Asymptotic expansions for the surface waves generated by a submerged body moving with rapidly oscillating velocity (Q583983)

The problem considered describes the waves generated by a completely submerged body whose velocity oscillates with a small period about a certain positive value. The first two terms of the formal two-scale asymptotic expansions in powers of the small velocity oscillation period are found for the velocity potential and the elevation of the free surface. These make it possible to write down asymptotic equations for the wave drag and other hydrodynamic characteristics. It is found that for writing the leading terms of the asymptotic expansions of the hydrodynamic characteristics averaged over the period it is insufficient to know the velocity potential describing the motion of the body with the mean velocity. The asymptotic expansions of the hydrodynamic characteristics obtained differ substantially from those for surface pressure moving with rapidly oscillating velocity and for a sharply accelerating submerged body.