Analysis of energy of internal waves in a three­layer semi­infinite hydrodynamic system

Olga Avramenko,Maria Lunyova

doi:10.15587/1729-4061.2018.128641

Abstract

Energy characteristics of waves propagation along the contact surfaces in a hydrodynamics system "liquid half-space – layer –layer with a rigid lid" are explored. Based on the solutions of first approximation to a weakly non-linear model, the integral relations for wave motion energy in each layer and for the total energy of the system were obtained. An analysis of energy of wave processes revealed that an increase in wave number causes a decrease in energy of wave motion of the upper layers, and energy of wave motion of the lower half-space at some values of wave number reaches extreme values. In this case, total energy of the system is descending in nature and rather quickly approaches its limit value.The numerical values of energy for three different cases of propagation of progressive waves were obtained: only along the upper contact surface, only along the lower contact surface, along both surfaces simultaneously. Comparison of the obtained values of energy revealed that in the case of waves propagation along both contact surfaces simultaneously, the total energy of the system is close to the sum of energies of the system at waves propagation along one of the surfaces

Highlights

At the present stage of development of continuum mechanics, more intensive research is carried out into internal and surface waves in fluids of different types
The aim of present study is qualitative and quantitative analysis of energy of internal waves that propagate along contact surfaces in a three-layer hydrodynamic system “liquid half-space – layer – layer with a rigid lid”
It was found that energy of the middle and upper layer of a three-layer hydrodynamic system is descending in character at an increase in the value of wave number k and converges fast enough to a certain limit value, which for short waves does not depend on thickness of the upper layer

Summary

Introduction

At the present stage of development of continuum mechanics, more intensive research is carried out into internal and surface waves in fluids of different types. Similar studies are among the most complex ones in modern science as they require construction of complex mathematical models. Practical use of the energy component of waves’ propagation and interaction was the impetus to study wave processes. The relevance of qualitative and quantitative analysis of energy characteristics of the internal wave motion in the areas where the ocean has a layered structure is determined by the substantial influence of wave energy distribution between the fluid layers on the navigation safety in such areas. There is a need to develop the theoretical basis for designing new methods for cancellation of internal waves

Literature analysis and problem statement

The aim and objectives of the study

Conclusions