This paper represents some of the results obtained from a study which extended an exact linearized potential theory to include the problem of the thrust generated by an oscillating, flexible, flat, two‐dimensional plate of zero thickness moving near the free surface of an ideal incompressible fluid. Of particular interest is the applicability of the model to the problem of a thin flat fish (such as rays) swimming near the surface of a body of water. The theoretical expression for the thrust is presented and it is shown to reduce to that obtained previously by a different method for the case of swimming at an infinite depth. Numerical results are given for swimming at both shallow and infinite depths.
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