The damping of viscous gravity waves

Using a solution of the linearized Navier-Stokes equations, an approximate formula has been derived for the damping rate of gravity waves in viscous fluids. The proposed solution extends the results found by Lamb (1932) [5] for waves propagating in deep-water conditions for large Reynolds numbers and those derived by Biesel (1949) [14] under more general hypotheses. Specifically, comparisons with the Lamb solution highlight large differences in intermediate and shallow depths and/or for moderate Reynolds numbers while significant discrepancies are observed with the Biesel solution in deep-water conditions. For these reasons, the proposed solution is of great importance for the estimation of the viscous dissipations during the wave motion and represents a useful benchmark for the validation of numerical solvers. With respect to this, the theoretical findings have been compared with numerical simulations obtained by means of a well-known Smoothed Particle Hydrodynamics solver. (C) 2012 Elsevier B.V. All rights reserved.