共查询到20条相似文献，搜索用时 31 毫秒
1.
Abstract In order to show that aperiodic magnetic cycles, with Maunder minima, can occur naturally in nonlinear hydromagnetic dynamos, we have investigated a simple nonlinear model of an oscillatory stellar dynamo. The parametrized mean field equations in plane geometry have a Hopf bifurcation when the dynamo number D=1, leading to Parker's dynamo waves. Including the nonlinear interaction between the magnetic field and the velocity shear results in a system of seven coupled nonlinear differential equations. For D>1 there is an exact nonlinear solution, corresponding to periodic dynamo waves. In the regime described by a fifth order system of equations this solution remains stable for all D and the velocity shear is progressively reduced by the Lorentz force. In a regime described by a sixth order system, the solution becomes unstable and successive transitions lead to chaotic behaviour. Oscillations are aperiodic and modulated to give episodes of reduced activity. 相似文献
2.
Abstract The simplest model for geophysical flows is one layer of a constant density fluid with a free surface, where the fluid motions occur on a scale in which the Coriolis force is significant. In the linear shallow water limit, there are non-dispersive Kelvin waves, localized near a boundary or near the equator, and a large family of dispersive waves. We study weakly nonlinear and finite depth corrections to these waves, and derive a reduced system of equations governing the flow. For this system we find approximate solitary Kelvin waves, both for waves traveling along a boundary and along the equator. These waves induce jets perpendicular to their direction of propagation, which may have a role in mixing. We also derive an equivalent reduced system for the evolution of perturbations to a mean geostrophic flow. 相似文献
3.
Michael I. Bergman 《地球物理与天体物理流体动力学》2013,107(1-4):151-176
Abstract 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 the H layer. 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 the H layer, 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. 相似文献
4.
Nonlinear analysis of two-dimensional steady flows with density stratification in the presence of gravity is considered. Inadequacies of Long's model for steady stratified flow over topography are explored. These include occurrence of closed streamline regions and waves propagating upstream. The usual requirements in Long's model of constant dynamic pressure and constant vertical density gradient in the upstream condition are believed to be the cause of these inadequacies. In this article, we consider a relaxation of these requirements, and also provide a systematic framework to accomplish this. As illustrations of this generalized formulation, exact solutions are given for the following two special flow configurations: the stratified flow over a barrier in an infinite channel; the stratified flow due to a line sink in an infinite channel. These solutions exhibit again closed-streamline regions as well as waves propagating upstream. The persistence of these inadequacies in the generalized Long's model appears to indicate that they are not quite consequences of the assumptions of constant dynamic pressure and constant vertical density gradient in Long's model, contrary to previous belief. On the other hand, solutions admitted by the generalized Long's model show that departures from Long's model become small as the flow becomes more and more supercritical. They provide a nonlinear mechanism for the generation of columnar disturbances upstream of the obstacle and lead in subcritical flows to qualitatively different streamline topological patterns involving saddle points, which may describe the lee-wave-breaking process in subcritical flows and could serve as seats of turbulence in real flows. The occurrences of upstream disturbances in the presence of lee-wave-breaking activity described by the present solution are in accord with the experiments of Long (Long, R.R., “Some aspects of the flow of stratified fluids, Part 3. Continuous density gradients”, Tellus 7, 341--357 (1955)) and Davis (Davis, R.E., “The two-dimensional flow of a stratified fluid over an obstacle”, J. Fluid Mech. 36, 127–143 ()). 相似文献
5.
6.
