Surface-wave damping in closed basins

Abstract

The damping of surface waves in closed basins appears to be due to (a) viscous dissipation at the boundary of the surrounding basin, (b) viscous dissipation at the surface in consequence of surface contamination, and (c) capillary hysteresis associated with the meniscus surrounding the free surface. Boundary layer approximations are invoked in the treatment of (a) and (b) to reproduce and extend results that have been obtained previously by more cumbersome procedures. The surface film is assumed to act as a linear, viscoelastic surface and may be either insoluble or soluble; however, the relaxation time for the equilibrium of soluble films is neglected relative to the period of the free-surface oscillations. Capillary hysteresis is analysed on the hypothesis that both the advance and recession of a meniscus are opposed by constant forces that depend only on the material properties of the three-phase interface. The theoretical results for the logarithmic decrements of gravity waves in circular and rectangular cylinders are compared with the decay rates observed by Case & Parkinson and by Keulegan, which typically exceeded the theoretical value based on wall damping alone by factors of between two and three. It is concluded that both surface films and capillary hysteresis can account for, and are likely to have contributed to, these observed discrepancies. The theoretical effect of a surface film on wind-generated gravity waves is examined briefly and is found to be consistent with the observation that the addition of detergent to water can increase the minimum wind speed (required to produce waves) by one order of magnitude.