Far Fields of Internal Gravitational Waves from Moving Perturbance Sources
Authors: Bulatov V.V., Vladimirov Yu.V. | Published: 01.08.2018 |
Published in issue: #4(79)/2018 | |
DOI: 10.18698/1812-3368-2018-4-73-89 | |
Category: Physics | Chapter: Acoustics | |
Keywords: stratified medium, internal gravitational waves, far fields, uniform asymptotics, moving source |
An important mechanism for excitation of far fields of internal gravitational waves in natural (oceanic, atmospheric) and artificial stratified media is their generation by perturbance sources of various physical nature: natural (a moving typhoon, wind wave, unevenness of ocean relief, changes in density fields and currents, leeward mountains) and anthropogenic (marine technological structures, collapse of the field of turbulent mixing, underwater explosions). The system of hydrodynamic equations describing wave perturbations of stratified media in a general form is a rather complex mathematical problem both in terms of proving the existence and uniqueness theorems for solutions in the corresponding functional classes, and from the computational point of view. The main results of solving problems on generation of internal gravitational waves are presented in the most general integral form, and in this case the integral solutions obtained require the development of numerical and asymptotic methods for their investigation that allow qualitative analysis and rapid estimation of the solutions obtained. Therefore in modern scientific studies in the analysis of wave phenomena in real stratified media, simplified asymptotic and analytical models are widely used. In linear approximation, the existing approaches to describing the wave pattern of excited fields are based on the representation of wave fields by Fourier integrals. The work studies far fields of internal gravitational waves excited by a perturbance source moving in an infinite vertical stratified medium. The propagation of waves in an inviscid, incompressible medium with an exponential distribution of the unperturbed density is considered. In linear approximation and Boussinesq approximation, uniform asymptotics of the excited fields of internal gravitational waves were constructed far from the moving perturbance source, including the vicinity of the traverse plane and the horizon of motion. The obtained asymptotic solutions make it possible to efficiently calculate the main amplitude-phase characteristics of the excited far fields of internal gravitational waves under certain generation modes and, in addition, qualitatively analyze the solutions obtained, which is important for the correct formulation of more complex mathematical models of wave dynamics of real natural stratified media
This work was carried out within the framework of the state task (no. AAAA-A17-117021310375-7)
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