The paper starts with a discussion of the linear stochastic theory of ocean waves and its various nonlinear extensions. The directional spectrum, with its unique dispersion relation connecting frequency (ω) and wavenumber (k), is no longer valid for nonlinear waves, and examples of $\left( \mathbf{k},\omega\right) The paper starts with a discussion of the linear stochastic theory of ocean waves and its various nonlinear extensions. The
directional spectrum, with its unique dispersion relation connecting frequency (ω) and wavenumber (k), is no longer valid for nonlinear waves, and examples of ( k,w)\left( \mathbf{k},\omega\right) -spectra based on analytical expressions and computer simulations of nonlinear waves are presented. Simulations of the dynamic
nonlinear evolution of unidirectional free waves using the nonlinear Schr?dinger equation and its generalizations show that
components above the spectral peak have larger phase and group velocities than anticipated by linear theory. Moreover, the
spectrum does not maintain a thin well-defined dispersion surface, but rather develops into a continuous distribution in ( k,w)\left( \mathbf{k,}\omega\right) -space. The majority of existing measurement systems rely on linear theory for the interpretation of their data, and no measurement
systems are currently able to measure the full spectrum in the open ocean with high accuracy. Nevertheless, there exist a
few low-resolution systems where data may be interpreted within a minimal assumption of a non-restricted ( k,w)\left( \mathbf{k,}\omega\right) -spectrum. The theory is reviewed, and analyses based on conventional spectral analysis as well as a directional wavelet analysis
are carried out on data from a compact laser array at the Ekofisk field in the North Sea. The investigation confirms the strong
impact of the second order spectrum below the spectral peak, but is non-conclusive about the off-set in the support of the
first order spectrum seen in the dynamical simulations. 相似文献
7.
John W. Miles 《地球物理与天体物理流体动力学》2013,107(3-4):243-251
Abstract A variational approximation to the dispersion relation for trapped waves on a flat shelf of depth h 1, bounded internally by a vertical coast and externally by a semi-infinite ocean of depth h 2>h 1, is obtained through an integral-equation formulation that accounts for all of the non-propagated modes that are excited at the discontinuity in depth (the conventional formulation of the edge-wave problem allows only for the propagated mode on the shelf and the dominant, non-propagated mode in the deep water). Coriolis effects are neglected. The exact result in the limit ω2 h 2/g↓0 (ω = angular frequency) is obtained by conformal mapping and compared with the variational approximation, which proves to be quite accurate over the entire range 1>h 2/h 1>x. The effects of the higher-order, non-propagated modes are found to be small for the long waves observed over the Southern California shelf by Snodgrass, Munk and Miller (1962). 相似文献
8.
R. Grimshaw 《地球物理与天体物理流体动力学》2013,107(1):3-16
Abstract Continental shelf waves are examined in the long wavelength limit, and the effects of weak topographic dispersion calculated. These dispersive effects are then balanced against nonlinear terms and a Korteweg-de Vries equation is derived to describe the evolution of the wave amplitude. Two particular cases are worked in detail. 相似文献
9.
Abstract We study the nonlinear stability of MHD waves propagating in a two-dimensional, compressible, highly magnetized, viscous plasma. These waves are driven by a weak, shear body force which could be imposed by large scale internal fluctuations present in the solar atmosphere. The effects of anisotropic viscosity (leading to a cubic damping) and of the nonlinear coupling of the Alfven and the magnetoacoustic waves are analysed using Galerkin and multiple-scale analysis: the MHD equations are reduced to a set of nonlinear ordinary differential equations which is then suitably truncated to give a model dynamical system, representing the interaction of two complex Galerkin modes. For propagation oblique to the background magnetic field, analytical integration shows that the low-wavenumber mode is physically unstable. For propagation parallel to the background magnetic field the high-wavenumber wave can undergo saddlenode bifurcations, in way that is similar to the van der Pol oscillator; these bifurcations lead to the appearance of a hysteresis cycle. A numerical integration of the dynamical system shows that a sequence of Hopf bifurcations takes place as the Reynolds number is increased, up to the onset of nonperiodic behaviour. It also shows that energy can be transferred from the low- wavenumber to the high-wavenumber mode. 相似文献
10.
William K. Dewar 《地球物理与天体物理流体动力学》2013,107(1-4):53-85
Abstract The term ‘‘solitary wave'’ is usually used to denote a steadily propagating permanent form solution of a nonlinear wave equation, with the permanency arising from a balance between steepening and dispersive tendencies. It is known that large-scale thermal anomalies in the ocean are subject to a steepening mechanism driven by the beta effect, while at the smaller deformation scale, such phenomena are highly dispersive. It is shown here that the evolution of a physical system subject to both effects is governed by the ‘‘frontal semi-geostrophic equation'’ (FSGE), which is valid for large amplitude thermocline disturbances. Solitary wave solutions of the FSGE (here named planetons) are calculated and their properties are described with a view towards examining the behavior of finite amplitude solitary waves. In contrast, most known solitary wave solutions belong to weakly nonlinear wave equations (e.g., the Korteweg—deVries (KdV) equation). The FSGE is shown to reduce to the KdV equation at small amplitudes. Classical sech2 solitons thus represent a limiting class of solutions to the FSGE. The primary new effect on planetons at finite amplitudes is nonlinear dispersion. It is argued that due to this effect the propagation rates of finite amplitude planetons differ significantly from the ‘‘weak planeton'', or KdV, dispersion relation. Planeton structure is found to be simple and reminiscent of KdV solitons. Numerical evidence is presented which suggests that collisions between finite amplitude solitary waves are weakly inelastic, indicating the loss of true soliton behavior of the FSGE at moderate amplitudes. Lastly, the sensitivity of solitary waves to the existence of a nontrivial far field is demonstrated and the role of this analysis in the interpretation of lab experiments and the evolution of the thermocline is discussed. 相似文献
11.
