共查询到20条相似文献，搜索用时 31 毫秒
1.
Susan Friedlander 《地球物理与天体物理流体动力学》2013,107(3-4):189-200
Abstract It is shown that the turning surfaces associated with internal waves in a uniformly rotating, density stratified, Boussinesq fluid in the presence of an arbitrary gravitational field are regular points for the governing eigenvalue differential equation. The results are illustrated for two particular examples that have geophysical and astrophysical significance, namely radially directed spherical gravity, and the gravitational field in a rapidly rotating cylinder. 相似文献
2.
Susan Friedlander 《地球物理与天体物理流体动力学》2013,107(1-3):53-67
Abstract Investigations of an earlier paper (Friedlander 1987a) are extended to include the effect of an azimuthal shear flow on the small amplitude oscillations of a rotating, density stratified, electrically conducting, non-dissipative fluid in the geometry of a spherical shell. The basic state mean fields are taken to be arbitrary toroidal axisymmetric functions of space that are consistent with the constraint of the ‘‘magnetic thermal wind equation''. The problem is formulated to emphasize the similarities between the magnetic and the non-magnetic internal wave problem. Energy integrals are constructed and the stabilizing/destabilizing roles of the shears in the basic state functions are examined. Effects of curvature and sphericity are studied for the eigenvalue problem. This is given by a partial differential equation (P.D.E.) of mixed type with, in general, a complex pattern of turning surfaces delineating the hyperbolic and elliptic regimes. Further mathematical complexities arise from a distribution of the magnetic analogue of critical latitudes. The magnetic extension of Laplace's tidal equations are discussed. It is observed that the magnetic analogue of planetary waves may propagate to the east and to the west. 相似文献
3.
Susan Friedlander 《地球物理与天体物理流体动力学》2013,107(1-2):151-167
Abstract The effects of compressibility on the stability of internal oscillations in the Earth's fluid core are examined in the context of the subseismic approximation for the equations of motion describing a rotating, stratified, self-gravitating, compressible fluid in a thick shell. It is shown that in the case of a bounded fluid the results are closely analogous to those derived under the Boussinesq approximation. 相似文献
4.
L.G. Redekopp 《地球物理与天体物理流体动力学》2013,107(4):289-313
The pattern and propagation of waves generated by steady or oscillatory disturbances travelling horizontally in a rotating, stratified fluid are studied following a technique developed by Lighthill. Both two‐ and three‐dimensional distrubances are investigated. The results show how rotation modifies internal wave patterns in a stratified fluid and how stratification modifies inertial wave patterns in a rotating fluid. The results are used to compute the effective diminution of Taylor column length due to the presence of density stratification. They also show that the appearance of wave crests upstream of a disturbance is possible only when the disturbance is unsteady and that observations of upstream blocking in a two‐dimensional stratified flow can be explained by the existence of a certain class of plane waves as modified by viscosity. 相似文献
5.
AbstractA general linearized wave equation for a stratified rotating fluid is derived and applied to obtain a dispersion relation for waves of short latitudinal extent in a thin shell of fluid. Long period wave solutions in three ocean models are compared: (1) for a stratified ocean with both components of the rotation vector; (2) for a stratified ocean without the horizontal component of rotation, and finally, (3) for a homogeneous ocean without horizontal rotation. The inclusion of the horizontal component of the Earth's rotation is found to have no noticeable effect on the dispersion relation of long period waves; its only influence is the introduction of a vertical phase shift in the motions. The origin of this phase shift is found in the tendency of the motions to satisfy the Taylor-Proudman theorem. The phase shift is of possible oceanographic relevance only for bottom-trapped buoyancy waves in a relatively weak stratification. The differences between the three ocean models are also discussed with the help of graphs of the numerically integrated dispersion relations. The relative influences of shell thinness and stratification in inhibiting the influence of the horizontal component of the earth's rotation are also briefly discussed. 相似文献
6.
Summary The motion generated by an oscillatory point force in an inviscid incompressible rotating stratified fluid is studied, taking into account the effect of stratification on the inertia terms in the equations of motion. The solutions are obtained in closed form using Fourier transforms. The motion is axisymmetric (or not) according as the force acts along (or perpendicular to) the axis of rotation of the fluid. In the hyperbolic case, the motion is confined to the inner region of a cone with vertex at the origin. The solution when there is no rotation-no stratification-neither rotation nor stratification, is deduced and each case is found to differ from the case of rotating stratified fluid in many respects. The solution for a steady force is also deduced in the limit. 相似文献
7.
