Statically unstable layers produced by overturning internal gravity waves

Abstract

Internal waves in a uniformly stratified fluid of sufficiently large amplitude develop tilted layers in which the fluid is statically unstable. To investigate the evolution and subsequent development of this structure, experiments are made in which a horizontal rectangular tube containing a fluid of uniform density gradient is gently rocked at a selected frequency about a horizontal axis normal to the tube length. Large-amplitude standing internal gravity waves of the first mode are generated, and these steepen and overturn, the isopycnal surfaces folding to produce a vertically thin and horizontally extensive layer in which the fluid is statically unstable. In experiments with relatively small forcing, the layer persists for some 6 buoyancy periods, with no detected evidence of secondary instability, and static stability is re-established as the periodic flow reverses. The layer however breaks down, with consequent diapycnal mixing, when greater forcing is applied.The scale and growth rates of instability in the overturning internal gravity waves are estimated using the theory developed in a companion paper by Thorpe (1994a). For the parameters of the laboratory experiments with relatively small forcing, the growth rates are small, consistent with the absence of signs of secondary instability. Larger growth rates and disturbance amplification factors of about 70 are predicted for the conditions in the experiment in which mixing was observed to occur. The experimental observations are consistent with an instability having a longitudinal structure.We conclude that the form and development of breaking in internal gravity waves will vary according to the circumstances in which waves break, but depend on the Prandtl number of the fluid and, in particular, on the Rayleigh and Reynolds numbers of regions of static instability which develop as the waves overturn.