Internal waves generated by a moving sphere and its wake in a stratified fluid

The internal gravity waves and the turbulent wake of a sphere moving through stratified fluid were studied by the fluorescent dye technique. The Reynolds number Re=U·2a/v was kept nearly constant at about 3 · 10³ and the Froude number F;U/a N ranged from 0.5 to 12.5. It is observed that waves generated by the body are dominant only when F<4 and are replaced by waves generated by the large scale coherent structures of the wake when F>4.     

Internal wave field generated by a source at rest in a moving stratified fluid

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 58–61, July–August, 1989.     

Internal waves induced by moving periodic perturbations applied to the surface of a stratified fluid

Investigations of internal wave generation by moving perturbations are of considerable interest for submarine navigation, hydroacoustics, ocean seismology, etc. The main results for perturbations of constant intensity were published in [1–3]. In the present paper we continue the investigations and study moving perturbations whose intensity varies periodically in time. The perturbations are approximated by surface shape variations or an external pressure on the surface. The vertical displacement of the water particles relative to the equilibrium position is obtained in the form of a series in terms of waves modes for a given density stratification. A calculation algorithm and a program for computing each of the wave modes have been compiled. The boundaries of the wave regions and constant-phase lines are constructed and the displacement amplitudes are calculated. It is shown that there are resonance relations between the oscillation frequency and the perturbation velocity for which the displacement for a given mode becomes infinite (in the linear theory). Rostov-on-Don. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 130–135, July–August, 1994.     

Internal gravity waves excited by a source in stratified horizontally inhomogeneous media

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 124–128, January–February, 1991.     

Internal and inertial waves in a viscous rotating stratified fluid

The effects of viscosity on the propagation of a St. Andrew's cross wave which is generated by a simple-harmonic localized disturbance in a rotating stratified fluid are considered. A similarity solution of the linearised equations shows that the velocities decay and that the wave width increases away from the disturbance. Previous solutions in a stratified non-rotating fluid are recovered by letting the rotation tend to zero. The solutions are also valid in the limit of a homogeneous rotating fluid. Further solutions for waves in a realistic ocean and in an isothermal atmosphere on a rotating Earth are also included.     

Internal waves arising in the presence of the unsteady motion of a source in a continuously stratified fluid

A general approach to the investigation of linear internal and surface waves in a stably stratified fluid, arising from different types of perturbations, is presented in [1]. The methods of calculation of the internal waves generated by the motion of a mass source are developed for particular cases of steady horizontal motion in a continuously stratified fluid in [2] and arbitrary motion in an unbounded exponentially stratified fluid in [3]. Internal waves generated by other types of perturbations have also been investigated but only for particular cases of motion (see, for example, [4]). This paper presents a method for the calculation of unsteady, linear, internal gravity waves arising in an inviscid incompressible fluid with continuous stable stratification.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 122–130, July–August, 1985.     

Uniform far field asymptotics of internal gravity waves from a source moving in a stratified fluid layer with smoothly varying bottom

The far field asymptotics of internal waves is constructed for the case when a point source of mass moves in a layer of arbitrarily stratified fluid with slowly varying bottom. The solutions obtained describe the far field both near the wave fronts of each individual mode and away from the wave fronts and are expansions in Airy or Fresnel waves with the argument determined from the solution of the corresponding eikonal equation. The amplitude of the wave field is determined from the energy conservation law along the ray tube. For model distributions of the bottom shape and the stratification describing the typical pattern of the ocean shelf eract analytic expressions are obtained for the rays, and the properties of the phase structure of the wave field are analyzed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 111–120, May–June, 1998. This work was financially supported by the Russian Foundation for Basic Research (project No. 96-01-01120).     

Kinematic problem of an ideal incompressible fluid flow around an arbitrarily moving airfoil

An unsteady kinematic problem for arbitrary two-dimensional motion of an airfoil in an ideal incompressible fluid with formation of one and two vortex wakes is solved. The problem is solved by the method of conformal mapping of the flow domain onto a circle exterior; solution singularities in the vicinity of a sharp edge are analyzed, and the initial asymptotics of the solution is taken into account. The calculated results are found to be in good agreement with available experimental data on visualization of the flow pattern. The necessity of correct modeling of the initial stage of vortex-wake formation is demonstrated. A regular flow pattern is found to form after three and more periods of oscillations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 120–128, March-April, 2009.     

Large-scale edge waves generated by a moving atmospheric pressure

Long waves generated by a moving atmospheric pressure distribution, associated with a storm, in coastal region are investigated numerically. For simplicity the moving atmospheric pressure is assumed to be moving only in the alongshore direction and the beach slope is assumed to be a constant in the on-offshore direction. By solving the linear shallow water equations we obtain numerical solutions for a wide range of physical parameters, including storm size (2a), storm speed (U), and beach slope (α). Based on the numerical results, it is determined that edge wave packets are generated if the storm speed is equal to or greater than the critical velocity, U_cr, which is defined as the phase speed of the fundamental edge wave mode whose wavelength is scaled by the width of the storm size. The length and the location of the positively moving edge wave packet is roughly Ut/2 ≤ y ≤ Ut, where y is in the alongshore direction and t is the time. Once the edge wave packet is generated, the wavelength is the same as that of the fundamental edge wave mode corresponding to the storm speed and is independent of the storm size, which can, however, affect the wave amplitude. When the storm speed is less than the critical velocity, the primary surface signature is a depression directly correlated to the atmospheric pressure distribution.     

Nonlinear waves generated by a steadily moving line load on an elastic plate

The steady-state response of an infinite plate to a steadily moving line load is studied. The nonlinear plate theory of Herrmann is used. The plate response is governed by a set of nonlinear differential equations and, in addition, must satisfy the “radiation” conditions. Appropriate radiation conditions for the present nonlinear problem are developed. Exact solutions representing nonlinear waves generated by the moving load are constructed.     

The development of three-dimensional waves generated by perturbations of varying intensity in a flow of continuously stratified fluid

An analysis is made in the linear formulation of the three-dimensional structure of unsteady waves created in a flow of continuously stratified fluid by a region of pressures which are harmonic with respect to time.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 71–77, November–December, 1984.     

Waves generated on an ice cover by a source pulsating in fluid

A point source of variable intensity located at rest in a plane infinitely deep fluid layer under an ice cover is considered. The general expression for perturbations of the fluid-ice interface is obtained. In the case of the long operation in the pulsating regime the wave established on the ice cover is found.     

Surface effects of internal wave generated by a moving source in a two-layer fluid of finite depth

IntroductionInternalwaves,whichcanbeexcitedbymanykindsofdisturbancesfromthesurface,bottomorinteriorofastratifiedocean ,suchasthewindstrain ,theflowoverunevenbottomsandthemovingbodyatthesurfaceorunderwater,areremarkablyobviousasthereexistsapycnoclineorathermoclineintheocean[1,2 ] .ThepropagationofgravitysurfacewaveindeepwatergeneratedbyasteadilymovingdisturbanceisrestrictedinaV_shapedregionwithahalfangleθc =19.5°,whichiswell_knownKelvinshipwave[3 ] .Thewaveinducedbyamovingunderwaterobjectisa…