摘要:

The shallow water, linear model in cylindrical coordinates is used to investigate barotropic and inertial instabilities in the tropical cyclone outflow layer. When the mean state wind satisfies the condition |ζ|«|f0the instabilities found in our model are equivalent to the barotropic instabilities calculated with the quasi-geostrophic potential vorticity equation. The maximum instability is internal and appears at azimuthal wavenumber one.

ISSN:0309-1929    

DOI:10.1080/03091928908221814

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

We examine the linear instability of the observed two-dimensional (latitude/height) January 1979 zonal wind of the mid-latitude Southern Hemisphere. The model used is a 10-level, linear, quasi-geostrophic 45°S β-plane channel model, with 30 Fourier harmonics in the meridional direction and a single harmonic in the zonal direction. The fastest growing mode has a zonal wavelength corresponding to wavenumber 12 at 45°S. The mode corresponding to zonal wavenumber 5 at 45°S is also baroclinically unstable. Its latitude-height structure bears qualitative resemblance to the observed wavenumber 5 circulation, which frequently dominates the summer Southern Hemisphere mid-latitude circulation. The latitude of the maximum eddy amplitude at 50°s is simulated, but the maximum is located near the surface instead of aloft. Effects of surface dissipation and a normalization of the zonal wind by the cosine of latitude are also considered.

ISSN:0309-1929    

DOI:10.1080/03091928908221815

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Steady currents develop in oceanic turbulence above topography even in the absence of steady forcing. Mesoscale steady currents are correlated with mesoscale topography with anticyclonic eddies above topographic bumps, and large scale westward flows develop when β is non-zero. The relationship between those two kinds of steady currents, as well as their dependence on various parameters, is studied using a barotropic quasi-geostrophic channel model. The percentage of steady energy is found to depend on the forcing, friction and topography in a non-monotonic fashion. For example, the percentage of steady currents grows with the energy level in the linear regime (low energies) and decreases when the energy level increases in the nonlinear regime (high energies). Mesoscale steady currents are the energy source for the steady westward flowU, and thereforeUis the maximum when large scale and mesoscale currents are of the same order of magnitude. This happens when the ratioSof the large scale slope βH/f0and the mesoscale rms topographic slope α is of order one.Udecreases for both small and large values ofS.

ISSN:0309-1929    

DOI:10.1080/03091928908221816

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The stability properties of the filament model of Low (1981) are investigated. We use a two-dimensional formalism based on the magnetohydrodynamic energy principle of Bernsteinet al.(1958). For the parameter range observed in quiescent prominences this model describes stable horizontal oscillations with periods of about 3–6 min. In other parameter ranges we find instability which is driven exclusively by compressional effects. The Lorentz force has a continuously stabilizing influence. In addition, it seems that gravity is practically unimportant for the stability state of the equilibrium.

ISSN:0309-1929    

DOI:10.1080/03091928908221817

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Local barotropic instabilities developing in weakly non-parallel large-scale flows are investigated for weak supercriticality building-up on the WKB analysis of Bar-Sever and Merkine (1988). It is found that when the supercriticality is weak, in the parallel flow sense, its associated growth rate can be off-set by the decay rate induced by non-parallelism to generate a marginally unstable local instability. The marginal stability analysis pivots about the turning point region of the WKB solution which interacts with the critical layer of the local parallel problem where the gradient of the potential vorticity of the basic state vanishes. It is also found that for a finite range of supercriticality another critical layer must be encountered by the local eigenfunction of the upstream branch of the WKB solution. A criterion for this additional critical layer encounter is determined. The singularity of this upstream critical layer is removed by local non-parallel effects without affecting the downstream structure of the unstable wavepacket and its eigenfrequency. The instability seems to terminate when it encounters the critical layer. The analysis is supported by numerical simulations of the corresponding initial value problem.

ISSN:0309-1929    

DOI:10.1080/03091928908221818

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Chaotic thermal convection for infinite Prandtl number fluids in large aspect-ratio boxes is investigated within the framework of multimode mean-field theory. Various types of filtering models in the spectral space are employed to eliminate the excess energy which is present when only a few modes are taken in time-dependent spectral method. For Rayleigh numbers slightly in excess of 105the flow is chaotic but is still sufficiently regular so that the lowest three modes dominate the energetics of the flow. The quality of the filtering used in describing the real solution is evaluated in terms of the differences in compactness (fractal dimension) between the filtered strange attractor and the actual one.

