Instabilities of exact, time-periodic solutions of the incompressible Euler equations

Journal of Fluid Mechanics

Volumn 404, Issue , 2000, Pages 269-287

  Biello, Joseph A ^a   Saldanha, Kenneth I ^b   Lebovitz, Norman R ^b  

^a UNIVERSITY OF CHICAGO   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EULER FLOW; INCOMPRESSIBLE FLOW; INVISCID FLUID; MATHEMATICAL ANALYSIS;

EID: 0033913173     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112099007089     Document Type: Article

References (23)

1. BAYLY, B. J. 1986 Three-dimensional instability of elliptical flow. Phys. Rev. Lett. 57, 2160-2171.
2. BUSSE, F. 1968 Steady flow in a precessing ellipsoidal shell. J. Fluid Mech. 33, 739-752.
3. CHURCHILL, R. C., PECELLI, G. & ROD, D. L. 1980 Stability transitions for periodic orbits in Hamiltonian systems. Arch. Rat. Mech. Anal. 73, 313-347.
4. FORSTER, G. K. & CRAIK, A. D. D. 1996 The stability of three-dimensional time-periodic flows with ellipsoidal stream surfaces. J. Fluid Mech. 324, 379-391.
5. GLEDZER, E. B., NOVIKOV, YU. V., OBUKHOV, A. M. & CHUSOV, M. A. 1974 An investigation of the stability of liquid flows in a three-axis ellipsoid. Isv. Acad. Sci. USSR Atmos. Ocean. Phys. 10, 69-71.
6. GLEDZER, E. B. & PONOMAREV, V. M. 1977 Finite-dimensional approximation of the motions of an incompressible fluid in an ellipsoid cavity. Isv. Ocean. Phys. 13, 565-589.
7. GLEDZER, E. B. & PONOMAREV, V. M. 1992 Instability of bounded flows with elliptical streamlines. J. Fluid Mech. 240, 1-30.
8. GUCKENHEIMER, J. & MAHALOV, A. 1992 Instability induced by symmetry reduction. Phys. Rev. Lett. 68, 2257-2260.
9. KERSWELL, R. R. 1993 The instability of precessing flow. Geophys. Astrophys. Fluid Dyn. 72, 107-144.
10. KERSWELL, R. R. 1999 Secondary instabilities in rapidly rotating fluids: inertial wave breakdown. J. Fluid Mech. 382, 283-306.
11. KNOBLOCH, E., MAHALOV, A. & MARSDEN, J. E. 1994 Normal forms for three-dimensional parametric instabilities in ideal hydrodynamics. Physica D 73, 49-81.
12. LEBOVITZ, N. 1989 The stability equations for rotating, inviscid fluids: Galerkin methods and orthogonal bases. Geophys. Astrophys. Fluid Dyn. 46, 221-243.
13. LEBOVITZ, N. & LIFSCHITZ, A. 1996 New global instabilities of the Riemann ellipsoids Astrophys. J. 458, 699-713.
14. LEBOVITZ, N. R. & SALDANHA, K. I. 1999 On the weakly nonlinear development of the elliptic instability. Phys. Fluids 11, 3374-3379.
15. LIFSCHITZ, A. & FABIJONAS, B. 1996 A new class of instabilities of rotating fluids. Phys. Fluids 8, 2239-2241.
16. MALKUS, W. V. R. 1989 An experimental study of global instabilities due to the tidal (elliptical) distortion of a rotating elastic cylinder. Geophys. Astrophys. Fluid Dyn. 48, 123-134.
17. MASON, D. M. & KERSWELL, R. R. 1999 Nonlinear evolution of the elliptical instability: an example of inertial wave breakdown. J. Fluid Mech. 396, 73-108.
18. MORRISON, P. 1998 Hamiltonian description of the ideal fluid. Rev. Mod. Phys. 70, 467-521.
19. PIERREHUMBERT, R. T. 1986 Universal short-wave instability of two-dimensional eddies in an inviscid fluid. Phys. Rev. Lett. 57, 2157-2159.
20. POINCARÉ, H. 1910 Bull. Astron. 27, 321-356.
21. ROBERTS, P. H. & STEWARTSON, K. 1965 On the motion in a liquid in a spheroidal cavity of a precessing rigid body II. Proc. Camb. Phil. Soc. 61, 279-288.
22. WALEFFE, F. 1989 The 3D instability of a strained vortex and its relation to turbulence. PhD Thesis, Massachusetts Institute of Technology.
23. WALEFFE, F. 1990 On the three dimensional instability of strained vortices. Phys. Fluids A 2, 76-80.