Damping of surface waves in an incompressible liquid

Abstract

The damping of surface waves of small amplitude in liquid contained in cylinders has been calculated. Viscous dissipation in an assumed laminar boundary layer was taken to be the primary cause of damping. Experimental results were obtained for the logarithmic decrement as a function of the ratio of liquid height to cylinder radius for several water-filled cylinders. Theory and experiment were found to be in good agreement.

Observation of nonlinear sloshing induced by wetting dynamics

“…Natural frequency computed in this framework differs from the experimental values from less than 1% [5,6] up to around 10% [7][8][9]. In contrast, measurements of damping are associated with larger discrepancies: a theory based on dissipation localized in bottom and wall boundary layers underestimates experimental dissipation from a few percent [7] to as much as a few hundred percent [5,8,9]. These disparities have been ascribed to both surface contamination and capillary effects close to the contact line.…”

“…Note that although this expression has been derived in [7] in the absence of gas, it also describes the present experiment given that phases have almost the same height and kinematic viscosity. Equation (12) Such terms could result from surface contamination, but we regard this possibility as unlikely.…”

“…The very small kinematic viscosity of fluids close to the critical point (a few times 10 −8 m 2 .s −1 ) compared to the ones of more usual fluids (1.10 −6 for water) makes this parameter small enough not to consider second order contributions (as bulk dissipation), that can be of importance otherwise [20]. If neither surface contamination nor capillary effects close to the meniscus are considered, damping thus reduces to the contributions of top, bottom and lateral boundary layers and [7] …”

Instability analysis of nonlinear surface waves in a circular cylindrical container subjected to a vertical excitation

“…Bernoff et al [26] completely solved the first-order damping for a rectangular container. Case and Parkinson [27] studied the damping of surface waves in a cylindrical container. The analytical expressions of the damping were obtained and their theory and experiment were found to be in good agreement.…”

Propagation characteristics of capillary ripples

“…Notable among these is a paper by Crapper (22) wherein he develops equations that are exact representations for progressive capillary waves of arbitrary amplitude. Case and Parkinson (23) have examined the damping of surface waves in liquids contained in cylinders. They use boundary layer theory to simplify the development of their theory.…”