Generation of Internal Gravity Waves Far from Moving Non-Local Source

Vitaly Bulatov,Yury Vladimirov

doi:10.3390/sym12111899

Abstract

We consider analytical solutions describing the generation of internal gravity waves far from a non-local source of disturbances. We suppose that the source moves on the surface of stratified medium of a finite depth. A model distribution of the non-local source shape with radial symmetry is used. This approximation correctly describes (qualitatively) the main spatiotemporal characteristics of natural sources of generation of internal gravity waves in the ocean. The resulting solution is the sum of wave modes. The solution is presented as a series of eigenfunctions of the spectral problem of internal gravity waves. The results of numerical calculations of internal gravity waves components at different depths are presented and discussed.

Highlights

In connection with the new problems arising in geophysics, oceanology, physics of atmosphere, usage of the cryogenic fluids in the engineering sphere, as well as the ecological problems, the operation of complex hydraulic engineering facilities, including the marine oil producing complexes, and a number of other actual problems facing the science and engineering fields, we can observe the growth of interest to the research on the wave dynamics of the different inhomogeneous fluids and, in particular, the stratified fluids [1,2,3,4,5,6,7]
The absolute variations in the bottom pressure, which are related to internal gravity waves (IGW), are proportional to multiplier NH/π; in the real ocean conditions, the latter is two orders of magnitude smaller than a similar multiplier for the surface waves, which is equal to gH
Function describes the pressure perturbation induced by propagation of IGW from In this paper, we examined thean linear

Summary

Introduction

In connection with the new problems arising in geophysics, oceanology, physics of atmosphere, usage of the cryogenic fluids in the engineering sphere, as well as the ecological problems, the operation of complex hydraulic engineering facilities, including the marine oil producing complexes, and a number of other actual problems facing the science and engineering fields, we can observe the growth of interest to the research on the wave dynamics of the different inhomogeneous fluids and, in particular, the stratified fluids [1,2,3,4,5,6,7]. In the real oceanic conditions, the density changes are small, the periods of oscillations of the internal waves range from several minutes (in the layers with rather fast change of the temperatures and the depth) up to several hours [5,6,7]. Such great periods of fluctuations mean that even at the big amplitude of the internal waves, they can achieve dozens of meters along the vertical direction, and the speeds of the particles in the internal wave are low—for the vertical components the speeds of the particles have the order of mm/s, and for the horizontal—cm/s. The second method provides for substitution of the function describing the form of the non-local source either with the rather simple function, or with the system of the point sources [8,9,11,12,13,14,15,16,18,19,20,21]

Formulation of the Problem and Integral Forms of Solutions

Analytic

Numerical Results and Discussion

Summary