Shallow-water waves on a rotating ocean due to oscillatory surface stresses

The initial-value problem of shallow-water waves due to an oscillatory surface stress distribution on a homogeneous rotating ocean is solved by the method of integral transforms. For the wave integral, an asymptotic analysis is given which is uniform across the line produced by the coalescing of the pole and the stationary point of the wave spectrum; the result, unlike previous findings, is non-singular when the circular frequency of oscillation equals the Coriolis parameter. Some limiting cases of interest are deduced and the asymptotic envelope of the progressive waves at the surface is illustrated graphically.