Melvin E. Stern 《地球物理与天体物理流体动力学》2013,107(2):127-130
Abstract Numerical solutions of the axisymmetric flows during the relatively early phase of spin-up from rest of a stratified fluid in a cylinder are presented. Detailed results are given for a cylinder of aspect ratio of O(l) and for a minute Ekman number, showing axisymmetric spin-up for three values of the stratification parameter. As the stratification increases, the meridional circulation is confined to a region closer to the Ekman layers. An axisymmetric shear wave propagates radially inward from the sidewall, but, unlike the strictly vertical front for a homogeneous fluid, the interface which separates rotating from nonrotating fluid is bow-shaped. For a stratified fluid, the axial vorticity distribution is nonuniform both in the vertical and in the radial directions. With increasing stratification, diffusive vorticity production near the sidewall is more pronounced. Axisymmetric flows in the early phase of spin-up of a stratified fluid are controlled by both the inviscid dynamic effect and the viscous diffusion effect. At a location close to the Ekman layers, the inviscid effect outweighs the viscous effect, in much the same way as in a homogeneous fluid. However, at a location close to mid-depth, the viscous diffusion effect, enhanced by substantial flow gradients in that region, is dominant. This points to the necessity of including the direct effect of viscous diffusion in the interior in formulating an analytical model of stratified spin-up problems. 相似文献
8.
This article commences by surveying the basic dynamics of Earth's core and their impact on various mechanisms of core-mantle coupling. The physics governing core convection and magnetic field production in the Earth is briefly reviewed. Convection is taken to be a small perturbation from a hydrostatic, “adiabatic reference state” of uniform composition and specific entropy, in which thermodynamic variables depend only on the gravitational potential. The four principal processes coupling the rotation of the mantle to the rotations of the inner and outer cores are analyzed: viscosity, topography, gravity and magnetic field. The gravitational potential of density anomalies in the mantle and inner core creates density differences in the fluid core that greatly exceed those associated with convection. The implications of the resulting “adiabatic torques” on topographic and gravitational coupling are considered. A new approach to the gravitational interaction between the inner core and the mantle, and the associated gravitational oscillations, is presented. Magnetic coupling through torsional waves is studied. A fresh analysis of torsional waves identifies new terms previously overlooked. The magnetic boundary layer on the core-mantle boundary is studied and shown to attenuate the waves significantly. It also hosts relatively high speed flows that influence the angular momentum budget. The magnetic coupling of the solid core to fluid in the tangent cylinder is investigated. Four technical appendices derive, and present solutions of, the torsional wave equation, analyze the associated magnetic boundary layers at the top and bottom of the fluid core, and consider gravitational and magnetic coupling from a more general standpoint. A fifth presents a simple model of the adiabatic reference state. 相似文献
9.
N. A. Silant'ev 《地球物理与天体物理流体动力学》2013,107(2-4):183-197
Abstract The exact numerical and approximate analytical solutions of the simplest nonlinear integral equation with second order nonlinearity for the averaged Green function are presented. It is assumed that the turbulence is stationary, homogeneous, isotropic and incompressible. Numerous examples of turbulent spectra are considered (peak-like spectrum, spectra of Kolmogorov's type with different forms of “pumping” regions, stepwise spectra etc.). Special emphasis is given to investigating the case of so called “frozen” turbulence when the parameter ξ =u 0τ/R→∞ where uτ0,R 0 are characteristic velocity, lifetime and space scale of turbulent pulsations, respectively. It is shown that these solutions allow us to calculate the turbulent diffusivities accurately for arbitrary spectra with any values of the parameter ξ. The results take into account the possible helicity of turbulence concerned only with scalar passive fields (number density and temperature). 相似文献
10.
BRUCE HUNT 《水文科学杂志》2013,58(3):331-342
ABSTRACT The Duhamel superposition integral is used to obtain some exact solutions for unit hydrograph applications. These equations and numerical examples are used to show that oscillations will occur in an S-curve when the time step is less than the excess rainfall duration if the measured hydrograph differs from a hydrograph that would be obtained by solving a linear differential equation with time-independent coefficients. The implications of this result with regard to the calculation of the instantaneous unit hydrograph (IUH) are discussed. 相似文献
11.
S. D. London 《地球物理与天体物理流体动力学》2013,107(1):259-286
Abstract An asymptotic approximation to the solution of the time-dependent linearized equations governing the motion of an incompressible, inviscid rotating fluid of spherical configuration having uniform density, variable depth and a free upper surface is obtained using the ray method without a shallow water assumption. This result is then modified to obtain a ray approximation to the solution of the time-reduced problem and the free oscillations of the fluid are studied. Axisymmetric modes covering the whole sphere and asymmetric modes trapped in both equatorial and non-equatorial regions are discovered, and all these modes are shown to have countably many resonance frequencies. A shallow water limit is defined and this limit of the time-reduced approximation is obtained. Most of the modes of free oscillation are lost in this limit and the limiting axisymmetric modes are shown to be trapped in the equatorial region and are singular at the wave region boundaries. The limiting approximation is compared to previous results obtained under a shallow water assumption. 相似文献
12.
