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.
2019-04-16T01:22
chapters
Analytical Models for Vertical Collapse and Instability in Stably Stratified Flows
153-177
false
http://link.springer.com/10.1007/978-94-010-0928-7_14
2000-01-01
chapter
2000
en
https://scigraph.springernature.com/explorer/license/
Pure Mathematics
Yoshifumi
Kimura
readcube_id
479b636a0c311ba9411917ff7221327c9dabdb2e551788e77c45b903063d77ac
Robert M.
Kerr
Springer Nature - SN SciGraph project
10.1007/978-94-010-0928-7_14
doi
Grote
M. J.
Dordrecht
Springer Netherlands
Shefter
M. G.
dimensions_id
pub.1015029826
A. J.
Majda
978-94-010-3794-5
IUTAM Symposium on Developments in Geophysical Turbulence
978-94-010-0928-7
Department of Mathematics ETH Zurich, Switzerland
Swiss Federal Institute of Technology in Zurich
Courant Institute of Mathematical Sciences, New York University, NY, 10012, New York
Courant Institute of Mathematical Sciences
Mathematical Sciences