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1.
Abstract

New rates of decay are presented for temporally-attenuated gravity waves in deep water, allowance being made for the energy dissipated in the Stokes interfacial boundary layer in the air. This decay-rate, involving air drag, may then be used to deduce a new “free-surface” boundary condition for the problem of the mass transport velocity due to progressive waves; for shallow-water waves, two specific velocity profiles are calculated, and indicate large differences in comparison with the corresponding profiles of Longuet-Higgins (1953) for a vacuum-water interface.  相似文献   

2.
In this paper we solve analytically wave kinematic equations and the wave energy transport equation, for basic long surface gravity wave in the coastal upwelling zone. UsingGent andTaylor's (1978) parameterization of drag coefficient (which includes interaction between long surface waves and the air flow) we find variability of this coefficient due to wave amplification and refraction caused by specific surface water current in the region. The drag coefficient grows towards the shore. The growth is faster for stronger current. When the angle between waves and the current is less than 90° the growth is mainly connected with the waves steepness, but when the angle is larger, it is caused by relative growth of the wave phase velocity.  相似文献   

3.
Abstract

The mutual interaction of fields induced by spatially separated potential vorticity sources in a quasi-geostrophic barotropic flow is investigated using the weakly nonlinear approach. It is found that a powerful nonlinear response can be triggered by Rossby lee waves. This resonance phenomenon which dominates all other nonlinear corrections depends on certain global resonance conditions and on the change in the phase of the Rossby lee wave across the distance separating the sources. The response is particularly strong for topographic forcing possessing δ-function characterisitics.  相似文献   

4.
The characteristics of the disturbances in the atmosphere and oceans and in other stably stratified and rotating fluids are analyzed according to their phase and group velocities. It is shown that both stable stratification and rotation augment the velocity of the sound waves, and that the internal gravity waves and inertial waves are mutually exclusive when the Brunt-Väisälä frequency is different from the Coriolis parameter. It is also shown that both the barotropic and the internal Rossby waves are well separated from the gravity waves and that they can be represented accurately by the quasi-geostrophic potential vorticity equation, even close to the equator, except for the one member withn=0 which is coupled with an eastward propagating gravity wave.  相似文献   

5.

Form-preserving, uniformly translating, horizontally localized solutions (modons) are considered within the framework of nondissipative quasi-geostrophic dynamics for a two-layer model with meridionally sloping bottom. A general classification of the beta-plane baroclinic topographic modons ( g -BTMs) is given, and three distinct domains are shown to exist in the plane of the parameters. The first domain corresponds to the regular modons with the translation speed outside the range of the phase speeds of linear waves. In the second domain, modons cannot exist: only non-localized solutions are permissible here. The third domain contains both linear periodic waves and the so-called anomalous modons traveling without resonant radiation. Exact modon solutions with piecewise linear relation between the potential vorticity and streamfunction are found and analyzed. Special attention is given to the smooth regular dipole-plus-rider solutions (anomalous modons cannot carry a smooth axisymmetric rider). As distinct from their flat-bottom analogs, g -BTMs may have nonzero total angular momentum. This feature combined with the ability of g -BTMs to bear smooth riders of arbitrary amplitude provides the existence of almost monopolar (in both layers) stationary vortices.  相似文献   

6.

A ray theory is applied to the problem of three‐dimensional propagation of inertial‐internal waves in the presence of a mean baroclinic current which does not vary in the downstream coordinate. As time increases, the Doppler‐shifted wave frequency, or intrinsic frequency, tends to a limiting value determined by the horizontal and vertical variations of the mean current and density fields. The limiting value of the intrinsic frequency determines critical surfaces where energy is transferred to the mean motion. Also, the group velocity tends to the mean current velocity, and the phase velocity tends to be oriented towards or away from the core of the mean current, depending upon whether the wave is either initially propagating with a wave number component antiparallel or parallel to the mean current.  相似文献   

7.
A method of wave mode determination, which was announced in Balikhin and Gedalin, is applied to AMPTE UKS and AMPTE IRM magnetic field measurements downstream of supercritical quasiperpendicular shock. The method is based on the fact that the relation between phase difference of the waves measured by two satellites, Doppler shift equation, the direction of the wave propagation are enough to obtain the dispersion equation of the observed waves. It is shown that the low frequency turbulence mainly consists of waves observed below 1 Hz with a linear dependence between the absolute value of wave vector |k| and the plasma frame wave frequency. The phase velocity of these waves is close to the phase velocity of intermediate waves Vint = Vacos().  相似文献   

