Damping rate measurements and predictions for gravity waves in an air-oil-water system

Dissipation of standing gravity waves of frequencies within 1-2 Hz is investigated experimentally. The waves are generated in a rectangular tank filled with water, the surface of which is covered with an oil layer of mean thickness, d. Damping rates are measured as a function of d, and compared with results from established theoretical models-in particular, with those from a recently developed three-fluid dissipation model that considers waves in a system of semi-infinitely deep fluids that lie above and below an interfacial fluid layer of finite thickness. Based on a comparison of experimental data with predictions, the oil-water interfacial elasticity, E-2, is empirically determined to be a linear function of d. The theoretical predictions include contributions from the three-fluid dissipation model, which accounts for energy losses due to shear layers at the interfaces, friction in the fluid bulk, and compression-expansion oscillations of the elastic interfaces; and from a boundary-layer dissipation model, which accounts for energy losses due to boundary layers at the tank's solid surfaces. The linear function, E-2(d), is used to compute the three-fluid model damping rate. An effective viscosity of the oil-water system is used to compute the boundary-layer model damping rate. The theoretical predictions are, on average, within 5% of measurements for all the wave frequencies considered. The promise shown by the three-fluid model is highlighted, as are the assumptions involved in the analysis and comparisons.

Automated summary

The dissipation of standing gravity waves with frequencies within 1-2 Hz is experimentally investigated. The results are compared with established theoretical models, particularly a three-fluid dissipation model and a boundary-layer dissipation model. The empirical findings indicate a linear relationship between the oil-water interfacial elasticity and the thickness of the oil layer. The theoretical predictions are within 5% of the experimental measurements on average, highlighting the potential of the three-fluid model and noting the assumptions made in the analysis and comparisons.