EULAG is a computational model for simulating flows across a wide range of scales and physical scenarios. A standard option
employs an anelastic approximation to capture nonhydrostatic effects and simultaneously filter sound waves from the solution.
In this study, we examine a localized gravity wave packet generated by instabilities in Held-Suarez climates. Although still
simplified versus the Earth’s atmosphere, a rich set of planetary wave instabilities and ensuing radiated gravity waves can arise. Wave packets
are observed that have lifetimes ≤ 2 days, are negligibly impacted by Coriolis force, and do not show the rotational effects
of differential jet advection typical of inertia-gravity waves. Linear modal analysis shows that wavelength, period, and phase
speed fit the dispersion equation to within a mean difference of ∼ 4%, suggesting an excellent fit. However, the group velocities
match poorly even though a propagation of uncertainty analysis indicates that they should be predicted as well as the phase
velocities. Theoretical arguments suggest the discrepancy is due to nonlinearity — a strong southerly flow leads to a critical
surface forming to the southwest of the wave packet that prevents the expected propagation. 相似文献
12.
L. Nocera 《地球物理与天体物理流体动力学》2013,107(1-4):239-252
Abstract We study the propagation of nonlinear MHD waves in a highly magnetized plasma cavity. The cavity's moving boundaries generate Alfvén waves, which in turn drive and interact with slow magnetosonic waves. The interacting wave system is analyzed by a Galerkin and multiple-scale analyses leading to simple dynamical equations. When the frequency of the forcing provided by the moving boundaries and that of the fundamental Alfvén eigenmode are close, the cavity behaves like a Duffing oscillator. Application of the Melnikov function theory shows that the Alfvén wave's amplitude undergoes both flip and saddle-node bifurcations as the amplitude and the phase of the boundary forcing vary. Direct numerical integration confirms these results and provides an estimate of the amount of energy dissipated in the bifurcations. 相似文献
13.
《Journal of Atmospheric and Solar》2003,65(3):355-358
FAST observations have indicated signatures of large amplitude solitary waves in the auroral zone of the earth's ionosphere. Our objective here is to propose a model for the generation of density cavities by the ponderomotive force of electron-acoustic waves. For this purpose, we derive a nonlinear Schrödinger equation for the electron-acoustic wave envelope as well as a driven (by the electron-acoustic wave ponderomotive force) ion-acoustic wave equation. Possible stationary solutions of our coupled equations are obtained. 相似文献
14.
In 1996, St Pierre (1996) reported numerical simulations of a buoyant blob migrating across the earth's outer core and subject to the combined effects of rotation and an azimuthal magnetic field. He noted that the blob rapidly fragments into a series of plate-like structures. Quite independently, Davidson (1995, 1997) discovered a similar behaviour in the context of low- R m turbulence (without a Coriolis force) and showed that this phenomenon has its roots in the destruction of angular momentum by the Lorentz force. The purpose of this paper is to pull together these earlier studies and, in particular, to determine whether or not St. Pierre's platelets are also a consequence of the destruction of angular momentum. We confirm that this is indeed the case. 相似文献
15.
A. D. Sneyd 《地球物理与天体物理流体动力学》2013,107(1-3):141-151
Abstract Formation of electric current sheets in the corona is thought to play an important role in solar flares, prominences and coronal heating. It is therefore of great interest to identify magnetic field geometries whose evolution leads to variations in B over small length-scales. This paper considers a uniform field B 0[zcirc], line-tied to rigid plates z = ±l, which are then subject to in-plane displacements modeling the effect of photospheric motion. The force-free field equations are formulated in terms of field-line displacements, and when the imposed plate motion is a linear function of position, these reduce to a 4 × 4 system of nonlinear, second-order ordinary differential equations. Simple analytic solutions are derived for the cases of plate rotation and shear, which both tend to form singularities in certain parameter limits. In the case of plate shear there are two solution branches—a simple example of non-uniqueness. 相似文献
16.
