The gravitational collapse of a mixed region into a linearly stratified fluid

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Abstract
A theoretical and experimental investigation of the collapse of a mixed region into a linearly stratified fluid is presented. An analytical model is developed for the motion of the nose of the mixed region, valid for small dimensionless times and it compares well with the experimental results of the present study and previous investigators. For longer times the length of the mixed region did not increase as the square root of the dimensionless time, as previously reported (Wu 1969), for an aspect ratio (half the initial vertical extent divided by the initial horizontal extent) equal to one. In our experiments the length did increase as a power of the dimensionless time also, but with values of the exponent between 0·89 and 0·38, depending on the values of the various parameters. It is concluded that the motion cannot be described by a simple quasi-steady buoyancy-inertia balance only. We argue that the production of internal solitary waves and their interaction with the mixed region are critical to a complete understanding of the experimental results.