Abstract
In this paper, we find a new large scale instability displayed by a stratified rotating flow in forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptotic method of multi-scale development. There is no other special constraint concerning the force. In previous papers, the force was either helical or violating parity invariance. The nonlinear equations for the instability are obtained at the third order of the perturbation theory. In this article, we explain a detailed study of the linear stage of the instability.
Highlights
Large scale instabilities are very important in fluid dynamics
We develop an analytical theory of the new large scale instability which generates large scale vortices in a stratified rotating flow with a constant temperature gradient under the action of a small scale external force which does not have any particular properties
The joint action of these forces generates an internal helicity, which in turn generates an instability. The theory of this instability is developed rigourously using the method of asymptotic multi-scale development similar to what was done by Frisch, She and Sulem for the theory of the AKA effect [11]
Summary
Large scale instabilities are very important in fluid dynamics. They generate vortices which play a fundamental role in turbulence and in transport processes. We develop an analytical theory of the new large scale instability which generates large scale vortices in a stratified rotating flow with a constant temperature gradient under the action of a small scale external force which does not have any particular properties (especially it is nonhelical and it does not lack parity invariance). The joint action of these forces generates an internal helicity, which in turn generates an instability The theory of this instability is developed rigourously using the method of asymptotic multi-scale development similar to what was done by Frisch, She and Sulem for the theory of the AKA effect [11]. The Reynolds stress and internal helicity are calculted in Appendices A and B, respectively
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