E. Knobloch 《地球物理与天体物理流体动力学》2013,107(1-2):133-158
Abstract Angular momentum driven instabilities in a stratified differentially rotating star are investigated. In the strong buoyancy limit axisymmetric instabilities of the Goldreich-Schubert type are the most important. A detailed discussion of the linear and small amplitude theories at an arbitrary latitude is given. The bifurcation to finite amplitude steady modes is typically transcritical, and occurs whenever the angular momentum or its gradient is neither parallel not perpendicular to local gravity. Such misalignments enhance the time scale for transport of angular momentum by the Goldreich-Schubert instability. Depending on the turbulent viscosity produced by secondary shear instabilities time scales as short as the Kelvin-Helmholtz time scale are possible. 相似文献
13.
Abstract The paper consists of two parts. The first introduces the dynamo equation into a rotating gaseous disk of finite thickness and then searches for its solution for the generation and maintenance of large-scale bisymmetric spiral (BSS) magnetic fields. We determine numerically the dynamo strength and vertical thickness of the gaseous disk which are necessary for the BSS magnetic fields to rotate as a wave over large area of the disk. Next we present linearized equations of motion for the self-gravitating disk gas under the Lorentz force due to the BSS magnetic fields. Since the angular velocity of the BSS field is very close to that of the spiral density wave, a nearly-resonant interaction is caused between these two waves to produce large-amplitude condensation of gas in a double-spiral way. The BSS magnetic field is considered as a promising agency to trigger and maintain the spiral density wave. 相似文献
14.
Willem V.R. Malkus 《Physics of the Earth and Planetary Interiors》1979,20(2-4):181-184
The linear solvability conditions are found for any field of force leading to steady motion in a stratified rotating medium. A general solution for such motion is determined. For the Lorentz force, it is shown that a unique relation between all axisymmetric poloidal and toroidal magnetic fields is specified. A path to solutions for the non-linear -dynamo stability problem compatible with these constraints is outlined. 相似文献
15.
Abstract The problem of topographic forcing by an obstacle against the boundary of a rotating flow is considered in various parameter regimes. The timescale for the motion is the topographic vortex-stretching time, which is inversely proportional to the background rotation rate and the fractional height of the obstacle. For slow flows this time is short compared with the advection time and the governing equation of conservation of potential vorticity is linear. The final state satisfies the non-linear equation for the advection of potential vorticity, however, and so time dependence has given a specific solution to a non-linear problem. The presence of the sidewall causes a stagnant Taylor column to be set up far more rapidly than cases with no sidewall. It is shown that viscosity and mixing arrests the inviscid evolution at some stage, thus some fluid still crosses the obstacle in the steady state. These solutions suggest that experimental results on separation obtained by Griffiths and Linden (1983) can tentatively be ascribed to entrainment and expulsion of fluid through vertical shear layers at the edge of the topography. 相似文献
16.
Abstract A study has been made of a basic state of axisymmetric flow, at large rotational Reynolds numbers, in a double-diffusive stratified fluid contained in a vertically-mounted, differentially-rotating cylindrical cavity. The aim is to describe the qualitative characteristics of the flow of a fluid, the density of which is stratified by two diffusive effects, i.e., temperature and salinity gradients. Attention is confined to situations in which the temperature and salinity gradients make opposing contributions to the overall density profile, the undisturbed stratification being gravitationally stable. Finite difference numerical solutions of the governing Navier-Stokes equations have been obtained using the Boussinesq approximation. The results are presented in a way that illustrates the explicit effects of double-diffusivity when the cavity aspect ratio, height/radius, is O(1). The principal non-dimensional parameters characterizing the flow field are identified. In the interior core, the primary dynamic balance is between the horizontal density gradient and the vertical shear of the prevailing azimuthal velocity. The effective stratification is seen to decrease as the double-diffusivity increases, even if the overall stratification parameter, St, is held constant. The solute field contains a very thin boundary layer structure at large Lewis numbers. The effective stratification increases with the Prandtl number. Results have been derived for extreme values of the cavity aspect ratio. For small cavity aspect ratios, the dominant dynamic ingredients are viscous diffusion and rotation. For large aspect ratios, the bulk of the flow field is determined by the rotating sidewall. In this case, the direct influence of the double-diffusivity is minor. 相似文献
17.
