VISCOUS POTENTIAL FLOW FOR WATER WAVES

摘要

A potential flow solution to the Navier-Stokes equations for a viscous incompressible fluid is constructed for gravity waves on deep water. Using this solution, it is shown that the amplitude of the wave decays at one half of the rate originally found by Lamb [6]. The rate of decay deduced from the exact analytical solution derived here is in exact agreement with the direct calculation of Funada and Joseph [2]. The physical consequence of the new rate of decay is discussed.