Subsonic leaky Rayleigh waves at liquid-solid interfaces

The paper is devoted to the study of leaky Rayleigh waves at liquid-solid interfaces close to the border of the existence domain of these modes. The real and complex roots of the secular equation are computed for interface waves at the boundary between water and a binary isotropic alloy of gold and silver with continuously variable composition. The change of composition of the alloy allows one to cross a critical velocity for the existence of leaky waves. It is shown that, contrary to popular opinion, the critical velocity does not coincide with the phase velocity of bulk waves in liquid. The true threshold velocity is found to be smaller, the correction being of about 1.45%. Attention is also drawn to the fact that using the real part of the complex phase velocity as a velocity of leaky waves gives only approximate value. The most interesting feature of the waves under consideration is the presence of energy leakage in the subsonic range of the phase velocities where, at first glance, any radiation by harmonic waves is not permitted. A simple physical explanation of this radiation with due regard for inhomogeneity of radiated and radiating waves is given. The controversial question of the existence of leaky Rayleigh waves at a water/ice interface is reexamined. It is shown that the solution considered previously as a leaky wave is in fact the solution of the bulk-wave-reflection problem for inhomogeneous waves.