Stable and unstable vortices attached to seamounts

Journal of Fluid Mechanics

Volumn 507, Issue , 2004, Pages 71-94

  Nycander, J ^a   Lacasce, J H ^b  

^a STOCKHOLM UNIVERSITY   (Sweden)

^b NORWEGIAN METEOROLOGICAL INSTITUTE   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; SIGNAL FILTERING AND PREDICTION; STORMS;

BAROTROPIC FLOWS; POTENTIAL VORTICITY (PV); SEAMOUNTS;

VORTEX FLOW;

FLUID FLOW; INSTABILITY; MATHEMATICAL ANALYSIS; MODEL; STABILITY; VORTEX;

EID: 2542604579     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112004008730     Document Type: Article

References (38)

1. ARNOL'D, V. I. 1966 On an a priori estimate in the theory of hydrodynamic stabillity. Izv. Vyssh. Uchebn. Zaved. Matematika 54 (5), 3-5. (English transl. Am. Math. Soc. Transl., Series 2, 79, 267-269 (1969).)
2. ARNOL'D, V. I. 1978 Mathematical Methods of Classical Mechanics. Springer.
3. BENJAMIN, T. B. 1976 The alliance of practical and analytical insights into the nonlinear problems of fluid mechanics. In Applications of Methods of Functional Analysis to Problems in Mechanics (ed. A. Dold & B. Eckman). Lecture Notes in Mathematics, vol. 503, pp. 8-29. Springer.
4. BRETHERTON, F. B. & HAIDVOGEL, D. B. 1976 Two-dimensional turbulence over topography. J. Fluid Mech. 78, 129-154.
5. BURTON, G. R. 1987 Rearrangements of functions, maximization of convex functionals, and vortex rings. Math. Ann. 276, 225-253.
6. BURTON, G. R. 1988 Steady symmetric vortex pairs and rearrangements. Proc. R. Soc. Edin. 108A, 269-290.
7. BURTON, G. R. & NYCANDER, J. 1999 Stationary vortices in three-dimensional quasi-geostrophic shear flow. J. Fluid Mech. 389, 255-274.
8. CARNEVALE, G. F. & FREDERIKSEN, J. S. 1987 Nonlinear stability and statistical mechanics of flow over topography. J. Fluid Mech. 175, 157-181.
9. CARNEVALE, G. F., KLOOSTERZIEL, R. C. & VAN HEIJST, G. J. F. 1991 Propagation of barotropic vortices over topography in a rotating tank. J. Fluid Mech. 233, 119-139.
10. CARNEVALE, G. F. & VALLIS, G. K. 1990 Pseudo-advective relaxation to stable states of inviscid two-dimensional fluids. J. Fluid Mech. 213, 549-571.
11. CARTON, X. 1989 In Mesoscale/Synoptic Coherent Structures in Geophysical Turbulence (ed. J. C. J. Nihoul & B. M. Jamart). Elsevier.
12. DRITSCHEL, D. G. 1986 The nonlinear evolution of rotating configurations of uniform vorticity. J. Fluid Mech. 172, 157-182.
13. EMAMIZADEH, B. 2000 Steady vortex in a uniform shear flow of an ideal fluid. Proc. R. Soc. Edin. 130A, 801-812.
14. FILIPPOV, D. V. & YAN'KOV, V. V. 1986 Two-dimensional electron vortices. Soc. J. Plasma Phys. 12, 548-552.
15. FLIERL, G. R., MALANOTTE-RIZZOLI, P. & ZABUSKY, N. J. 1987 Nonlinear waves and coherent vortex structures in barotropic β-plane jets. J. Phys. Oceanogr. 17, 1408-1438.
16. GENIN, A., NOBLE, M. & LONSDALE, P. F. 1989 Tidal currents and anticyclonic motions on two North Pacific seamounts. Deep-Sea Res. 36, 1803-1815.
17. GREENSPAN, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press. 325 pp.
18. HOGG, N. G. 1973 On the stratified Taylor column. J. Fluid Mech. 58, 517-537.
19. JOHNSON, E. R. 1978 Trapped vortices in rotating flow. J. Fluid Mech. 86, 209-224.
20. KRAICHNAN, R. H. 1967 Inertial ranges of two dimensional turbulence. Phys. Fluids 10, 1417-1423.
21. KRAICHNAN, R. H. & MONTGOMERY, D. 1980 Two-dimensional turbulence. Rep. Prog. Phys. 43, 547-619.
22. KUNZE, E. & TOOLE, J. M. 1997 Tidally driven vorticity, diurnal shear, and turbulence atop Fieberling Seamount. J. Phys. Oceanogr. 27, 2663-2693.
23. LACASCE, J. H. 1998 A geostrophic vortex over a slope. J. Phys. Oceanogr. 28, 2362-2381.
24. LODER, J. W. 1980 Topographic rectification of tidal currents on the sides of Georges Bank. J. Phys. Oceanogr. 10, 1399-1416.
25. MCWILLIAMS, J. C. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 21-43.
26. MCWILLIAMS, J. C. 1990 The vortices of two-dimensional turbulence. J. Fluid Mech. 219, 361-385.
27. MERRYFIELD, W. J., CUMMINS, P. F. & HOLLOWAY, G. 2001 Equilibrium statistical mechanics of barotropic flow over finite topography. J. Phys. Oceanogr. 31, 1880-1890.
28. NYCANDER, J. 1995 Existence and stability of stationary vortices in a uniform shear flow. J. Fluid Mech. 287, 119-132.
29. NYCANDER, J. 2003 Stable vortices as maximum or minimum energy flows. In Nonlinear Processes in Geophysical Fluid Dynamics (ed. O. U. Velasco Fuentes, J. Sheinbaum & J. L. Ochoa de la Torre). Kluwer.
30. NYCANDER, J. & EMAMIZADEH, B. 2003 Variational problem for vortices attached to seamounts. Nonlinear Anal. 55, 15-24.
31. PATTERSON, G. S. & ORSZAG, S. A. 1971 Spectral calculations of isotropic turbulence: efficient removal of aliasing interactions. Phys. Fluids 14, 2538-2541.
32. SALMON, R., HOLLOWAY, G. & HENDERSHOTT, M. C. 1976 The equilibrium statistical mechanics of simple quasi-geostrophic models. J. Fluid Mech. 75, 691-703.
33. SAUNDERS, P. M. & KING, B. A. 1995 Bottom currents derived from a shipborne ADCP in WOCE cruise A11 in the South Atlantic. J. Phys. Oceanogr. 25, 329-347.
34. SHNIRELMAN, A. I. 1993 Lattice theory and flows of ideal incompressible fluid. Russian J. Math. Phys. 1, 105-114.
35. SOBOLEV, S. L. 1963 On a theorem of functional analysis. Am. Math. Soc. Transl. 34, 39-68.
36. TAYLOR, G. I. 1917 Motions of solids in fluids when the flow is not irrotational. Proc. R. Soc. Lond. A 93, 99-113.
37. VANNESTE, J. 1995 Explosive resonant interaction of baroclinic Rossby waves and stability of multilayer quasi-geostrophic flow. J. Fluid Mech. 291, 83-107.
38. ZIMMERMAN, J. T. F. 1978 Topographic generation of residual circulation by oscillatory (tidal) currents. Geophys. Astrophys. Fluid Dyn. 11, 35-47.