Abstract
We consider the hydrodynamical problem of a general three-dimensional smooth deformable body moving in a perfect fluid, which undergoes arbitrary continuous temporal variations in its shape. Special attention is payed to the phenomena of selfpropulsion (translation and rotation) of such a shape and reference is made to the dynamics of non-spherical deformable bubbles, cavities and drops. Some distinctive cases, in which the method can be applied to impulsively started highly-vibrating rigid surfaces, are also presented. The Lagally theorem for deformable surfaces, is applied to determine the induced velocity of self-propulsion. The general deformation is assumed to consist of a large scale volume-mode and superposed small scale shapemodes. The time-averaging procedure is introduced and the effect of persistent self-propulsion is shown to be generated as a result of nonlinear interactions between these modes, which must preserve certain skew-symmetric and phase-difference properties. It is proven that, as a result of perfect symmetry, a spherical shape is a degenerate and an inefficient self-propulsor. The results are demonstrated for prolate (oblate) spheroidal shapes and simplified expressions are obtained as limiting cases for spherical, rod-like (slender) and circular disc shapes.
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Schedule a callMore From: Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
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