Abstract
An asymptotic analysis is conducted of the effect surface vibrations may play in mitigating the resistance present in the system consisting of a fluid contained between a pair of parallel flat plates in relative motion. Previous numerical computations of this situation, which has applications in both biological and technological contexts, have suggested that small vibrations that move at a fast phase speed can lead to substantial reductions in the resistance. The effect seems to be a somewhat intricate function of the wavelength of the vibration modes. Our analysis uncovers the properties of the various phenomena that are at work and describes the interplay between them. The techniques employed here lend themselves to the extension to other situations including problems in which propulsion effects in fluid systems can be induced by vibrations.
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