The Rossby-inertia-buoyancy instability in baroclinic vortices

Physics of Fluids

Volumn 20, Issue 9, 2008, Pages

  Hodyss, Daniel ^a   Nolan, David S ^b  

^a NAVAL RESEARCH LABORATORY   (United States)

^b UNIVERSITY OF MIAMI   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BUOYANCY; EIGENVALUES AND EIGENFUNCTIONS;

ANELASTIC MODELS; COMPLICATED STRUCTURES; EIGENVALUE PROBLEM; FULLY NONLINEAR; POTENTIAL VORTICITY; RADIAL DISTANCE; RADIAL MOMENTUM; VERTICAL STRUCTURES;

VORTEX FLOW;

EID: 53549088626     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2980354     Document Type: Article

References (36)

1. D. S. Nolan and M. T. Montgomery, "Nonhydrostatic, three-dimensional perturbations to balanced, hurricane-like vortices, Part I: Linearized formulation, stability, and evolution," J. Atmos. Sci. JAHSAK0022-492810.1175/ 1520-0469(2002)059<2989:NTDPTB>2.0.CO;2 59, 2989 (2002).
2. L. Rayleigh, "On the stability or instability of certain fluid motions," Proc. London Math. Soc. PLMTAL0024-6115 s1-11, 57 (1879).
3. D. J. Shea and W. M. Gray, "The hurricane's inner core region, I: Symmetric and asymmetric structure," J. Atmos. Sci. JAHSAK0022-492810.1175/1520-0469(1973)030<1544:THICRI>2.0.CO;2 30, 1544 (1973).
4. C. E. Samsury and E. J. Zipser, "Secondary wind maxima in hurricanes: Airflow and relationship to rainbands," Mon. Weather Rev. MWREAB0027-0644 62, 408 (1995).
5. K. J. Mallen, M. T. Montgomery, and B. Wang, "Reexamining the near-core radial structure of the tropical cyclone primary circulation: Implications for vortex resiliency," J. Atmos. Sci. JAHSAK0022-492810.1175/JAS-3377.1 62, 408 (2005).
6. R. Ford, "The instability of an axisymmetric vortex with monotonic potential vorticity in rotating shallow water," J. Fluid Mech. JFLSA70022-112010.1017/S0022112094002946 280, 303 (1994).
7. D. A. Schecter and M. T. Montgomery, "Damping and pumping of a vortex Rossby wave in a monotonic cyclone: Critical layer stirring versus inertia-buoyancy wave emission," Phys. Fluids PHFLE61070-663110.1063/1.1651485 16, 1334 (2004).
8. R. J. Briggs, J. D. Daugherty, and R. H. Levy, "Role of Landau damping in crossed-field electron beams and inviscid shear flow," Phys. Fluids PFLDAS0031-917110.1063/1.1692936 13, 421 (1970).
9. R. A. Cairns, "The role of negative energy waves in some instabilities of parallel flows," J. Fluid Mech. JFLSA70022-112010.1017/S0022112079000495 92, 1 (1979).
10. M. E. McIntyre and T. G. Shepherd, "An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnold's stability theorems," J. Fluid Mech. JFLSA70022-112010.1017/S0022112087002209 181, 527 (1987).
11. Y. Afanasyev, "Spontaneous emission of gravity waves by interacting vortex dipoles in a stratified fluid: Laboratory experiments," Geophys. Astrophys. Fluid Dyn. GAFDD30309-192910.1080/ 0309192031000114349 97, 79 (2003).
12. R. Ford, "The response of a rotating ellipse of uniform potential vorticity to gravity wave radiation," Phys. Fluids PHFLE61070-663110.1063/1.868360 6, 3694 (1994).
13. D. S. Schecter and M. T. Montgomery, "Conditions that inhibit the spontaneous radiation of spiral inertia-gravity waves from an intense mesoscale cyclone," J. Atmos. Sci. JAHSAK0022-492810.1175/JAS3641.1 63, 435 (2006).
14. R. Plougonven and V. Zeitlin, "Internal gravity wave emission from a pancake vortex: An example of wave-vortex interaction in strongly stratified flows," Phys. Fluids PHFLE61070-663110.1063/1.1448297 14, 1259 (2002).
15. D. Hodyss and D. S. Nolan, "Linear anelastic equations for atmospheric vortices," J. Atmos. Sci. JAHSAK0022-492810.1175/ JAS3991.1 64, 2947 (2007).
16. W. D. Smyth and J. C. McWilliams, "Instability of an axisymmetric vortex in a stably stratified, rotating environment," Theor. Comput. Fluid Dyn. TCFDEP0935-496410.1007/s001620050095 11, 305 (1998).
