Abstract
Research into propagation and interaction of waves in a three-layer hydrodynamic system is one of the relevant problems of modern theoretical and experimental hydrodynamics. The authors studied propagation and interaction of waves along contact surfaces of the three-layer hydrodynamic system "liquid half-space – layer – layer with a rigid lid". By applying a method of large-scale approximations, the first three linear approximations of the correspondent weakly nonlinear problem were obtained. The structure of wave motions on contact surfaces was explored. Dependence of amplitudes of waves-responses on contact surfaces at various geometrical and physical parameters was analyzed. In particular, for large values of thickness of the upper layer, it was found that a change in value of the wave number leads to rapid convergence of amplitudes of waves-responses to the common limited value. The authors showed the need for a detailed study of the limited case in the absence of density jump, in which one of the solutions of dispersion equation tends to zero. Results of the present research can be used in the design of algorithms for detection of wave motions in various liquid media.
Highlights
Exploration of wave phenomena in fluids of different types is one of the most difficult problems of modern science as it needs serious mathematical methods and construction of quite sophisticated mathematical models
Dependences of amplitudes of waves that run along contact surfaces at various geometrical and physical parameters of the hydrodynamic system were constructed
If density jump on the lower contact surface is smaller than density jump on the upper contact surface, wave-responses that appear on the lower surface are larger than wave-responses on the upper surface
Summary
Exploration of wave phenomena in fluids of different types is one of the most difficult problems of modern science as it needs serious mathematical methods and construction of quite sophisticated mathematical models. Numerical and analytical research in such models requires creation of new approaches and application of modern CMS. A new impetus to the study of waves in the World Ocean was given by practical use of the energy component of propagation and interaction of waves. One of the problems with this is timely detection of internal wave motions
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