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We obtain a general solution for the water waves resulting from a general,time-dependent surface pressure distribution, in the presence of a shearcurrent of uniform vorticity beneath the surface, in three dimensions.Linearized governing equations and boundary conditions including the effects ofgravity, a distributed external pressure disturbance, and constant finitedepth, are solved analytically, and particular attention is paid to classicinitial value problems: an initial pressure impulse and a steady pressuredistribution which appears suddenly. In the present paper, good agreement withprevious results is demonstrated. We subsequently show both analytically andnumerically how transient waves from a suddenly appearing steady pressuredistribution vanis for large times, and steady ship waves remain. The transientcontribution to wave resistance was derived. The results show that a shearcurrent has significant impact on the transient wave motions, resulting inasymmetry between upstream and downstream waves. The case of the suddenlyappearing steady pressure is an intermediate case between ring waves and shipwaves, starting out as the former and evolving gradually into the latter. Theship's direction of motion relative to the current is found to be crucial indetermining how quickly effects of transient waves die out. Transient effectstake much longer to doe out for a ship going against the shear flow than forone going downstream, when the two ships have the same velocity relative to thewater surface. For ship motion against the shear current, thus, wave effects oftransients, e.g., due to maneuvering could accumulate and be far moresignificant than on a uniform current.

Water Waves from General, Time-Dependent Surface Pressure Distribution in the Presence of a Shear Current