Interactions of flexural-gravity and interfacial waves in a two-layer fluid with a discontinuous background mean flow

This study investigates the interactions between flexural-gravity waves and interfacial waves in a two-layer fluid, focusing on wave blocking. Both liquid layers are of finite depth bounded on top by a viscoelastic thin plate. Both liquids are incompressible and inviscid, and their flows are two-dimensional and potential. Linear wave theory and a linear equation of a thin floating viscoelastic plate of constant thickness are used. We analyse the phenomenon of wave blocking and Kelvin–Helmholtz (KH) instability in a two-layer fluid with a discontinuous background mean flow. A quartic dispersion relation for frequency as a function of wavenumber and other parameters of the problem is derived. Two cases of uniform current and layers moving with different velocities are studied. Wave blocking occurs when roots of the dispersion relation coalesce without accounting for plate viscosity, leading to zero group velocity. Our findings indicate that wave blocking can occur for both flexural-gravity and interfacial waves under various frequency and current speed conditions, provided that plate viscosity is absent. The role of different parameters and the flow velocities of the upper and lower layers are investigated in the occurrence of wave blocking and KH instability. The loci of the roots of the dispersion relation involving plate viscosity depict that no root coalescence occurs irrespective of the values of wavenumber and frequency in the presence of plate viscosity. The amplitude ratio of the interfacial wave elevation to that of floating viscoelastic plate deflection exhibits the dead-water phenomenon as a density ratio approaches unity.