A numerical investigation of the barotropic instability on the equatorial β-plane

Theoretical and Computational Fluid Dynamics

Volumn 27, Issue 3-4, 2013, Pages 491-512

  Kacimi, Abderrahim ^a   Khouider, Boualem ^b  

^a UNIVERSITY OF SCIENCES AND TECHNOLOGY HOUARI BOUMEDIENE   (Algeria)

^b UNIVERSITY OF VICTORIA   (Canada)

Author keywords

Arakawa Jacobian; Atmospheric circulation; Barotropic instability; Equatorial Rossby waves; Essentially non oscillatory schemes; Shear flow; Stream function; Vorticity

Indexed keywords

ATMOSPHERIC CIRCULATION; BAROTROPIC; EQUATORIAL ROSSBY WAVES; ESSENTIALLY NON-OSCILLATORY SCHEMES; JACOBIANS; STREAMFUNCTIONS;

ALGORITHMS; CLIMATOLOGY; COMPUTER SIMULATION; OCEAN CURRENTS; STABILITY; VORTICITY;

SHEAR FLOW;

ALGORITHM; ATMOSPHERIC CIRCULATION; BAROTROPIC INSTABILITY; EASTERLY WAVE; EQUATORIAL DYNAMICS; FINITE DIFFERENCE METHOD; FLOW STABILITY; MONSOON; NUMERICAL MODEL; ROSSBY WAVE; SHEAR FLOW; VORTEX; VORTICITY;

XENOX;

EID: 84878280806     PISSN: 09354964     EISSN: 14322250     Source Type: Journal    
DOI: 10.1007/s00162-012-0260-3     Document Type: Conference Paper

References (40)

