Analysis of the Shape of Wave Packets in the “Half Space–Layer–Layer with Rigid Lid " Three-Layer Hydrodynamic System

Abstract

(ua) We study the process of propagation of weakly nonlinear wave packets on the contact surfaces of a “half space–layer–layer with rigid lid” hydrodynamic system by the method of multiscale expansions. The solutions of the weakly nonlinear problem are obtained in the second approximation. The condition of solvability of this problem is established. For each frequency of the wave packet, we construct the domains of sign constancy for the coefficient for the second harmonic on the bottom and top contact surfaces. The regularities of wave formation are determined depending on the geometric and physical parameters of the hydrodynamic system. We also analyze the plots of the shapes of deviations of the bottom and top contact surfaces typical of the constructed domains of sign-constancy of the coefficient. We discover the domains where the waves become ∪ - and ∩ -shaped and reveal a significant influence of wavelength on the shapes of deviations of the contact surfaces of the analyzed hydrodynamic system.