共查询到20条相似文献，搜索用时 46 毫秒
1.
Yakov Afanasyev 《地球物理与天体物理流体动力学》2013,107(2):79-95
Results from a new series of experiments on the geophysically important issue of spontaneous emission of internal gravity waves during unsteady interactions of vortical structures are presented. Vortex dipoles are a common element of a quasi-two-dimensional turbulent flow. Vortex dipoles perform translational motion and can collide with other vortices. During collision events the flow is unsteady and unbalanced and a further adjustment process associated with these events can therefore result in the spontaneous emission of gravity waves. Our laboratory experiments demonstrate that gravity waves are emitted when two translating vortex dipoles interact (collide) in a layered fluid, in accord with the current theoretical results. The emission was evident both in a two-layer system and in a fluid with a linear distribution of density with depth. The waves were generated during the period of deceleration of the secondary dipoles which constitute a vortex quadrupole emerging immediately after the collision of the primary dipoles. 相似文献
2.
S.A. Thorpe 《地球物理与天体物理流体动力学》2013,107(1):59-74
The effects of finite amplitude are examined in two-dimensional, standing, internal gravity waves in a rectangular container which rotates about a vertical axis at frequency f/ 2. Expressions are given for the velocity components, density fluctuations and isopycnal displacements to second order in the wave steepness in fluids with buoyancy frequency, N , of general form, and the effect of finite amplitude on wave frequency is given in an expansion to third order. The first order solutions, and the solutions to second order in the absence of rotation, are shown to conserve energy during a wave cycle. Analytical solutions are found to second order for the first two modes in a deep fluid with N proportional to sech( az ), where z is the upward vertical coordinate and a is scaling factor. In the absence of rotation, results for the first mode in the latter stratification are found to be consistent with those for interfacial waves. An analytical solution to fourth order in a fluid with constant N is given and used to examine the effects of rotation on the development of static instability or of conditions in which shear instability may occur. As in progressive internal waves, an effect of rotation is to enhance the possibility of shear instability for waves with frequencies close to f . The analysis points to a significant difference between the dynamics of standing waves in containers of limited size and progressive internal waves in an unlimited fluid; the effect of boundaries on standing waves may inhibit the onset of instability. A possible application of the analysis is to transverse oscillations in long, narrow, steep-sided lakes such as Loch Ness, Scotland. 相似文献
3.
Thermal instabilities in the form of oscillatory magnetoconvection representing diffusively modified Alfvén waves in an electrically-conducting Bénard fluid layer of rigid walls in the presence of a vertical magnetic field are investigated. Emphasis of the article is on the transition from a nearly undamped Alfvén wave to diffusively modified Alfvén waves, and on the effect of physically realisable magnetic field boundary conditions on magnetoconvection. It is found that the extra magnetic dissipation in the magnetic Hartmann boundary layers can enhance oscillatory magnetoconvection in the form of strongly modified Alfvén waves. Oscillatory magnetoconvection produced solely by the Alfvén wave mechanism can be the most unstable mode even in the presence of a strong viscous effect. This article also represents the first study on the effect of an electrically conducting wall on magnetoconvection which is associated with a nonlinear eigenvalue problem. We find that the electrically perfectly conducting condition does not yield a good approximation for magnetoconvection with an electrically highly conducting wall. The size of oscillation frequency with an electrically highly conducting wall can be more than a factor of 2 larger than that obtained using the perfectly conducting condition. 相似文献
4.
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
5.
The weakly nonlinear dynamics of packets of equatorial Kelvin waves is studied using singular perturbation theory applied to the shallow water wave equations. Within the limits of the perturbation theory, which is formally restricted to weak mean shear and weak nonlinearity, we derive a Nonlinear Schroedinger equation to describe the envelope of the wave packet. We find that nonlinearity has a defocusing effect so that coherent wave packets must owe their existence entirely to the generation mechanism rather than to nonlinear focusing of a broad initial disturbance. 相似文献
6.
