The disturbance produced by an oscillatory pressure distribution in uniform translation on the surface of a liquid

SummaryExpressions are derived for the two-dimensional surface elevation resulting from an oscillatory translating surface pressure distribution. The surface elevation is given as the sum of four terms, each of which is associated with an improper integral having a simple pole singularity. Results are presented for the delta function and the uniform spatial pressure distribution.The mean work done on the fluid per unit time by the delta function pressure distribution is given. Numerical results are presented for the surface elevation resulting from the uniform pressure distribution.