1. Arakawa A.: Computational design for long-term numerical integration of the equations of fluid motion, two-dimensional Incompressible flow. J. Comput. Phys. 1, 119-143 (1966)
2. Arakawa A.; Lamb V.: A potential enstrophy and energy conserving scheme for the shallow water equations. MWR 109, 18-136 (1981)
3. Abba A.; Bonaventura L.: A vorticity preserving finite difference discretization for the incompressible Navier-stokes equations. Int. J. Num. Methods Fluids 56, 1101-1106 (2008)
4. Benoit Cushman R.; Jean-Marie B.: Introduction to Geophysical Fluid Dynamics: Physical and Numerical Aspects. Academic Press, Waltham, MA (2011)
5. Bonaventura L.; Ringler T.: Analysis of discrete shallow water models on geodesic Delaunay grids with C-type staggering. MWR 133, 2351-2373 (2005)
6. Burpee R.W.: The origin and structure of easterly waves in the lower troposphere of North Africa. J. Atmos. Sci. 29, 77-90 (1972)
7. Dunn G.E.; Miller B.I.: Atlantic Hurricanes, pp. 377. Louisiana State University Press, Baton Rouge, Louisiana (1960)
8. Ferguson J.; Khouider B.; Namazi M.: Two-way interactions between equatorially-trapped waves and the barotropic flow. Chin. Ann. Math. Ser. B 30, 2943-2975 (2009)
9. Fjortof R.: Application of integral theorems in deriving creteria of stability for laminar flow and the baroclinic circular vortex. Geofys. Publ. 17, 52 (1950)
10. Gill A.: Atmosphere-Ocean Dynamics. Academic Press, New York, NY (1982)
11. Howard L.N.; Drazin P.G.: On instability of parallel flow of inviscid fluid in rotating system with variable Coriolis parameter. J. Math. Phys. 43, 83-99 (1964)
12. Janjic Z.I.: Nonlinear advection schemes and energy cascade on semi-staggered grids. MWR 111, 1234-1245 (1984)
13. Kacimi, A.; Aliziane, T.; Khouider, B.: The Arakawa Jacobian method and a fourth-order essentially nonoscillatory scheme for the beta-plane barotropic equations. Int. J. Numer. Anal. Model. Submitted (2011)
14. Keshavamurty R.N.; Asnani G.C.; Pillai P.V.; Das S.K.: Some studies of the growth of monsoon disturbances. Proc. Indian Acad. Sci. E & P Sci. 87A(3), 61-75 (1978)
15. Khouider B.; Majda A.: A non-oscillatory balanced scheme for an idealized tropical climate model. Part I: Algorithm and validation. Theor. Comput. Fluid Dyn. 19, 1-24 (2005)
16. Khouider B.; Majda A.: A non-oscillatory balanced scheme for an idealized tropical climate model. Part II: Nonlinear coupling and moisture effects. Theor. Comput. Fluid Dyn. 19, 355-375 (2005)
17. Kuo H.L.: Dynamic instability of two-dimensional non divergent flow in a barotropic atmosphere. J. Meteor. 6, 105-122 (1949)
18. LeVeque R.J.: Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, Cambridge (2002)
19. Leveque R.L.: Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems. SIAM, Philadelphia, PA (2007)
20. Lindzen R.S.; Rosenthal A.J.: On the instability of Helmholtz velocity profiles in stably stratified fluids when a lower boundary is present. J. Geophys. Res. 81, 1561-1571 (1976)
21. Lindzen R.S.; Tung K.K.: Wave overreflection and shear instability. J. Atmos. Sci. 35, 1626-1632 (1978)
22. Majda A.; Biello J.: The nonlinear interaction of barotropic and equatorial baroclinic Rossby waves. J. Atmos. Sci. 60, 1809-1821 (2003)
23. Majda A.: Introduction to PDE and Waves for Atmosphere and Ocean. Courant Lecture Notes in Mathematic vol. 9. American Mathematical Society, Providence (2003)
24. Morton K.W.; Roe P.L.: Vorticity preserving Lax-Wendrof type schemes for the system wave equation. SIAM J. Sci. Comp. 23, 170-192 (2001)
25. Nielsen J.E.; Schoeberl M.R.: A numerical simulation of barotropic instability. Part II: Wave-wave interaction. J. Atmos. Sci. 41, 2869-2881 (1984)
26. Osher S.; Shu O.: High-order essentialy nonoscillatory schemes for Hamilton-Jacobi equations. SIAM J. Numer. Anal. 28, 907-922 (1991)
27. Pedlosky J.: The stability of currents in the atmosphere and the oceans. Part I. J. Atmos. Sci. 21, 201-219 (1964)
28. Perot B.: Conservation properties of unstructured staggered mesh schemes. JCP 159, 58-89 (2000)
29. Rayleigh L.: On the instability of the jets. Sci. Pap. 1, 361-371 (1879)
30. Rayleigh, L.: On the stability, or instability, of certain fluid motions. Proc. Lond. Math. Soc. 9, 57-70 (1880). (Reprinted in Scientific Papers by Lord Rayleigh, 3, 594-596 (1880))
31. Rayleigh, L.: On the stability or instability of certain fluid motions, II. Proc. Lond. Math. Soc. 1887 (also in Lord Rayleigh, Scientific Papers, 3, Cambridge, pp. 17-23 (1887))
32. Riehl, H.: Waves in the easterlies and the polar front in the tropics. Misc. Rep. No. 17, Department of Meteorology, University of Chicago, p. 79 (1945)
33. Ringler T.D.; Randall D.A.: A potential enstrophy and energy conserving numerical scheme for solution of the shallow-water equations a geodesic grid. MWR 130, 1397-1410 (2002)
34. Ringler T.D, Thuburn J.; Klemp J.B.; Skamarock W.C.: A unified approach to energy conservation and potential vorticity dynamics for arbitrarily- structured C-grids. JCP 229, 3065-3090 (2010)
35. Sadourny R.: The dynamics of finite difference models of the shallow water equations. JSA 32, 680-689 (1975)
36. Schoeberl M.R.; Lindzen R.S.: A numerical simulation of barotropic instability. Part I. Wave-mean flow interaction. J. Atmos. Sci. 41, 1368-1379 (1984)
37. Schoeberl M.R.; Nielsen J.E.: A numerical simulation of barotropic instability. Part III. Wave-wave interaction with dissipation. J. Atmos. Sci. 41, 2869-2881 (1984)
38. Solomon A.; Lindzen R.S.: The impact of resolution on a numerical simulation of barotropic instability. J. Atmos. Sci. 57, 3799-3816 (1999)
39. Talley L.D.: Radiating barotrpic instability. J. Phys. Oceanogr. 13, 972-987 (1983)
40. Talley, L.D.: Instabilities and radiation of thin, baroclinic jets. Thesis (PhD). Massachusetts Institute of Thechnology and the Woods Hole Oceanographic Institutions (1982)