17. J. J. Riley and M. P. Lelong, "Fluid motions in the presence of strong stable stratification," Annu. Rev. Fluid Mech. ARVFA30066-418910.1146/annurev.fluid.32.1.613 32, 613 (2000).
18. S. M. Churilov, "Stability analysis of stratified shear flows with a monotonic velocity profile without inflection points," J. Fluid Mech. JFLSA70022-112010.1017/S0022112005005318 539, 25 (2005).
19. D. S. Nolan, M. T. Montgomery, and L. D. Grasso, "The wavenumber one instability and trochoidal motion of hurricane-like vortices," J. Atmos. Sci. JAHSAK0022-492810.1175/ 1520-0469(2001)058<3243:TWOIAT>2.0.CO;2 58, 3243 (2001).
20. J. Pedlosky, Geophysical Fluid Dynamics, 2nd ed. (Springer-Verlag, New York, 1987), Chap. 7.3, p. 499.
21. D. S. Schecter, "The spontaneous imbalance of a solitary vortex at high Rossby number," J. Atmos. Sci. JAHSAK0022-492810.1175/ 2007JAS2490.1 65, 2498 (2008).
22. M. T. Montgomery and L. J. Shapiro, "Generalized Charney-Stern and Fjortoft theorems for rapidly rotating vortices," J. Atmos. Sci. JAHSAK0022-492810.1175/1520-0469(1995)052<1829:GCAFTF>2.0.CO;2 52, 1829 (1995).
23. S. Ren, "Further results on the stability of rapidly rotating vortices in the asymmetric balance formulation," J. Atmos. Sci. JAHSAK0022-492810.1175/1520-0469(1999)056<0475:FROTSO>2.0.CO;2 56, 475 (1999).
24. J. R. Holton, An Introduction to Dynamic Meteorology, 3rd ed. (Academic, New York, 1992).
25. R. H. Levy, "Dicotron instability in a cylindrical geometry," Phys. Fluids PFLDAS0031-917110.1063/1.1761400 8, 1288 (1965).
26. W. H. Schubert, M. T. Montgomery, R. K. Taft, T. A. Guinn, S. R. Fulton, J. P. Kossin, and J. P. Edwards, "Polygonal eyewalls, asymmetric eye contraction, and potential vorticity mixing in hurricanes," J. Atmos. Sci. JAHSAK0022-492810.1175/ 1520-0469(1999)056<1197:PEAECA>2.0.CO;2 56, 1197 (1999).
27. L. N. Howard, "Note on a paper of John Miles," J. Fluid Mech. JFLSA70022-112010.1017/S0022112061000317 10, 509 (1961).
28. D. S. Nolan and L. D. Grasso, "Nonhydrostatic, three-dimensional perturbations to balanced, hurricane-like vortices, Part II: Symmetric response and nonlinear simulations," J. Atmos. Sci. JAHSAK0022-492810.1175/1520-0469(2003)060<2717:NTPTBH>2.0.CO;2 60, 2717 (2003).
29. D. S. Nolan, Y. Moon, and D. P. Stern, "Tropical cyclone intensification from asymmetric convection: Energetics and efficiency," J. Atmos. Sci. JAHSAK0022-492810.1175/JAS3988.1 64, 3377 (2007).
30. R. Laprise, "The Euler equations of motion with hydrostatic pressure as an independent variable," Mon. Weather Rev. MWREAB0027-064410.1175/1520-0493(1992)120<0197:TEEOMW>2.0.CO;2 120, 197 (1992).
31. L. J. Wicker and W. C. Skamarock, "Time-splitting methods for elastic models using forward time schemes," Mon. Weather Rev. MWREAB0027-064410.1175/1520-0493(2002)130<2088:TSMFEM>2.0.CO;2 130, 2088 (2002).
32. W. C. Skamarock, J. B. Kemp, J. Dudhia, D. O. Gill, D. M. Barker, W. Wang, and J. G. Powers, "A description of the advanced research WRF version 2," NCAR Technical Note No. NCAR/TN-468+STR, 2005.
33. D. S. Nolan and M. T. Montgomery, "The algebraic growth of wavenumber one disturbances in hurricane-like vortices," J. Atmos. Sci. JAHSAK0022-492810.1175/ 1520-0469(2000)057<3514:TAGOWO>2.0.CO;2 57, 3514 (2000).
34. B. M. Lewis and H. F. Hawkins, "Polygonal eyewalls and rainbands in hurricanes," Bull. Am. Meteorol. Soc. BAMIAT0003-000710.1175/ 1520-0477(1982)063<1294:PEWARI>2.0.CO;2 63, 1294 (1982).
35. T. Muramatsu, "The structure of a polygonal eye of a typhoon," J. Meteorol. Soc. Jpn. JMSJAU0026-1165 64, 913 (1986).
36. J. P. Kossin and W. H. Schubert, "Mesovortices, polygonal flow patterns, and rapid pressure falls in hurricane-like vortices," J. Atmos. Sci. JAHSAK0022-492810.1175/ 1520-0469(2001)058<2196:MPFPAR>2.0.CO;2 58, 2196 (2001).