Elastohydrodynamic wake and wave resistance

TL;DR

This paper theoretically investigates the deformation, wake shape, and wave resistance caused by a moving pressure disturbance on a lubricated elastic sheet, considering effects of speed, disturbance size, and material properties.

Contribution

It extends previous viscous wake studies to elastic sheets, analyzing how external disturbances generate stationary deformations and calculating the resulting wave resistance.

Findings

Wake shape depends on disturbance speed and size.

Wave resistance varies with material and flow parameters.

Deformation profiles decay in the far field.

Abstract

The dynamics of a thin elastic sheet lubricated by a narrow layer of liquid is relevant to various situations and length scales. In the continuity of our previous work on viscous wakes, 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 analyzed in detail.