Fluid flow with flexible boundaries

Abstract

I am fortunate in having as my task to review a field of recent research activity that has undoubtedly attracted a great deal of general interest. It is a field with important antecedents extending as far back as the work of the Victorian pioneers of theoretical hydrodynamics, but in it there have been several auspicious dawnings of new light in the last few years. The main focus of this lecture will be on the progress of studies whose aim has been to explore the exciting idea originated by Krämer [1] four years ago, namely that the application of pliant coatings to streamlined bodies may reduce hydrodynamic drag in consequence of stabilizing the laminar boundary layer against transition to turbulence. However, I hope to present a more general and more scientifically rewarding view of the class of problems posed in this connexion — including the complementary problem of surface-wave excitation by shear flows — than would be afforded merely by an appraisal of Kramer’s invention as a practical measure. I must concede at the outset of this discussion that the experimental findings so far reported on the subject are rather meagre and on the whole disappointing, so that at the present time it is still impossible to give a definite verdict on the practical value of this device. On the other hand, there is now a substantial body of theoretical work on the stability of boundary layers and other shear flows over flexible surfaces, and the net outcome of all this work leaves no doubt whatever that a large stabilizing effect is at least a theoretical possibility. Indeed, the most recent analytical results seem particularly encouraging, and I think they stand as a powerful incentive to further experimental investigation