Elastohydrodynamic wake and wave resistance

Abstract

The dynamics of a thin elastic sheet lubricated by a narrow layer of liquid is relevant to various situations and length scales. As a continuation of our previous work on viscous wakes (Ledesma-Alonso et al., J. Fluid Mech., vol. 792, 2016, pp. 829–849), we study theoretically the effects of an external pressure disturbance moving at constant speed along the surface of a thin lubricated elastic sheet. In the comoving frame, the imposed pressure field creates a stationary deformation of the free interface that spatially vanishes in the far-field region. The shape of the wake and the way it decays depend on the speed and size of the external disturbance, as well as the rheological properties of both the elastic and liquid layers. The wave resistance, namely the force that has to be externally furnished in order to maintain the wake, is analysed in detail.