The evolution of localised jets and periodic nonlinear waves in rotating shallow water magnetohydrodynamics (rotating SWMHD) and standard rotating shallow water model (RSW) is compared within the framework of translationally-invariant 1.5-dimensional configurations, which are traditionally used in geophysical fluid dynamics for studying geostrophic adjustment and frontogenesis. Such configurations also allow for exact nonlinear wave solutions in both models. A theory of the magneto-geostrophic adjustment, i.e. adjustment of an arbitrary initial configuration to a state of magneto-geostrophic equilibrium in RSWMHD, is developed and confirmed by numerical simulations with a finite-volume well-balanced code. The code is resolving all kinds of waves in the model and corresponding weak solutions equally well. It is benchmarked by reproducing exact solutions – steady essentially nonlinear Alfvèn and mixed magneto-inertia-gravity waves – and used to demonstrate robustness of these solutions with respect to localised along-wave perturbations. It is also shown how the results on adjustment can be extended to the fully 2-dimensional case. 相似文献
18.
P. J. Mason 《地球物理与天体物理流体动力学》2013,107(1):137-154
Abstract Measurements have been made of the net horizontal force F acting on a sphere moving with horizontal velocity U (Reynolds numbers in the range 102-104) through a stratified fluid rotating about a vertical axis with uniform angular velocity Ω. In both homogeneous and stratified rotating fluids with small Rossby number R(R = U/Ωa ? 1 where a is the radius of the sphere) the force F is of magnitude 2ΩρUV (where ρ is the density of the fluid and V is the volume of the sphere). In a homogeneous fluid the relative directions of F and U were found to depend on the quantity F = 8Ωa 2/UD (where D is the depth of the fluid in which the object is placed (Mason, 1975)). In a rotating stratified fluid the relative directions of F and U are found to depend on the inverse Froude number k(k = Na/U where N 2 = (g/δ)?ρ/?z) provided D > 4aΩ/N. In a homogeneous fluid with F ? 1 the force F is mainly in the U direction (a drag force due to inertial wave radiation) and is ～ ?0.4 |MX 2ΩρUV For F ? 1 a “Taylor column” occurs and the force, in correspondence with theoretical expectations, is ～ - 2Ω |MX UρV In a rotating stratified fluid with N ～2Ω and k ? 1 the force F is mainly in the U direction but is roughly one half of that occurring in the homogeneous situation with F ? 1 (tentatively explained as due to the evanescence of inertia-gravity disturbances). In a rotating stratified fluid with k ? 1 the flow should have no vertical motion (as with F ? 1) and again in correspondence with theoretical expectations the drag is ～ ?2 Ω |MX UρV. In a non-rotating stratified fluid the drag coefficient C D(C D = F U/½?ρU 2) was measured in the range k = 0.1 to 10 and had a maximum value ～ 1.2 for k ～ 3. 相似文献
19.
The forward computation of the gravitational and magnetic fields due to a 3D body with an arbitrary boundary and continually varying density or magnetization is an important problem in gravitational and magnetic prospecting. In order to solve the inverse problem for the arbitrary components of the gravitational and magnetic anomalies due to an arbitrary 3D body under complex conditions, including an uneven observation surface, the existence of background anomalies and very little or no a priori information, we used a spherical coordinate system to systematically investigate forward methods for such anomalies and developed a series of universal spherical harmonic expansions of gravitational and magnetic fields. For the case of a 3D body with an arbitrary boundary and continually varying magnetization, we have also given the surface integral expressions for the common spherical harmonic coefficients in the expansion of the magnetic field due to the body, and a very precise numerical integral algorithm to calculate them. Thus a simple and effective method of solving the forward problem for magnetic fields due to 3D bodies of this kind has been found, and in this way a foundation is laid for solving the inverse problem of these magnetic fields. In addition, by replacing the parameters and unit vectors in the spherical harmonic expansion of a magnetic field by gravitational parameters and a downward unit vector, we have also derived a forward method for the gravitational field (similar to that for the magnetic case) of a 3D body with an arbitrary boundary and continually varying density. 相似文献
20.
E. I. Ryzhak Sh. A. Mukhamediev S. V. Sinyukhina 《Izvestiya Physics of the Solid Earth》2016,52(6):787-802
Various geophysical processes which can lead to the origination of gravitational instability of the Rayleigh-Taylor type in layered bulk-elastic geomasses are analyzed. The analysis is based on obtained by the authors general results of theoretical study of two-layer systems of heavy bulk-elastic materials which are arbitrarily stratified over depth and occupy domains of arbitrary shape. Additionally some presented in a number of recent publications erroneous assertions related to considered issues of stability, are criticized. 相似文献