Experimental study of eddy viscosity for breaking waves on sloping bottom and comparisons with empirical and numerical predictions

Abstract

Focus is on the turbulence for a plunging breaker. Laser Doppler anemometer point measurements were used to determine the velocity matrix of a breaking wave on a sloping bottom. Using the Reynolds stress anisotropy for incompressible fluid, it was found that the ensemble averaged measured velocity predicted eddy viscosity is associated with peaks, which are absent in the broadly accepted empirical predictions. The instantaneous eddy viscosity coefficient was determined according to the Reynolds stresses, modified mean velocity and its gradient components and turbulent kinetic energy. The modified mean velocity and its derivatives improve eddy viscosity predictions during the wave period, which gives evidence that the velocity used corresponds well to a rotational part. In addition to the measurement predictions, empirical formulae were used to estimate the eddy viscosity values during the wave period. Furthermore, a meshless numerical model is proposed to determine artificial viscosity and demonstrate its dependence on eddy viscosity in the case of weakly compressible fluid.

Keywords

• artificial viscosity
• breaking wave
• eddy viscosity
• experiment
• turbulence.