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- Title
On short-wave instability of the stratified Kolmogorov flow.
- Authors
Kurgansky, M. V.
- Abstract
The problem of the linear stability of the stratified Kolmogorov flow driven by a sinusoidal in space force in a viscous and diffusive Boussinesq fluid is re-visited using the Floquet theory, Galerkin approximations and the method of (generalized) continued fractions. Numerical and analytical arguments are provided in favor of a conjecture that an ideal stratified Kolmogorov flow is prone to short-wave instability for Richardson numbers markedly greater than the critical Richardson number Ri = ¼ that appears in the Miles–Howard theorem. The short-wave instability of the stratified Kolmogorov flow is conjectured to be due to a resonance amplification of the Doppler-shifted internal gravity wave modes, in the presence of critical levels of the main flow that are ignored in the proof of the Miles–Howard theorem, but it is emphasized that the complete resolution of the above paradox is a task for future research.
- Subjects
STRATIFIED flow; INTERNAL waves; FLOQUET theory; GRAVITY waves; RICHARDSON number; CONTINUED fractions
- Publication
Theoretical & Computational Fluid Dynamics, 2022, Vol 36, Issue 4, p575
- ISSN
0935-4964
- Publication type
Article
- DOI
10.1007/s00162-022-00613-2