ISSN:0309-1929    

DOI:10.1080/03091928908221819

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Numerical simulations of two-dimensional time-dependent thermal convection in a Boussinesq, isoviscous, infinite Prandtl number fluid with isothermal, stress-free boundaries have been performed in large aspect-ratio configurations, in which the fluid is heated from below as well as internally. The value of the basal heated Rayleigh number ranged from 16000 to 800 000 and the Rayleigh number based on internal heat generation was varied from zero to 4 500 000. Large aspect-ratio cells are found to exist, however, they are time-dependent even at small values of the Rayleigh number. In the absence of internal heating, the onset of time-dependence occurs as a regular oscillation in the flow characteristics (Nusselt number, kinetic energy), and is accompanied by the presence of boundary layer instabilities (BLI) which exist within a large aspect-ratio circulation. At high values of the Rayleigh number the BLI are powerful features which leave the confines of the boundary layer and strongly perturb the large aspect-ratio circulation giving the flow a multi-scale character. Convective mixing of these powerful BLI results in heterogeneity in the cell interior which plays a role in the excitation of new BLI and establishes a negative temperature gradient in the cell interior. We have developed a fluid loop model which gives a qualitative explanation for the variation of the onset of time-dependence with aspect-ratio. The addition of internal heating tends to destabilize the large aspect-ratio cell configuration. Multi-cellular states last longer and occur more frequently with increasing amounts of internal heating. These calculations shed new light on a variety of time-dependent phenomena in geodynamics such as subduction, back-arc spreading, intraplate deformation, and the average geotherm. Recently, Jeanloz and Morris proposed that the seismic inhomogeneity parameter (η) can be used to measure the importance of internal heating in mantle convection. However, our calculations indicate that η cannot be used to gauge the importance of internal heating in mantle convection.

ISSN:0309-1929    

DOI:10.1080/03091928908221820

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

We investigate the nature of subcritical, finite-amplitude, double-diffusive convection in the infinite Prandtl number regime, applicable to magma chambers and the D″-layer at the core-mantle boundary, by a two-dimensional, finite-element method based on stream-function, compositional and temperature fields. Grid refinement is used for resolving the disparately-scaled thermal and chemical boundary layers present for the large ratios of the thermal to mass diffusivity (Lewis number) characteristic of magmas. In the diffusive regime a large enoughLeis required for the establishment of steady double-diffusive convection under subcritical conditions. This criticalLevaries nonlinearly with the buoyancy ratioRp, the ratio of the chemical to thermal buoyancy. For largeLe, the steady-state heat transport in the diffusive regime depends weakly onLeand approaches that found for pure thermal convection. In accordance with steady-state boundary-layer scaling, the chemical Nusselt numberNucis found numerically to vary asNuc= 1.02Le0.49Nutfor stress-free boundaries andNuc=0.96Le0.34Nutfor rigid boundaries, withNutthe thermal Nusselt number. For larger aspect-ratios a more complicated bifurcation pattern withLeis found, with the sequence ranging from no steady states, to three steady states and then to a single elongated cell, asLeis increased. Subcritical steady-state solutions can be attained by integrating the set of time-dependent double-diffusive equations. Applications of these results to the chemical boundary layers at the core-mantle boundary would suggest the D″-layer, if it is chemically stratified there, must be a time-dependent feature. Time-dependent calculations show a strong sensitivity to the initial conditions. Subcritical convective solutions in the finger regime exhibit transitions, leading to complex time-dependent flows. The tendency to form narrow cells in the subcritical, finite-amplitude, finger regimes may account for laterally variable composition in a nearly conductive thermal state. Subcritical finger instabilities are found to be able to penetrate through the entire layer in a narrow slot, as in finite Prandtl number calculations.

ISSN:0309-1929    

DOI:10.1080/03091928908221821

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The spectral method previously introduced for the solution of the Lagrangian perturbation equations of rotating, inviscid fluids is applied to the problem of the stability of a class of Riemann ellipsoids. The description of the basis previously outlined is completed and shown to have two particularly desirable features in the present context: it respects a further invariance of the linear operators unique to the present problem, and it diagonalizes the operator representing the perturbation of the self-gravitational potential. This diagonalization property holds both when the fluid is assumed incompressible and, as in the gasdynamic case considered here, when it is compressible.

ISSN:0309-1929    

DOI:10.1080/03091928908221822

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The Gauss coefficients of the geomagnetic field since 1903 are used as a time-dependent boundary condition for the poloidal field in the Earth's mantle. The coefficients are Fourier transformed, and the induction equation for the mantle field is solved in Fourier space. The phase advance of the poloidal field at the base of the mantle, and of the ensuing “poloidal” electromagnetic couple, is investigated as a function of the conductivity profile.

ISSN:0309-1929    

DOI:10.1080/03091928908221823

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor