Quasi-linear approximation for description of turbulent boundary layer and wind wave growth

Abstract

This study describes an approximate quasi-linear model for the description of the turbulent boundary layer over steep surface waves. The model assumes that wave-induced disturbances of the atmospheric turbulent boundary layer could be reasonably described in a linear approximation with the momentum flux from wind to waves retained as the only nonlinear effect in the model. For the case of periodic long-crested waves, the model has been verified with a set of the original laboratory and numerical experiments. The laboratory experimental study of the airflow over the steep waves was performed by means of the PIV technique. The numerical study was performed with direct numerical simulation (DNS) of the turbulent airflow over waved surface at Re=15,000 for quasi-homogeneous waves, wave trains and parasitic capillaries riding on the crest of a steep waves. Examples are given of the application of the quasi-linear approximation to describe the turbulent boundary layer over waves with the continuous spectrum under the assumption of random phases of harmonics. In the latter case the quasi-linear model provides the growth rate of surface waves in the inertial interval of the surface wave spectrum proportional to w7/3 in agreement with predictions in [1].