共查询到20条相似文献，搜索用时 31 毫秒
1.
S. V. Shagalov V. P. Reutov G. V. Rybushkina 《Izvestiya Atmospheric and Oceanic Physics》2010,46(1):95-108
The generation of narrow-band Rossby wave packets and the modulated vortex chains induced by them in a weakly-dissipative
zonal flow on the beta-plane with a velocity profile in the form of a shear layer is studied. The analysis is performed within
the framework of the asymptotic approach based on the distinguishing a thin critical layer inside of which the vortex chains
are formed. The evolution equations, describing the simultaneous development of a wave packet envelope and vorticity perturbations
in a nonlinear critical layer, are derived for a weakly supercritical flow. A transition to the complex dynamics of a wave
packet (low-mode turbulence) is studied within the framework of a numerical solution of the derived equations and its mechanism
is revealed. The onset of chaotic advection and anomalous diffusion of passive scalar in the critical layer is considered,
and the exponent of the diffusion law is calculated. 相似文献
2.
G. D. Aburjania 《Izvestiya Atmospheric and Oceanic Physics》2011,47(4):491-502
The generation and further linear and nonlinear dynamics of planetary magnetized Rossby waves (MRWs) in the rotating dissipative ionosphere are studied in the presence of a zonal wind (shear flow). MRWs are caused by interaction with the spatially nonuniform geomagnetic field and are ionospheric manifestations of ordinary tropospheric Rossby waves. A simplified self-consistent set of model equations describing MRW-shear flow interaction is derived on the basis of complete equations of ionospheric magnetohydrodynamics. Based on an analysis of an exact analytical solution to the derived dynamic equations, an effective linear mechanism of MRW amplification in the interaction with nonuniform zonal wind is ascertained. It is shown that operators of linear problems are non-self-adjoint in the case of shear flows, and the corresponding eigenfunctions are nonorthogonal; therefore, the canonically modal approach is of little use when studying such flows; a so-called nonmodal mathematical analysis is required. It is ascertained that MRWs effectively get shear flow energy during the linear stage of evolution and significantly increase (by several orders of magnitude) their energy and amplitude. The necessary and sufficient condition of shear flow instability in an ionospheric medium is derived. Nonlinear self-localization begins with the development of shear instability and an increase in the amplitude, and the process ends with the self-organization of strongly localized isolated large-scale nonlinear vortex structures. Thus, a new degree of freedom and a way for perturbation evolution to occur appear in medium with shear flow. The nonlinear systems can be a pure monopole vortex, a vortex streets, or vortex chains depending of the shape of the sheared flow velocity profile. The accumulation of such vortices in the ionospheric medium can produce a strongly turbulent state. 相似文献
3.
A. E. Gledzer E. B. Gledzer A. A. Khapaev Yu. L. Chernous’ko 《Izvestiya Atmospheric and Oceanic Physics》2014,50(2):122-133
Results of experiments are considered for flows generated by different sources-sinks of mass in the rotating annular channel with beta-effect simulation using the inclined bottom. Diagrams of regimes are presented in parameters of the dimensionless angular velocity of the zonal flow averaged over the channel width and the dimensionless angular velocity of transport of vortex perturbations of cyclonic and anticyclonic types. In experiments and the simplest linear theories, most attention is paid to diagram regions with a slow motion of vortices relative to the rotating coordinate system near the parameters for stationary Rossby waves. 相似文献
4.
The equations of dynamics of eddy—wave disturbances of two-dimensional stratified flows in an ideal incompressible fluid that are written in a Hamiltonian form are used to study the resonant interaction of waves of discrete and continuous spectra. A gravity—shear wave generated at a jump of the density and vorticity of the undisturbed flow and a wave generated at a weak vorticity jump, which is similar to a wave of a continuous spectrum, participate in the interaction. The equations are written in terms of normal variables to obtain the system of evolution equations for the amplitudes of the interacting waves. The stability condition for eddy—wave disturbances is derived within the framework of the linear theory. It is shown that a cubic nonlinearity may lead to the stabilization of unstable disturbances if the coefficient of the nonlinear term is positive. 相似文献
5.