8.
Abstract

A 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   

9.
Abstract

Marked oscillations in wind speed, wind direction and pressure with periods of between 5 and 15 minutes were recorded on a number of occasions and it is assumed that they were produced by atmospheric gravity waves. Gossard and Munk (1954) have shown that the phase velocity of a gravity wave can be calculated using wind and pressure fluctuation data from a single station by means of the “impedance equation”. It is also possible to measure the phase velocity of a gravity wave using an array of microbarovariographs. In this investigation, the phase velocity of gravity waves calculated using these two different methods are compared and the feasibility of deriving wave characteristics from single point measurements is discussed. The results show that, while in a few isolated cases the two velocities agree reasonably well, the application of the impedance equation to data from a single station is limited due to the superposition of local wind systems upon the wave-induced perturbations.  相似文献   

10.
Summary It has been found that when seismic energy propagates along the surface of the homogeneous crust beside usual Rayleigh waves, it produces certain instability in layers through which it propagates. In the light of this instability, a type of motion corresponding to longitudinal wave will be prominent in horizontal component compared to the vertical component; while transverse wave will be prominent in the vertical component but weak in the horizontal component, a contradiction with the existing knowledge. This has been identified withP F phase. On taking the medium of propagation as slightly heterogeneous which allows existence of low velocity layer, a few larger number of such instabilities have been found. Velocity equation for Rayleigh waves for such media reveals existence of different velocities corresponding to vertical and horizontal components. Table for these velocities has been furnished.  相似文献   

11.
Geostrophic dynamics in the horizontally differential super-rotation of Venus are examined using fA (the Coriolis parameter defined by the angular velocity of a basic flow in an inertial frame) and Γ (the differential rotation parameter defined by the latitudinal gradient of the angular velocity) under the conditions that vertical shear of the basic field is not considered and the intrinsic phase velocity has a magnitude comparable to that of an eddy horizontal flow. The geostrophic and quasi-geostrophic approximations are valid in the regions of weakly differential and rigid-body super-rotations; however, they are invalid in the regions of strongly differential super-rotation even when the Rossby number R O is sufficiently smaller than unity for synoptic eddies. In a general circulation model of a Venus-like atmosphere, the horizontal divergence that results from the strong differential cannot be ignored over a wide range within latitudes ±60° and below 60?km elevation because of large Γ/fA (≥1/2).  相似文献   

12.
Aki (1969) first modeled coda waves of a local earthquake as a superposition of scattered surface waves. This paper attempts to clarify the constituents of surface-wave coda at long periods at very long lapse times. For a large earthquake of magnitude 7 or larger, vertical component oscillation in periods from 90 to 180 s persists for more than 20 hours from the earthquake origin time. Although the early portion of the coda envelope is successfully modeled by assuming incoherent scattered Rayleigh waves by heterogeneities distributed all over the Earth, the later potion of the observed coda envelope (roughly later than 35,000 s) has systematically larger amplitude than theoretical prediction. To clarify the cause of this discrepancy, we studied the constituents of vertical-component seismograms of three large earthquakes recorded by the F-net in Japan using the f-k power spectral analysis. We found that the direct and scattered fundamental-mode Rayleigh waves of velocity about 3.7 km/s are dominant in the earlier part of each envelope. It justifies the use of a scattering model of the fundamental Rayleigh waves for synthesizing the envelope. At lapse times later than 20,000 s–35,000 s, higher modes with phase velocities around 20 km/s become dominant. The transition time to the dominance of higher modes is found to become earlier for a deeper focus earthquake. The small coda attenuation factor from (1.90±0.23) × 10−3 to (2.38±0.32) × 10−3 estimated from later coda envelopes recorded at IRIS stations distributed worldwide also agrees with the attenuation factor of spheroidal modes according to PREM. We may interpret that higher mode waves are uniformly distributed at large lapse time due to large velocity dispersion and/or scattering and they dominate over the fundamental mode waves because of smaller attenuation in the lower mantle. The coda attenuation measurement proposed by Aki is found to be useful even for long periods and at very large lapse times.  相似文献   

13.
Abstract

The generation of stationary Rossby waves by sources of potential vorticity in a westerly flow is examined here in the context of a two-layer, quasi-geostrophic, β-plane model. The response in each layer consists of a combination of a barotropic Rossby wave disturbance that extends far downstream of the source, and a baroclinic disturbance which is evanescent or wave-like in character, depending on the shear and degree of stratification. Contributions from each of these modes in each layer are strongly dependent on the basic flows in each layer; the degree of stratification; and the depths of the two layers. The lower layer response is dominated by an evanescent baroclinic mode when the upper layer westerlies are much larger than those in the lower layer. In this case, weak stationary Rossby waves of large wavelengths are confined to the upper layer and the disturbance in the lower layer is confined to the source region.