Diurnal sea breeze effects on inner-shelf cross-shore exchange 总被引：1，自引：0，他引：1
Cross-shore exchange by strong (cross-shore wind stress, τsx>0.05 Pa) diurnal (7–25 h) sea breeze events are investigated using two years of continuous wind, wave, and ocean velocity profiles in 13 m water depth on the inner-shelf in Marina, Monterey bay, California. The diurnal surface wind stress, waves, and currents have spectral peaks at 1, 2, and 3 cpd and the diurnal variability represents about 50% of the total variability. During sea breeze relaxation (−0.05<τsx<0.05 Pa), a background wave-driven inner-shelf Eulerian undertow profile exists, which is equal and opposite to the Lagrangian Stokes drift profile, resulting in a net zero Lagrangian transport at depth. In the presence of a sea breeze (τsx>0.05 Pa), a uniform offshore profile develops that is different from the background undertow profile allowing cross-shore Lagrangian transport to develop, while including Lagrangian Stokes drift. The diurnal cross-shore current response is similar to subtidal (>25 h) cross-shore current response, as found by Fewings et al. (2008). The seasonality of waves and winds modify the diurnal sea breeze impact. It is suggested that material is not transported cross-shore except during sea breeze events owing to near zero transport during relaxation periods. During sea breeze events, cross-shore exchange of material appears to occur onshore near the surface and offshore near the sea bed. Since sea breeze events last for a few hours, the long-term cross-shore transport is incremental each day. 相似文献
7.
8.
Abstract For the purpose of deriving an analytical parametrization, oceanic mesoscale eddies are represented as a horizontally propagating wave field in a non-uniform environment. The mathematical analysis rests upon the assumption of scale disparity between a short eddy scale and a long mean-flow scale. The novelty resides in the treatment of finite-amplitude eddies, which, moreover, form either a band-like or a cell-like pattern. A barotropic ocean is chosen as a first step to illustrate the mathematical analysis, but dissipation is included. The main result is an analytical derivation of a mesoscale-eddy parametrization: the mean-flow equation contains Reynolds-stress terms which are computed from parameters of the eddy field, which, in turn, are predicted by separate evolution equations. Due to restrictive assumptions (barotropy, orthogonal waves,…), the parametrization established here should be viewed only as a first step toward the design of a more practical parameterization for large-scale modelling. 相似文献
9.
Abstract In this paper we consider the propagation of magneto-acoustic-gravity waves in a compressible, conducting isothermal atmosphere permeated by a uniform horizontal magnetic field. The singular levels, arising in a horizontal magnetic field, are considered in their most general form. Exact analytical solutions for a number of particular cases of wave propagation are obtained. The wave transformation is analyzed for all these cases using the solutions obtained. Based on the theory of wave propagation across a magnetic field, low-frequency wave trapping in a chromospheric resonator is explained, and some properties of running penumbral waves are discussed. 相似文献
10.
A formal theory is presented for the balanced evolution of a small-amplitude, small-scale wave field in the presence of an axisymmetric vortex initially in gradient-wind balance and the accompanying changes induced in the vortex by the azimuthally averaged wave fluxes. The theory is a multi-parameter, asymptotic perturbation expansion for the conservative, rotating, f-plane, shallow-water equations. It extends previous work on Rossby-wave dynamics in vortices and more generally provides a new perspective on wave/mean-flow interaction in finite Rossby-number regimes. Some illustrative solutions are presented for a perturbed vortex undergoing axisymmetrization. 相似文献
11.
Abstract We have studied the behavior of nonlinear waves in isothermal atmospheres using an improved beam scheme method. It is shown that although the magnitude of the mass leakage due to side beams is significant, nevertheless in a motion close to hydrostatic equilibrium it can be suppressed, if special density distributions and/or suitable mesh intervals are selected. We adopt as the parameters for our model of the atmospheres M=1 M[odot], R=50 R[odot] and T=4864 K. The time variation of the physical quantities in each cell is found for several oscillation periods. The critical frequency for the model atmosphere in the case of waves with a weak nonlinearity seems to be consistent with that in the linear theory. 相似文献
12.