17.
The diagnostics of large scale geostrophy in a stratified atmosphere are revisited in pressure coordinates using a full Coriolis force. This formulation of geostrophy includes the horizontal and vertical projections of the planetary rotation vector, is valid for shallow and deep atmospheres, accounts for the spherical geometry of the atmosphere, is not singular at the equator, and provides partial information about vertical velocities. The new expressions, although an improvement over the standard approach, are still only estimates because of the terms that are being neglected and because of the uncertainties in the observational data. The magnitudes of the errors are discussed. The accuracy of the standard hydrostatic approximation in the geostrophic regime is gauged and an alternative approach is discussed. The standard hydrostatic approximation predicts much smaller wind shears than those derived from the primitive equations. The observations are a set of global temperature maps of the upper Jovian troposphere at pressures, between 100 and 400 mbar, obtained from mid-infrared observations in June, 1996. Maps of the large-scale thermal winds show higher concentration of longitudinal structures and vertical velocities along two particular zonal bands at latitudes near 15°N and 15°S. Observational criteria are proposed to validate the standard versus the new diagnostic as well as the possible geostrophic regime of Jupiter's zonal jets. 相似文献
18.
J. P. Louis 《地球物理与天体物理流体动力学》2013,107(1):229-239
Abstract The possible interaction of trapped midoceanic boundary waves with a nearby coastline is examined by considering a step trench-ridge topography adjoining a semi-infinite straight coastline. The full dispersion equation, including the effect of the earth's rotation, is derived for long waves over this topography. It is shown that the presence of the coastline begins to have a significant effect on the behaviour of quasigeostrophic ridge waves whenever the wave length is greater than three times the ridge coastline separation. As an example, the dispersion curves are presented for the topography of the Heceta Bank off the coast of Oregon and it is conjectured that the presence of this off-shore ridge may provide an explanation for the anomalous direction of propagation of the 0.1 c.p.d. shelf wave reported by Mooers and Smith (1968). 相似文献
19.
Stefano Pierini 《地球物理与天体物理流体动力学》2013,107(1-4):97-108
Abstract In the context of ageostrophic theory in a homogeneous ocean, a nondimensional number is determined which corresponds to the Ursell number for long gravity waves. It is defined as Q = NL 2/h 3, where N is the amplitude of the wave travelling along the long length-scale direction, L is its length and h (which for gravity waves is the water depth) is given by h=(l 4 f 2/g)1/3. where l is the short length-scale, f the Coriolis parameter and g the acceleration due to gravity. The physical meaning of Q is as follows: if Q? O(1) the free evolution of the wave is linear and weakly dispersive, if Q = O(1) nonlinear and dispersive effects balance out and finally if Q ?O(1) the evolution is nonlinear and non-dispersive. Expressions for the time scales for the development of dispersive and nonlinear effects are also determined. These results apply to topographically trapped waves, namely barotropic continental shelf and double Kelvin waves travelling along a rectilinear topographic variation. 相似文献
20.
W. H. Raymond 《Pure and Applied Geophysics》2000,157(10):1767-1779
--This study examines two-dimensional large-scale atmospheric circulations that are centered over the equator. The influence of terms that contain the Coriolis parameter &gif1; is highlighted in a simple linear inviscid equatorial beta model. Two general types of oscillatory circulations are identified within the y-z plane. In a neutral or stably stratified atmosphere one circulation is expressed in terms of an analytic solution that contains Hermite polynomials, while a second solution is described in terms of a Bessel function. In the more traditional Hermite polynomial solution the influence of f' is small as suggested by scale analysis. Neutral stability provides the only exception. In contrast to these findings, the Bessel solution contains frequencies with semiannual periods that depend entirely on &gif2;. This solution describes cross-equatorial flow with a maximum meridional velocity at the equator. Consequently, this indicates that to model the atmosphere it is necessary to include in the model equations all terms containing f', since they influence oscillatory circulations that describe internal waves with periods that vary from a few days to semiannual. 相似文献