Beams of harraonic internal waves in a liquidIntroduction. Two types of internal waves are traditionally distinguished: waves localized on densitydiscontinuity layers and volumetric waves, which propagate over the entire thickness of the liquid [1]. Their properties are studied in the approximation of perfect [2] or viscous [3] liquids. In a medium with an exponential distribution of density, the waves propagate along radius-vectors whose slope to the horizon 0 is determined as the ratio of the wave frequency co to the buoyancy frequency N: sin 0 --co/N. In a medium with an arbitrary stratification, regular waves exist in regions where co < N. As the critical level co = N is approached, the wave beam deflects from the vertical, the wave vectors become horizontal, the further propagation of the waves is impossible, and beam reflection occurs [4].Allowance for viscosity and diffusion substantially changes the description of internal waves. In this case, a compact source generates a field of internal waves that is regular over the entire space [3]. Significant disturbances are concentrated in narrow wave beams that contain one and a half to two spatial oscillations. Asymptotic solutions are in agreement with measurements and observations of internal waves under laboratory conditions even near the source [5].When internal-wave beams axe reflected from a flat rigid surface, boundary flows with split scales of velocity and density arise owing to viscosity and diffusion effects [6][7][8]. A marked portion of energy of the incident-wave beam is converted to a boundary flow periodic in time [9].In most cases, models of internal waves are constructed for smooth distributions of density [10]. Under natural conditions, a fine structure of the medium with expressed discontinuity layers of density and its derivatives (up to high-order derivatives) is observed. In this connection, it is of interest to study the effect of discontinuity in the gradient of density and its higher derivatives (in the absence of a jump in density) on the propagation of internal-wave beams taking into account the effects of viscosity and diffusion and to calculate the corresponding disturbances originating on inhomogeneities of stratification. By analogy with [8, 9], the wave beam can be expected to transform into different forms of spatially localized motions with nonwave natural scales.The purpose of the present paper is a dynamic consideration of the problem of the propagation of internal-wave beams in an arbitrarily stratified medium taking into account the dissipative effects (viscosity and diffusion), wave reflection on the critical level, a calculation of energy losses due to this reflection, and a study of propagation of the beams in the vicinity of density derivative discontinuities in the medium.

No abstract

No abstract

No abstract

No abstract