A. E. Gledzer 《Izvestiya Atmospheric and Oceanic Physics》2014,50(3):292-303
This paper presents the results of numerical calculations using shallow water equations for the currents in the laboratory experiments with a rotating circular channel. An axial symmetric function of mass source is introduced into the equations for the depth of the layer to model experimental sources and sinks of fluid, which induces opposing zonal flows together with the Coriolis force. Different configurations and amplitudes of mass sources lead to the appearance of vortex motions in the channel with different circular motions in the vortices and azimuthal displacements of their centers along the channel. Diagrams of regimes are presented in the parameters of relative angular velocities of the mean zonal flow and vortex transport around the axis of the system rotation. The differences of the theory and real experiments with currents of finite depth in a channel are discussed. 相似文献
6.
K. A. Gorshkov I. A. Soustova D. A. Sergeev 《Izvestiya Atmospheric and Oceanic Physics》2007,43(6):785-793
On the basis of the perturbation theory developed previously by the authors for localized hydrodynamic vortices, the influence of a specified jet flow and of the structure of individual vortices on the stability of the Karman street is investigated. It is shown that, for a street of vortices with a power law of decrease in the azimuthal velocity, the jet flow suppresses instability only with respect to perturbations with wavelengths from a certain range determined by the parameters of the flow. At the same time, for streets formed from vortices with a Gaussian profile of the azimuthal velocity, even in the absence of a specified flow, there is a certain region of the street’s parameters in which the street is stable against perturbations of all scales. Thus, for the purposes of modeling quasi-two-dimensional flows in a stratified fluid by a sequence of localized vortices, which is discussed in this study, vortices with a Gaussian profile of the azimuthal velocity turn out to be preferable. The results of this study are consistent with numerous experiments on the structure of a quasi-two-dimensional wake behind a body in a stratified fluid at large Reynolds and Froude numbers. 相似文献
7.
An integral description of the propagation of steady-state perturbations of the heavy liquid surface
The system of equations of motion describing the gravity wave propagation in a perfect heavy liquid layer is transformed into
a new integral equation for the free surface elevations. In the limit cases, this integral equation describes the linear and
nonlinear periodic waves as well as the known types of solitary waves. In this case a dispersion equation arises because perturbations
of the second and higher orders of smallness are neglected. The integral equation allows for the propagation of invariable
surface perturbations of arbitrary forms if their spatial spectrum is concentrated near small wave numbers (compared to the
inverse wave amplitude). Several examples of solutions are presented. 相似文献
8.
A model for a two-layer ocean is applied to consider, in terms of the geometrical optics approximation, the effect of mean
flows propagating within the upper layer upon the dynamics of Rossby waves. The case is theoretically analysed, with the depth
of the ocean's upper layer much smaller than that of the underlying layer. In this case, the flow's impact upon the baroclinic
mode of Rossby waves is ubiquitous, with the exception of synchronicity. Depending on the parameters, four types of wave packets'
behaviour in the vicinity of synchronicity points are singled out, namely, the elimination of the peculiarity, shadowing,
and convective/absolute instability. For the mean flow profile simulating cyclonic and anticyclonic gyres, we have obtained
wave packet trajectories and have studied the wave packet's interaction with the current. Specifically, it has been demonstrated
that, given some modulus of the wave packet, vigorous energy exchange between the wave vector and the flow takes place.
Translated by Vladimir A. Puchkin. 相似文献
9.
