Abstract
Some of the batoid fishes (rays) swim by generating short-length deformation waves that propagate along their fins with phase velocity that exceeds the swimming velocity. This swimming gait is known as ‘undulatory’. Taking into consideration the characteristic length scales involved, it is suggested that (in spite of the moderateness of the aspect ratio of their fins) undulatory swimming of batoid fishes can be analyzed in the framework of the basic strip theory. Consequently, remarkably simple analytical expressions are obtained for the propulsive force and for the propulsion efficiency. The accuracy of these expressions and the adequacy of the strip theory for the analysis of moderate aspect ratio wings are confirmed by numerical simulations. Perhaps the most conspicuous result of the present study is that for the same phase velocity, the propulsion efficiency of the undulatory swimming gait is essentially independent of the aspect ratio of the swimmer.
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