An extension of Arnol'd's second stability theorem for the Euler equations

Physica D: Nonlinear Phenomena

Volumn 94, Issue 4, 1996, Pages 161-167

  Wolansky, G ^a   Ghil, M ^b  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Arnol'd stability; Energy Casimir method; Fluid dynamics; Planetary flows

Indexed keywords

EID: 0041075897     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-2789(95)00312-6     Document Type: Article

References (9)

1. V.I. Arnol'd, Conditions for nonlinear stability of stationary plane curvilinear flows of an ideal fluid, Sov. Math. Dokl. 6 (1965) 773-776.
2. V.I. Arnol'd, On an a priori estimate in the theory of hydrodynamical stability, Amer. Math. Soc. Transl. Ser. 2 79 (1969) 267-269.
3. H.G.B. Casimir, Ueber die Konstruktion einer zu den irreduziblen Darstellungen halbeinfacher kontinuierlicher Gruppen gehörigen Differentialgleichung, Proc. R. Soc., Amsterdam 34 (1931) 844-846.
4. D.D. Holm, Nonlinear stability of fluid and plasma equilibria, Phys. Rep. 123(1,2) (1985) 1-116.
5. M.E. McIntyre and T.G. Shepherd, An exact local conservation theory for finite-amplitude disturbance to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems, J. Fluid Mech. 131 (1987) 527-565.
6. G. Wolansky, On nonlinear stability of polytropic galaxies, Arch. Rat. Mech. (1994), submitted.
7. L. Rayleigh, On the stability, or instability, of certain fluid motions, Proc. Lond. Math. Soc. 11 (1880) 57-70.
8. T.G. Shepherd, Rigorous bounds on the nonlinear saturation of instabilities of parallel shear flows, J. Fluid Mech. 196 (1988) 291-322.
9. G. Wolansky and M. Ghil, Stability of quasi-geostrophic flow in a periodic channel, Phys. Lett. A 202 (1995) 111-116.