A finite-difference scheme and a modified marker-and-cell (MAC) algorithm have been developed to investigate the interactions of fully nonlinear waves with two- or three-dimensional structures of arbitrary shape. The Navier–Stokes (NS) and continuity equations are solved in the computational domain and the boundary values are updated at each time step by the finite-difference time-marching scheme in the framework of a rectangular coordinate system. The fully nonlinear kinematic free-surface condition is implemented by the marker-density function (MDF) technique developed for two fluid layers.To demonstrate the capability and accuracy of the present method, the numerical simulation of backstep flows with free-surface, and the numerical tests of the MDF technique with limit functions are conducted. The 3D program was then applied to nonlinear wave interactions with conical gravity platforms of circular and octagonal cross-sections. The numerical prediction of maximum wave run-up on arctic structures is compared with the prediction of the Shore Protection Manual (SPM) method and those of linear and second-order diffraction analyses based on potential theory and boundary element method (BEM). Through this comparison, the effects of non-linearity and viscosity on wave loading and run-up are discussed. 相似文献
10.
The combined wave-current flow has been solved by researchers by assuming wave over either depthwise constant or linear current
profile. Some complicated nonlinear current profiles have also been considered to simulate various shear currents. We consider
a nonlinear current vertically logarithmic in nature and examine its interaction with a periodic surface wave. The Navier-Stokes
equations for incompressible flow are solved for the current part and by using periodic boundary conditions. The effect of
logarithmic current on wave components is assessed. The corresponding celerity and dispersion equation yields a close-form
solution for the shallow-wave approximation. Several comparative trends between wave-only, wave with log current, and wave
with constant current for the wave following/opposing these currents have been discussed. The flow properties of the first
order are presented which can be applicable to the real inland and coastal flows, where progressive waves are ubiquitous over
a depthwise logarithmic current. The work is further extended to the second-order semiempirical wave component by using past
experimental data on the wave spectrum of combined flow.
Published in Morskoi Gidrofizicheskii Zhurnal, No. 3, pp. 20–40, May–June, 2008. 相似文献
11.
《Ocean Modelling》2007,16(1-2):95-105
In a number of flows that support coupled free-waves, instability results when free-wave dispersion relations calculated without the coupling cross or approach one another. The propagation of long planetary wave perturbations of a two-and-a-half layer model subtropical gyre is one such oceanographically important instance. This note points out that, for a baroclinically unstable two-and-a-half layer model subtropical gyre, numerically aliased long wave dispersion relation plots display extra crossings that are artifacts of the discretization, and these may lead both to spurious numerical instabilities and to numerical misrepresentation of actual instabilities. Paradoxically, the numerical instability may in some instances manifest itself more strongly as the numerical resolution is improved. The aliasing mechanism may be related to the zone of small scale activity found in the southwestern corner of a time dependent model subtropical gyre in the numerical perturbation experiments of (Dewar, W., Huang, R., 2001. Adjustment of the ventilated thermocline. J. Phys. Oceanogr. 13, 293–309). Similar multilayer models are often discussed in the literature, so that the results may be widely useful. 相似文献
12.
Freak waves are generated based on the mechanism of wave focusing in a 2D numerical wave tank. To set up the nonlinear numerical wave tank, the Boundary Element Method is used to solve potential flow equations incorporated with fully nonlinear free surface boundary conditions. The nonlinear properties of freak waves, such as high frequency components and wave profile asymmetry, are discussed. The kinematic data, which can be useful for the evaluation of the wave forces exerted on structures to avoid underestimation of linear predictions, are obtained, and discussed, from the simulated results of freak waves. 相似文献
13.
