Parametric instability in a rotating cylinder of gas subject to sinusoidal axial compression. Part 2. Weakly nonlinear theory

Journal of Fluid Mechanics

Volumn 595, Issue , 2008, Pages 291-321

  Racz, J P ^a   Scott, J F ^a  

^a ECOLE CENTRALE DE LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

AXIAL COMPRESSION; HOPF BIFURCATION; NONLINEAR SYSTEMS; ROTATIONAL FLOW; VORTEX FLOW;

EXPONENTIAL DIVERGENCE; FLOW INSTABILITY; MEAN FLOW;

FLOW OF GASES;

AXIAL COMPRESSION; FLOW OF GASES; HOPF BIFURCATION; NONLINEAR SYSTEMS; ROTATIONAL FLOW; VORTEX FLOW;

AMPLITUDE; BIFURCATION; COMPRESSIBLE FLOW; CYLINDER; GAS; GEOSTROPHIC FLOW;

EID: 38049184498     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112007009226     Document Type: Article

References (21)

1. BUSSE, F. H. 1968 Steady fluid flow in a precessing spheroidal shell. J. Fluid Mech. 33, 739-751.
2. DOUADY, S. 1990 Experimental study of Faraday instability. J. Fluid Mech. 221, 383-409.
3. DUGUET, Y., SCOTT, J. & LE PENVEN, L. 2005 Instability inside a rotating gas cylinder subject to axial periodic strain. Phys. Fluids 17, 114103.
4. ELOY, C., LE GAL, P. & LE DIZÉS, S. 2003 Elliptic and triangular instabilities in rotating cylinders. J. Fluid Mech. 476, 357-388.
5. FULTZ, D. 1959 A note on overstability, and the elastoid-inertia oscillations of Kelvin, Solberg and Bjerknes. J. Met. 16, 199-208.
6. GRAFTIEAUX, L. 2003 Etude expérimentale de l'instabilité d'un cylindre de gaz tournant sourmis à une compression périodique. PhD thesis, Ecole Centrale de Lyon.
7. GRAFTIEAUX, L., LE PENVEN, L., SCOTT, J. F. & GROSJEAN, N. 2002 A new parametric instability in rotating cylinder flow. In Advances in Turbulence IX (ed. I. P. Castro & P. E. Hancock). CIMNE, Barcelona, Spain.
8. GREENSPAN, H. 1969 On the non-linear interaction of inertial modes. J. Fluid Mech. 36, 257-264.
9. GUNN, J. S. & ALDRIDGE, K. D. 1990 Inertial wave eigenfrequencies for a non-uniformly rotating fluid. Phys. Fluids A 2(11), 2055-2060.
10. KERSWELL, R. R. 1999 Secondary instabilities in rapidly rotating flows: Inertial wave breakdown. J. Fluid Mech. 382, 283-306.
11. KERSWELL, R. R. 2002 Elliptical instability. Annu. Rev. Fluid Mech. 34, 83-114.
12. McEWAN, A. D. 1970 Inertial oscillations in a rotating fluid cylinder. J. Fluid Mech. 40, 603-640.
13. MALKUS, W. V. R. 1989 An experimental study of the global instabilities due to tidal (elliptical) distortion of a rotating elastic cylinder. Geophys. Astrophys. Fluid Dyn. 48, 123-134.
14. MANASSEH, R. 1992 Breakdown regimes of inertia waves in a precessing cylinder. J. Fluid Mech. 243, 261-296.
15. 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.
16. MILES, J. 1993 On Faraday waves. J. Fluid Mech. 248, 671-683.
17. MILNER, S. T. 1991 Square patterns and secondary instabilities in driven capillary waves. J. Fluid Mech. 225, 81-100.
18. RACZ, J.-P. 2006 Instabilité paramétrique dans un cylindre de gaz en rotation soumis à la compression périodique d'un piston. PhD thesis, Ecole Centrale de Lyon.
19. RACZ, J.-P. & SCOTT, J. F. 2008 Parametric instability in a rotating cylinder of gas subject to sinusoidal axial compression. Part 1. Linear theory. J. Fluid Mech. 595, 265-290.
20. WALEFFE, F. 1989 The 3D instability of a strained vortex and its relation to turbulence. PhD thesis, MIT.
21. WALEFFE, F. 1990 On the three-dimensional instability of strained vortices. Phys. Fluids A 2, 76-80.