Increasing the upper layer flow (with the lower layer flow fixed) increases the Rossby wavelength and decreases the amplitude. Decreasing the lower layer flow (with the upper layer flow fixed) decreases the wavelength and increases the amplitude. Stratification increases the contribution from the barotropic wave-like mode and causes the response to be confined to the lower layer.

The finite amplitude response to westerly flow over two sources of potential vorticity is also considered. In this case stationary Rossby waves induced by both sources interact to reinforce or diminish the downstream wave pattern depending on the separation distance of the sources relative to the Rossby wavelength. For fixed separation distance, enhancement of the downstreatm Rossby waves will only occur for a narrow range of flow variables and stratification.  相似文献   

14.
Abstract

In this, the first part of a three part study, we develop a model for the theoretical analysis of 3‐dimensional internal gravity waves in atmospheres with arbitrary distributions of basic temperature, molecular weight, viscosity and conductivity (both eddy and molecular), Newtonian cooling, anisotropic hydromagnetic (ion) drag, and thermal excitation. Attention is given to the physical bases for our models, and a detailed outline is given of the numerical method used to solve the resulting system of equations.

As an application of the above development, we study the ability of five particular gravity waves (chosen for their observed importance in the neighborhood of 90–100 km—four of the waves are simulated tidal modes) to propagate from 90 km into the thermosphere. We choose to define the thermosphere as that portion of the atmosphere above the turbopause (ca. 110 km). Among the most significant results to emerge are the following: (i) the effects of molecular viscosity and conductivity appear to be more significant than the effects of hydromagnetic drag, and (ii) while most waves considered are significantly attenuated somewhere between 90 Ian and the thermosphere, the main semidiurnal tidal mode is not. In fact, semidiurnal temperature oscillations of only a few degrees amplitude at 90 km can give rise to oscillations of over a hundred degrees amplitude in the exosphere.  相似文献   

15.
The application of standard array processing techniques to the study of coda presents difficulties due to the design criteria of these techniques. Typically the techniques are designed to analyze isolated, short arrivals with definite phase velocity and azimuth and have been useful in the frequency range around 1 Hz. Coda is long in time and may contain waves of different types, phase velocities and azimuths. Nonetheless, it has proved possible to use or adapt array methods to answer two questions: what types of waves are present in coda and where are they scattered? Most work has been carried out on teleseismicP coda; work on local coda has lagged due to lack of suitable data and the difficulties of dealing with high frequencies. The time domain methods of beamforming and Vespagram analysis have shown that there is coherent energy with a high phase velocity comparable toP orPP in teleseismicP coda. These methods can detect this “coherent” coda because it has a fairly definite phase velocity and the same, or close to, azimuth as firstP orPP. This component must consist ofP waves and is either scattered near the source, or reflected in the mantle path as apdpP or precursorPP reflection. The Fourier transform method of the frequency-wavenumber spectrum has been adapted by integrating around circles of constant phase velocity (constant total wavenumber) to produce the wavenumber spectrum, which shows power as a function of wavenumber, or phase velocity. For teleseismicP coda, wavenumber spectra demonstrate that there is a “diffuse” coda of shear,Lg or surface waves scattered from teleseismicP near the receiver. Wavenumber spectra also suggest that the coherent coda is produced by near-source scattering in the crust, not mantle reflection, since it is absent or weak for deep-focus events. Crustal earthquakes have a very strong coherent component of teleseismic coda, suggesting scattering from shear to teleseismicP near the source. Three-component analysis of single-station data has shown the presence of off-azimuth arrivals and may lead to the identification of waves scattered from a single scatterer.  相似文献   

16.
An often observed and still unexplained feature of the high-m Alfvén waves in the terrestrial magnetosphere is their equatorward phase motion, in contrast with low-m waves. We suggest an explanation of this fact in terms of a model of wave excitation by an azimuthally drifting particle inhomogeneity injected during substorm activity. The azimuthal direction of the phase velocity coincides with that of the cloud. If the drift velocity increases with the radial coordinate, the particle cloud is stretched into spiral in the equatorial plane which leads to a radial component of the phase velocity directed toward Earth, that is, an equatorward phase propagation.  相似文献   