W. D. McKee 《Pure and Applied Geophysics》1977,115(4):937-949
The refraction and reflection of linear water waves entering a following jet-type current is considered. A short-wave asymptotic solution is presented and the reflection coefficient found. This varies continuously from zero when the waves are normal to the current to unity when they are very oblique to it. The trapping of waves by an opposing current is also considered. 相似文献
13.
The time-dependent three-dimensional distribution of a population of Karenia brevis is explored through the use of an Eulerian model. The model combines a previously developed physiologically based behavioral model of these dinoflagellates with a simple model for a three-dimensional wind driven flow field over a variable-depth continental shelf. The behavioral model is simplified from that used in previous applications and sigma coordinates are utilized in the model. Model results indicate that even for the relatively weak wind driven currents used in our simulation a non-quantized population can develop into two spatially distinct quantized populations in a period as short as 1 day where, for present purposes, a quantized population is one in which all cells are at the same stage of the cell cycle. 相似文献
14.
In viscoelastic media, the slowness vector p of plane waves is complex-valued, p = P + iA. The real-valued vectors P and A are usually called the propagation and the attenuation vector, repectively. For P and A nonparallel, the plane wave is called inhomogeneousThree basic approaches to the determination of the slowness vector of an inhomogeneous plane wave propagating in a homogeneous viscoelastic anisotropic medium are discussed. They differ in the specification of the mathematical form of the slowness vector p. We speak of directional specification, componental specification and mixed specification of the slowness vector. Individual specifications lead to the eigenvalue problems for 3 × 3 or 6 × 6 complex-valued matrices.In the directional specification of the slowness vector, the real-valued unit vectors N and M in the direction of P and A are assumed to be known. This has been the most common specification of the slowness vector used in the seismological literature. In the componental specification, the real-valued unit vectors N and M are not known in advance. Instead, the complex-valued vactorial component p
of slowness vector p into an arbitrary plane with unit normal n is assumed to be known. Finally, the mixed specification is a special case of the componental specification with p
purely imaginary. In the mixed specification, plane represents the plane of constant phase, so that N = ±n. Consequently, unit vector N is known, similarly as in the directional specification. Instead of unit vector M, however, the vectorial component d of the attenuation vector in the plane of constant phase is known.The simplest, most straightforward and transparent algorithms to determine the phase velocities and slowness vectors of inhomogeneous plane waves propagating in viscoelastic anisotropic media are obtained, if the mixed specification of the slowness vector is used. These algorithms are based on the solution of a conventional eigenvalue problem for 6 × 6 complex-valued matrices. The derived equations are quite general and universal. They can be used both for homogeneous and inhomogeneous plane waves, propagating in elastic or viscoelastic, isotropic or anisotropic media. Contrary to the mixed specififcation, the directional specification can hardly be used to determine the slowness vector of inhomogeneous plane waves propagating in viscoelastic anisotropic media. Although the procedure is based on 3 × 3 complex-valued matrices, it yields a cumbersome system of two coupled equations. 相似文献
15.
In modeling solute transport with mobile‐immobile mass transfer (MIMT), it is common to use an advection‐dispersion equation (ADE) with a retardation factor, or retarded ADE. This is commonly referred to as making the local equilibrium assumption (LEA). Assuming local equilibrium, Eulerian textbook treatments derive the retarded ADE, ostensibly exactly. However, other authors have presented rigorous mathematical derivations of the dispersive effect of MIMT, applicable even in the case of arbitrarily fast mass transfer. We resolve the apparent contradiction between these seemingly exact derivations by adopting a Lagrangian point of view. We show that local equilibrium constrains the expected time immobile, whereas the retarded ADE actually embeds a stronger, nonphysical, constraint: that all particles spend the same amount of every time increment immobile. Eulerian derivations of the retarded ADE thus silently commit the gambler's fallacy, leading them to ignore dispersion due to mass transfer that is correctly modeled by other approaches. We then present a particle tracking simulation illustrating how poor an approximation the retarded ADE may be, even when mobile and immobile plumes are continually near local equilibrium. We note that classic “LEA” (actually, retarded ADE validity) criteria test for insignificance of MIMT‐driven dispersion relative to hydrodynamic dispersion, rather than for local equilibrium. 相似文献
16.
