the magnetic field strength appropriate for theHlayer, the real parts of the eigenfrequencies do not change appreciably from their non-magnetic values. We estimate a phase velocity of the lowest modes that is rather rapid compared with the core fluid speed typically presumed from the secular variation.

ISSN:0309-1929    

DOI:10.1080/03091929308203566

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The steady and transient flow induced by a vertical cylinder of buoyant electrically conducting fluid immersed in an infinite extent of slightly denser fluid in the presence of a horizontal magnetic field is investigated, with the aim of elucidating the small-scale flow within the Earth's core. The evolution from a state of rest may be divided into three regimes. For short times [t< O(L2μ[sgrave]) whereLis the horizontal scale of the plume] Alfvén waves propagate a distanceVAtalong the magnetic field lines, accelerating the fluid to a speed of order (Δρ)gL/ρVAwhereVA=B/(ρμ)½is the Alfvén speed and Δρ is the density deficit of the buoyant plume. For intermediate times [O(L2μ[sgrave])t<O(L2/v)] lateral ohmic diffusion becomes important and the rise speed and lateral extent grow as the square-root of time: O[(Δρg/B)(t/ρ[sgrave])½] and O[LB([sgrave]t/ρ)½], respectively. For large times [t> O(L2/v)] lateral viscous diffusion also becomes important and a quasi-steady state is reached having rise speed of order (Δρ)gL/B(ρ[sgrave]v)½and lateral extent of orderL2B([sgrave]/ρv)½. For values of parameters thought to be relevant to the core, the short-time solution lasts roughly an hour and the intermediate-time solution lasts several decades. The long-time solution may not be relevant to the core as the fluid can rise to the top during the intermediate-time regime. The rise speeds associated with this plume flow may exceed those estimated from secular variation, but this result is sensitive to the size of the density deficit, which is poorly known, and to the particular orientation of the plume that has been chosen.

ISSN:0309-1929    

DOI:10.1080/03091929308203567

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor

摘要:

The mean fieldBin the dynamo equation can be interpreted as a longitude-averaged field, and this implies that there are fluctuations in the mean parameters characterizing the turbulent flow. In this paper we study the effect of fluctuations in the mean helicity numerically and analytically in a very simple spherical α2-dynamo: there is no differential rotation and the non-fluctuating parts of α and β do not depend on position (we call this the α2-sphere dynamo). The dynamo equation then contains a term ∇ × δα(t)B, which describes the effect of the fluctuations in the mean helicity. We show that this type of random forcing implies that the dynamo has to operate (slightly) subcritically, and that in addition many eigenmodes are excited, rather than only the fundamental mode. The advantage of this simple α2-dynamo model is that we can support the numerical results with analytical estimates, for instance, for the value of the dynamo number at which the dynamo operates, the relative excitation levels of the modes, and their spectra. This is achieved with the help of an expansion technique:Bis expanded in terms of a complete, orthogonal set of eigenfunctions. We have taken the mean helicity fluctuations to be position-independent for simplicity. This, however, renders the dynamo model so simple that only dipole fields are excited and magnetic field reversals are absent. We also briefly study the effect of non-linearities, in particular of α-effect quenching. Non-linearities provide a reference level to the fundamental mode, but do not affect the relative excitation levels of the modes.

ISSN:0309-1929    

DOI:10.1080/03091929308203568

出版商:Taylor & Francis Group    

年代:1993

数据来源: Taylor