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The damping of surface water waves in containers with grooved surfaces Gettel, Lorne Edward

Abstract

The damping, of surface waves on shallow water can be affected by the roughness of the container walls as well as by surfactant layers present on the air-water interface. The increase in the damping caused by a grooved wave tank base has been studied both theoretically and experimentally. In any experimental investigation into the effect of surface roughness on the damping, surfactants can obscure the effects of wall roughness. An experimental technique is described to enable the relative importance of these two effects to be determined unambiguously. Initially experiments were conducted with the groove amplitude much smaller than the viscous boundary layer thickness. It was found that the increase in the damping caused by the grooved base was small (< 5% increase). The damping has also been studied for large amplitude grooves on the base of the wave tank (dimensions much larger than the viscous boundary layer thickness). It is shown theoretically that, for grooves of triangular or approximately sinusoidal cross section, the damping is increased by an amount proportional to the total surface area of the grooved surface, and is independent of the direction of flow with respect to the grooves. The theoretical model applies when the groove spacing and amplitude are small compared to the fluid depth and wavelength of the surface waves, but are large compared to the viscous boundary layer thickness. Experiments were conducted to test these predictions. By carrying out observations on two surface modes, it is shown that the observed increased damping is due to the grooved surface alone and cannot be attributed to spurious surfactant effects. It was found experimentally that the damping was independent of flow direction with respect to the grooves, and the increase in the damping was strictly proportional to the fractional increase in the area of the base, in complete agreement with the theoretical predictions.

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