Abstract
Following earlier work of two of the authors (Majda and Grote, 1997), analytic models with vertical collapse in strongly stratified fluids are studied here through exact laminar solutions of the equations describing low Froude number limiting dynamics. It is found that fairly weak rotation with moderately large Rossby numbersRo =1, 5, can prevent the vertical collapse process in these exact solutions; the collapse process is also suppressed for sufficiently low Reynolds numbers of orderRe =100. In a complimentary direction, the authors propose a new explicit criterion for development of additional instabilities in the Boussinesq equations at low Froude number as compared with the low Froude number limiting dynamics. This criterion is developed through an analytic study of elementary exact solutions of the Boussinesq equations at low Froude numbers and involves the relative magnitudes of the local vertical vorticity and horizontal strain.
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