17.
Theoretical and simulation approaches to E-region irregularities (gradient drift and Farley-Buneman instabilities) are reviewed, and an account is given of some relevant observations. A new hybrid linear dispersion relation is also derived and presented. The most important problem that cannot be explained by more straightforward theories is the saturation of the phase velocity to the ion acoustic speed (Cs saturation). This phenomenon is well-known from equatorial electrojet radar observations. Recent particle simulations have yielded an interesting new explanation for the (Cs saturation, which has been named flow angle stabilization: the phase velocity is not actually (Cs saturated, but the flow angle distribution of the spatial power spectrum is highly asymmetric. The asymmetry is such that the most intense waves propagate at the k⋅E < 0 edge of the linearly unstable sector, and thus the phase velocity of the most intense waves is close to (Cs. Depending on the level of larger scale turbulence, the radar observes varying degrees of (Cs saturation. If the larger scale turbulence level is high (equatorial electrojet case), the local flow angle fluctuates, and there are always subregions within the scattering volume with local flow angles favorable for the detection of the most intense waves. Under these conditions, the spectra show (Cs saturation. If the larger scale turbulence level is lower, there will not always be enough mixing of the flow angle for even the most intense waves to be observed. In these cases, the mean Doppler shift will be proportional to the electric fied, i.e. it will obey the linear theory.  相似文献   

18.
Abstract

A two-dimensional, nonlinear, time-dependent, non-hydrostatic, anelastic, numerical model is used to assess the effect of condensation on the evolution and structure of gravity waves generated by the passage of a stable, moist stream over topography. Precipation is ignored but water phase changes are taken into account explicitly.

The main effect of condensation is to damp the wave intensity and to reduce the wave drag, which can be diminished by as much as 50% compared to its value in dry simulations. This result agrees with some earlier analytical models and some more recent fully compressible numerical models.

This model also confirms that the presence of condensation delays the overturning of isentropes, and the formation of the critical layer that accompanies wave-breaking.  相似文献   

19.
Abstract

The instability of a current with a geostrophic surface density front is investigated by means of a reduced gravity model having a velocity profile with nearly uniform potential vorticity. It is shown that currents are unstable when the mean potential vorticity decreases toward the surface front at the critical point of the frontal trapped waves investigated by Paldor (1983). This instability is identical with that demonstrated by Killworth (1983) in the longwave limit.

The cross-stream component of mass flux and the rates of energy conversions among the five energy forms defined by Orlanski (1968) are also calculated. The main results are as follows, (a) The mass flux toward the surface front is positive near the front and negative around the critical point. The positive mass flux near the front does not vanish at the position of the undisturbed surface front, so that the mean position of the front moves outward and the region of the strong current spreads. (b) The potential energy of the mean flow integrated over the fluid is released through the work done by the force of the pressure gradient of the mean flow on the fluid, and is converted into the kinetic energy of the mean flow. (c) In the critical layer, the mean flow is rapidly accelerated with the growth of the unstable wave. This acceleration is caused by the rapid phase shift of the unstable wave in the critical layer.  相似文献   

20.
The observation of the fault-zone trapped waves was conducted using a seismic line with dense receivers across surface rupture zone of the M=8.1 Kunlun Mountain earthquake. The fault zone trapped waves were separated from seismograms by numerical filtering and spectral analyzing. The results show that: a) Both explosion and earthquake sources can excite fault-zone trapped waves, as long as they locate in or near the fault zone; b) Most energy of the fault-zone trapped waves concentrates in the fault zone and the amplitudes strongly decay with the distance from observation point to the fault zone; c) Dominant frequencies of the fault-zone trapped waves are related to the width of the fault zone and the velocity of the media in it. The wider the fault zone or the lower the velocity is, the lower the dominant frequencies are; d) For fault zone trapped waves, there exist dispersions; e) Based on the fault zone trapped waves observed in Kunlun Mountain Pass region, the width of the rupture plane is deduced to be about 300 m and is greater than that on the surface. Foundation item: Joint Earthquake Science Foundation of China (201001). Contribution No. RCEG200305, Research Center of Exploration Geophysics, China Earthquake Administration.  相似文献   

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