Astronomy and Astrophysics – Astrophysics
Scientific paper
Sep 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977rspsa.356..411d&link_type=abstract
Royal Society (London), Proceedings, Series A, vol. 356, no. 1686, Sept. 15, 1977, p. 411-432.
Astronomy and Astrophysics
Astrophysics
33
Gravity Waves, Internal Waves, Inviscid Flow, Stratified Flow, Boundary Layer Stability, Catastrophe Theory, Floquet Theorem, Flow Stability, Richardson Number, Wave Interaction
Scientific paper
The linear stability of an internal gravity wave of arbitrary finite amplitude propagating in an unbounded stratified inviscid Boussinesq fluid is analyzed. The Floquet system that governs the wave instability is derived, and a method of solution for parametric instability is applied which is suitable for quite general high-order Floquet systems. The parametric instability is related to resonant wave interactions, Thom's (1975) catastrophe theory is used in specifying the stability boundary, and numerical results are presented for some stability-boundary calculations. It is concluded that an internal gravity wave is always unstable, regardless of how large its minimum local Richardson number may be, and that parametric resonance is the prime physical mechanism of the instability.
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