An analytical study of the influence of three-wave resonant interactions on the evolution of unstable wave disturbances is
presented in the Kelvin-Helmholtz model. These results may be of interest in analyzing the dynamics of disturbances at the
ocean-atmosphere interface and in two-layer flows which arise in the ocean and are characterized by large gradients of flow
velocity at the boundary of layers. In the case under consideration, the instability arises when eigenfrequencies coincide
in the framework of a single mode and the instability is algebraic. The amplitudes of the two other interacting stable waves
are assumed to be small compared to the amplitude of the third, unstable, mode. The system of amplitude equations for this
case is investigated using the WKB method. As a result, we obtain the formulas coupling the solutions for the time before
and after a transition through a singular point, where the amplitude of the linearly unstable wave has a local minimum. These
formulas give the rule of transformation of the parameter that characterizes a phase shift between fast and slow modes and
determines the behavior of the system. It is shown that, in a transition through a singular point, this parameter changes
randomly. As long as the parameter is positive, the amplitude of the linearly unstable wave remains limited and oscillates
stochastically. In a transition of the parameter through zero, we exit the stabilization region and have an infinite growth
of amplitude. The transition into the instability region is random. However, if the time interval where the amplitude remains
limited is large enough, the scenario of the behavior of the system we have obtained can be treated as the partial stabilization
of instability. The results make it possible for us to investigate the stochasticity caused by the nonlinear interaction of
gravity-capillary waves in a two-layer model of a shear flow. These results are also of interest in analyzing secondary flows
in laboratory facilities modeling the ocean and atmospheric processes. 相似文献
14.
The problem of finding optimal perturbations, which are perturbations with a maximum ratio of the final energy to the initial energy, is considered in the Eady model of baroclinic instability. The solution to the problem uses explicit expressions for the energy functional, which are functions of parameters of an initial perturbation. For perturbations with zero potential vorticity, the basic parameters are the amplitudes of the initial buoyancy distributions at the boundaries of the atmospheric layer and a phase shift between these distributions. Dependences of the optimal phase shift and maximum energy ratio on the wave number and time optimization are determined using an analysis for extremum. The parameters of the optimal perturbations are compared with those of the growing normal modes. It is found that only one exponentially growing mode is an optimal perturbation. 相似文献
15.
In this study, we investigate modulational instability in the presence of wind flow in a situation where sea states crossed over water with a finite depth. It is assumed that the wind flows in a specific direction to produce angles with two directions of propagation by two wave systems with the same carrier wave number and same frequency. The evolution equations considered in this study represent a balance among the effects of wind forcing, dispersion, and nonlinearity at the lowest order. These evolution equations are used to study the stability of the uniform wave solution in crossing seas. We show that in the presence of wind flow, the uniform waves grow super-exponentially. We also demonstrate that the region of asymptotic instability in the perturbed wave number plane is larger than that in the absence of wind flow. 相似文献
16.
Methods of studying the dynamics of wave disturbances in st;ratified shear flows of an ideal incompressible fluid are considered. The equations governing the motions of interest represent Hamilton equations and are derived by writing the velocity field in terms of Clebsch potentials. Equations written in terms of semi-Lagrangian variables are integrodifferential equations, which make it possible to consider both continuous and discontinuous solutions, as well as the cases where the parameters of the undisturbed medium are step functions. Two dynamic systems are presented. The first, canonical system of equations is most suitable for describing gravity waves in a shear flow in the case where the undisturbed medium is characterized by sharp gradients of density and flow velocity. The simplest model in which disturbances obey this system of equations is the well-known Kelvin-Helmholtz model. The second dynamic system describes, in particular, gravity-shear waves and, in the case of a homogeneous medium, shear waves in a two-dimensional flow. This system is most suitable for studying the dynamics of disturbances in models with sharp gradients of vorticity. On the basis of the approach developed in this study, the problem of the dynamics of disturbances in a flow with a continuous distribution of vorticity in a finite-thickness layer is solved. If the thickness of this layer is small compared to the characteristic wavelength and the gradient of the undisturbed vorticity in this layer is large, the solution has the form of a mode whose frequency is close to the frequency of the shear wave on a vorticity jump that would be obtained by letting the layer’s thickness approach zero. The results obtained allow, in particular, the estimation of the range of validity of finite-layer approximations for models with smooth profiles of flow and density. In addition, these results can be interpreted as the basis for the development of nonlinear aspects of the theory of hydrodynamic stability. 相似文献
17.
