Elliptical instability of a rapidly rotating, strongly stratified fluid

Physics of Fluids

Volumn 21, Issue 7, 2009, Pages

  Aspden, J M ^a   Vanneste, J ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

GROWTH RATE;

ANALYTIC EXPRESSIONS; ANTICYCLONIC FLOW; ASYMPTOTIC RESULTS; ELLIPTICAL INSTABILITY; EXPONENTIAL ASYMPTOTICS; NUMERICAL SOLUTION; ROTATING STRATIFIED FLUID; STRONG STRATIFICATION;

STABILITY;

EID: 70350704940     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3177354     Document Type: Article

References (22)

1. R. R. Kerswell, "Elliptical instability," Annu. Rev. Fluid Mech. ARVFA30066-4189 34, 83 (2002). 10.1146/ annurev.fluid.34.081701.171829
2. T. Miyazaki, "Elliptical instability in a stably stratified rotating fluid," Phys. Fluids A PFADEB0899-8213 5, 2702 (1993). 10.1063/1.858733
3. S. Leblanc, "Internal wave resonances in strain flows," J. Fluid Mech. JFLSA70022-1120 477, 259 (2003). 10.1017/S0022112002003221
4. J. C. McWilliams and I. Yavneh, "Fluctuation growth and instability associated with a singularity of the balance equations," Phys. Fluids PHFLE61070-6631 10, 2587 (1998). 10.1063/1.869772
5. M. J. Molemaker, J. C. McWilliams, and I. Yavneh, "Baroclinic instability and loss of balance," J. Phys. Oceanogr. JPYOBT1520-0485 35, 1505 (2005). 10.1175/JPO2770.1
6. J. Vanneste and I. Yavneh, "Unbalanced instabilities of rapidly rotating stratified shear flows," J. Fluid Mech. JFLSA70022-1120 584, 373 (2007). 10.1017/S002211200700643X
7. J. C. McWilliams, M. J. Molemaker, and I. Yavneh, "Ageostrophic, anticyclonic instability of a geostrophic, barotropic boundary current," Phys. Fluids PHFLE61070-6631 16, 3720 (2004). 10.1063/ 1.1785132
8. R. Plougonven, D. J. Muraki, and C. Snyder, "A baroclinic instability that couples balanced motions and gravity waves," J. Atmos. Sci. JAHSAK0022-4928 62, 1545 (2005). 10.1175/JAS3426.1
9. Note that we use the conventional form of Rossby number rather than its inverse as used in Ref..
10. J. Vanneste and I. Yavneh, "Exponentially small inertia-gravity waves and the breakdown of quasi-geostrophic balance," J. Atmos. Sci. JAHSAK0022-4928 61, 211 (2004). 10.1175/ 1520-0469(2004)061<0211:ESIWAT>2.0.CO;2
11. J. Vanneste, "Exponential smallness of inertia-gravity-wave generation at small Rossby number," J. Atmos. Sci. JAHSAK0022-4928 65, 1622 (2008). 10.1175/2007JAS2494.1
12. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (Springer, New York, 1999).
13. M. I. Weinstein and J. B. Keller, "Asymptotic behaviour of stability regions for Hill's equation," SIAM J. Appl. Math. SMJMAP0036-1399 47, 941 (1987). 10.1137/0147062
14. M. J. Ablowitz and A. S. Fokas, Complex Variables: Introduction and Applications (Cambridge University Press, Cambridge, 1997).
15. S. J. Friedlander and A. Lipton-Lifschitz, in Handbook of Mathematical Fluid Dynamics, edited by S. J. Friedlander and D. Serre (Elsevier Science, New York, 2003), Vol. 2, pp. 289-353.
16. S. Le Dizès, "Three-dimensional instability of a multipolar in a rotating flow," Phys. Fluids PHFLE61070-6631 12, 2762 (2000). 10.1063/1.1289774
17. D. Guimbard and S. Leblanc, "Local stability of the Abrashkin-Yakubovich family of vortices," J. Fluid Mech. JFLSA70022-1120 567, 91 (2006). 10.1017/S0022112006002114
18. R. B. Paris and A. D. Wood, "Stokes phenomenon demystified," Bull. Inst. Math. Appl. BULIM20905-5628 31, 21 (1995).
19. M. V. Berry, "Uniform asymptotic smoothing of Stokes's discontinuities," Proc. R. Soc. London, Ser. A PRLAAZ0950-1207 422, 7 (1989). 10.1098/rspa.1989.0018
20. Asymptotics Beyond All Orders, edited by H. Segur, S. Tanveer, and H. Levine (Plenum, New York, 1991).
21. V. Hakim, "Asymptotic techniques in nonlinear problems: Some illustrative examples," in Hydrodynamics and Nonlinear Instabilities, edited by C. Godrèche and P. Manneville (Cambridge University Press, Cambridge, 1998), Chap. 3, pp. 295-386.
22. A. B. Olde Daalhuis, S. J. Chapman, J. R. King, J. R. Ockendon, and R. H. Tew, "Stokes phenomenon and matched asymptotic expansions," SIAM J. Appl. Math. SMJMAP0036-1399 55, 1469 (1995). 10.1137/ S0036139994261769