Transient and periodic shear wave propagation in a solid–fluid coupled system

A coupled system composed of a Newtonian fluid located on a sinusoidally forced elastic solid is studied analytically and numerically. The focus is on the transient evolution from the beginning of the forced oscillations and on the periodic behaviour established once the transient has vanished. The analytical solution is expressed as series summations that elucidate the propagation and reflections of elastic transverse waves through the solid layer and the viscous dissipation of oscillations in the fluid layer. Short-term transients in both the fluid and the solid form at every interaction between an elastic wave and a solid boundary. The long-term transient, quantified by the power balance in the fluid layer, instead pertains to the formation of all the elastic waves in the solid layer. The system can be viewed as a generalized transient Stokes layer generated by the elastic waves or as a damped resonant oscillator when the velocity at the fluid–solid interface increases significantly with respect to the forcing amplitude. A parametric study is carried out for three applications of technological interest, i.e. the indirect measurement of fluid viscosity, the turbulent drag reduction by travelling shear waves and the sensing and manipulation of biological flows.