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
17.
For converted waves, stacking as well as AVO analysis requires a true common reflection point gather which, in this case, is also a common conversion point (CCP) gather. The coordinates of the conversion points for PS or SP waves, in a single homogeneous layer can be calculated exactly as a function of the offset, the reflector depth and the ratio vp/vs. An approximation of the conversion point on a dipping interface as well as for a stack of parallel dipping layers is given. Numerical tests show that the approximation can be used for offsets smaller than the depth of the reflector under consideration. The traveltime of converted waves in horizontal layers can be expanded into a power series. For small offsets a two-term truncation of the series yields a good approximation. This approximation can also be used in the case of dipping reflectors if a correction is applied to the traveltimes. This correction can be calculated from the approximated conversion point coordinates. 相似文献
18.
A. M. J. Davis 《地球物理与天体物理流体动力学》2013,107(4):175-194
Abstract By relaxing the rigid-lid approximation in the ocean, significant improvements are made to the mathematical and physical aspects of a previously presented model. The difficulties associated with |κ| in wavenumber space are eliminated and the velocities remain bounded at the coastal tip. The method of solution has significant changes but the well-known shelf waves are essentially unaltered and the overall conclusions are similar. 相似文献
19.
Jacob Padro 《Pure and Applied Geophysics》1977,115(3):473-489
An attempt is made to use the barotropic vorticity equation in spectral form in order to study barotropic instability when the basic current has east-west quasi-stationary asymmetries on the scale of long waves. This is done by expressing the spectral equations in three different ways. In the first experiment a 9-component system is integrated and the long waves are allowed to propagate freely. In the second experiment the long waves are constrained to propagate slowly and in the third experiment, they are removed altogether.The motivation behind the present investigation is due to observations made in the motion fields of the tropics. These are characterized by quasi-stationary long waves and very energetically active and propagating short waves.The presence of quasi-stationary long waves seems to enhance the energy exchanges between the short waves and the mean zonal current and also allow for larger energy values for the short waves. Long term integration (90 days) shows a 6-day mode in thev time spectra at latitude 10°N and a 15-day mode in theu time spectra at individual grid points in the equatorial latitudes. Any possible connection between this peak and the observed peak of 15 days in the completely different physics of Kelvin waves is left as a conjecture. 相似文献
20.
V. Červený 《Studia Geophysica et Geodaetica》2007,51(3):391-410
The reflection/transmission laws (R/T laws) of plane waves at a plane interface between two homogeneous anisotropic viscoelastic
(dissipative) halfspaces are discussed. Algorithms for determining the slowness vectors of reflected/transmitted plane waves
from the known slowness vector of the incident wave are proposed. In viscoelastic media, the slowness vectors of plane waves
are complex-valued, p = P + iA, where P is the propagation vector, and A the attenuation vector. The proposed algorithms may be applied to bulk plane waves (A = 0), homogeneous plane waves (A ≠ 0, P and A parallel), and inhomogeneous plane waves (A ≠ 0, P and A non-parallel). The manner, in which the slowness vector is specified, plays an important role in the algorithms. For unrestricted
anisotropy and viscoelasticity, the algorithms require an algebraic equation of the sixth degree to be solved in each halfspace.
The degree of the algebraic equation decreases to four or two for simpler cases (isotropic media, plane waves in symmetry
planes of anisotropic media). The physical consequences of the proposed algorithms are discussed in detail.
vcerveny@seis.karlov.mff.cuni.cz 相似文献