Hydraulic Modeling of A Curtain-Walled Dissipater by the Coupling of RANS and Boussinesq Equations 总被引：5，自引：1，他引：5
A hybrid numerical method for the hydraulic modeling of a curtain-walled dissipater of reflected waves from breakwa-ters is presented. In this method, a zonal approach that combines a nonlinear weakly dispersive wave (Boussinesq-type equation) method and a Reynolds-Averaged Navier-Stokes (RANS) method is used. The Boussinesq-type equation is solved in the far field to describe wave transformation in shallow water. The RANS method is used in the near field to re-solve the turbulent boundary layer and vortex flows around the structure. Suitable matching conditions are enforced at the interface between the viscous and the Boussinesq region. The Coupled RANS and Boussinesq method successfully resolves the vortex characteristics of flow in the vicinity of the structure, while unexpected phenomena like wave re-reflection are effectively controlled by lengthening the Boussinesq region. Extensive results on hydraulic performance of a curtain-walled dissipater and the mechanism of dissipation of reflected waves 相似文献
18.
O. A. Druzhinin 《Izvestiya Atmospheric and Oceanic Physics》2008,44(6):768-780
The onset of a three-dimensional jet flow in a stratified fluid is studied with the aid of a direct numerical simulation. An initially cylindrical jet with a Gaussian velocity profile is considered in a fluid with stable linear density stratification. The results indicate that, if an initial small perturbation of the velocity field has a wide spectrum, an exponential growth of the isolated quasi-two-dimensional mode occurs and its spectral maximum is shifted toward smaller wave numbers in comparison with the maximum of the helical mode of the instability of a nonstratified jet. The growth rate is proportional to Ri0.5, where Ri is the global Richardson number. The onset of the instability leads to the formation of the flow’s vortex structure, which consists of a collection of different-polarity quasi-two-dimensional vortices located in a horizontal plane near the longitudinal axis of the jet. At sufficiently long times (Nt > 100, where N is the buoyancy frequency and t is time), the growth of instability reaches the saturation stage and further fluctuations in velocity and density decay under the effect of viscous diffusion. At this stage, the flow becomes self-similar and the time dependences of the transverse and vertical widths of the jet are consistent with the asymptotic behaviors of integral parameters of the flow that are observed experimentally in the far stratified wake. The results suggest that the onset of the instability of a quasitwo-dimensional mode can play the determining role in the dynamics of flow in the far stratified wake. 相似文献
19.
M. V. Kalashnik 《Oceanology》2014,54(2):144-151
We studied trapped long quasi-inertial waves in horizontally inhomogeneous flows with low Rossby numbers. A simple heuristic derivation of two equations for the wave amplitude is presented. These equations are true for strong and weak density stratifications. A spectral problem is formulated to find the frequencies of trapped waves based on the amplitude equations. Exact solutions of the hyperbolic problem for a free hyperbolic shear layer are found. It is shown that the location of the trapping area principally depends on the stratification. If the buoyancy frequency is greater than the inertial frequency, trapping occurs in the region of anticyclonic velocity shear; if the buoyancy frequency is smaller than the inertial frequency, trapping occurs in the region of cyclonic velocity shear. Thus, in the first case, the frequencies of the trapped waves are smaller than the inertial frequency, while, in the second case, they are greater. The intense wave activity observed in the regions of oceanic fronts and jet currents can be related to the existence of trapped waves. 相似文献
20.
The present study aims to analyze the effects of different submerged bars nourishment strategies using a 2DV process-based morphodynamical model. A two-barred beach profile typical of the French Mediterranean micro-tidal storm-dominated coastline is chosen as a reference profile. Two different kinds of modified beach profiles are considered. (i) Only the outer bar is nourished, the inner bar being unchanged (ii) both bars are nourished. Three typical wave forcing regimes are considered. The behavior of the natural profile is first investigated under the 3 wave forcing regimes. Then the behavior of the various nourished profiles is analyzed in terms of wave dynamics and bars behavior. On the basis of the model results, the outer bar only nourishment strategy appears to be preferable. 相似文献