DAMPING OF NEARLY INVISCID WATER WAVES

The complete spectrum of decaying small-amplitude water waves is descr ibed. Viscosity is shown tu be responsible both for the decay of gravi ty-capillary waves and for the appearance of a class of viscous modes that are omitted in the standard potential formulation. For sufficient ly small viscosity [as measured by the parameter C = nu(gh(3))(-1/2) m uch less than 1, where nu is the kinematic viscosity, g the accelerati on due to gravity, and ir the undisturbed depth of the fluid] the visc ous modes decay more slowly than the gravity-capillary ones and must b e included in weakly nonlinear theories. The analysis indicates that f or realistic values of C second-order corrections to the decay rate of gravity-capillary waves are important and suggests a straightforward resolution of existing discrepancies between experimentally measured a nd theoretically calculated damping rates.