A STUDY OF THE BREAKDOWN OF STATICALLY GENERATED INTERNAL GRAVITY WAVES IN A STRATIFIED SHEAR FLOW WITH A MEAN VELOCITY.

摘要

An experimental study of artificially generated internal gravity waves in a low speed, two layer, stably stratified flow wind tunnel in the presence of a significant mean shear has shown the breakdown of the internal gravity waves by the growth of high frequency unstable waves of the Kelvin-Helmholtz type, either on the front face or the the back face of the primary internal wave. Using phase averaging techniques, based on the frequency of the primary internal gravity waves, data gathered at many different vertical locations was combined to create interface maps of the temperature and the two velocity components which provided detailed pictures of the deflection of the interface and the corresponding perturbation velocity field. The interface maps showed that the position of the fastest growing high frequency oscillations occurred at the point where the local minimum Richardson number was the smallest. Also, the appearance of the high frequency oscillations in the phase averaged interface maps indicated that the position of the unstable waves on the primary wave was not random. Further, the breakdown of the primary internal wave on only one face, when the entire flow was considerably below the critical value of the stability parameter (Richardson number equal to 1/4) suggested that standard results from linear theory may not be valid in a time dependent flow. It is shown by both a two-layer analytical model and results from a more realistic numerical model that the asymmetrical local minimum Richardson number pattern about the interface deflection is a direct result of the propagation of two finite amplitude internal gravity waves, generated by a single two-dimensional wave maker, both waves being advected downstream by the mean velocity. It is also shown, both experimentally and analytically, that the local minimum Richardson number reaches its smallest values when the modulated amplitude of the double wave is at a minimum. The importance of this double wave phenomenon, and the associated wave breakdown, in laboratory testing and in nature along with direct applications to other published studies is discussed.