Simplified two-layer models of precipitating atmosphere and their properties

Physics of Fluids

Volumn 23, Issue 4, 2011, Pages

  Lambaerts, J ^a   Lapeyre, G ^a   Zeitlin, V ^a   Bouchut, F ^b  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b UFR des Sciences et Technologie   (France)

Author keywords

[No Author keywords available]

Indexed keywords

PHYSICS;

CONSERVATION PRINCIPLES; CONVECTIVE DYNAMICS; FRONT PROPAGATION; PRECIPITATION FRONTS; QUASI-GEOSTROPHIC MODEL; SHALLOW WATER MODEL; VARIOUS BOUNDARY CONDITIONS; WATER VAPOR CONDENSATION;

FLUIDS;

EID: 79955456897     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3582356     Document Type: Article

References (33)

1. Bouchut F. Lambaerts J. Lapeyre G. Zeitlin V. Fronts and nonlinear waves in a simplified shallow-water model of the atmosphere with moisture and convection. Phys. Fluids 2009, 21:116604. PHFLE6, 1070-6631, 10.1063/1.3265970.
2. Gill A.E. Studies of moisture effetcs in simple atmospheric models: The stable case. Geophys. Astrophys. Fluid Dyn. 1982, 19:119. GAFDD3, 0309-1929, 10.1080/03091928208208950.
3. Frierson D.M. W. Majda A.J. Pauluis O.M. Large scale dynamics of precipitation fronts in the tropical atmosphere: A novel relaxation limit. Commun. Math. Sci. 2004, 2:591. ZZZZZZ, 1539-6746.
4. Stechmann S.N. Majda A.J. The structure of precipitation fronts for finite relaxation time. Theor. Comput. Fluid Dyn. 2006, 20:377. TCFDEP, 0935-4964, 10.1007/s00162-006-0014-1.
5. Pauluis O. Frierson D.M. W. Majda A.J. Precipitation fronts and the reflection and transmission of tropical disturbances. Q. J. R. Meteorol. Soc. 2008, 134:913. QJRMAM, 0035-9009, 10.1002/qj.250.
6. Lapeyre G. Held I.M. The role of moisture in the dynamics and energetics of turbulent baroclinic eddies. J. Atmos. Sci. 2004, 61:1693. JAHSAK, 0022-4928, 10.1175/1520-0469(2004)061<1693:TROMIT>2.0.CO;2.
7. Hoskins B.J. Bretherton F.P. Atmospheric frontogenesis models: Mathematical formulation and solution. J. Atmos. Sci. 1972, 29:11. JAHSAK, 0022-4928, 10.1175/1520-0469(1972)029<0011:AFMMFA>2.0.CO;2.
8. Emanuel K.A. Atmospheric Convection 1994, (Oxford University, New York, ), Chap. 4.
9. Zeitlin V. Introduction: Fundamentals of rotating shallow water model in the geo-physical fluid dynamics perspective. Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances 2007, V. Zeitlin, 10.1016/S1574-6909(06)02001-6, edited by (Elsevier, Amsterdam, ), Chap. 1.
10. Schecter D.A. Dunkerton T.J. Hurricane formation in diabatic Ekman turbulence. Q. J. R. Meteorol. Soc. 2009, 135:823. QJRMAM, 0035-9009, 10.1002/qj.405.
11. Betts A.K. Miller M.J. A new convective adjustement scheme. Part II: Single columns tests using GATE wave, BOMEX, ATEX and arctic air-mass data sets. Q. J. R. Meteorol. Soc. 1986, 112:693. QJRMAM, 0035-9009.
12. Holton J.R. An Introduction to Dynamic Meteorology 1972, (Academic, London, ).
13. Lambaerts J. Lapeyre G. Zeitlin V. Moist vs dry barotropic instability in a shallow water model of the atmosphere with moist convection. J. Atmos. Sci. 2011, 68. JAHSAK, 0022-4928, and.
14. Whitham G.B. Linear and Nonlinear Waves 1974, (Wiley, New York, ), Chap. 5.
15. Castro M.J. LeFloch P.G. Munoz-Ruiz M.L. Parés C. Why many theories of shock waves are necessary: Convergence error in formally path-consistent schemes. J. Comput. Phys. 2008, 227:8107. JCTPAH, 0021-9991, 10.1016/j.jcp.2008.05.012.
16. Wheeler M. Kiladis G.N. Convectively coupled equatorial waves: Analysis of clouds and temperature in the wavenumber-frequency domain. J. Atmos. Sci. 1999, 56:374. JAHSAK, 0022-4928, 10.1175/1520-0469(1999)056<0374:CCEWAO>2.0.CO;2.
17. Ovsyannikov L.V. Two-layer shallow water model. J. Appl. Mech. Tech. Phys. 1979, 20:127. JMPYAQ, 0021-8944, 10.1007/BF00910010.
18. Lax P.D. Hyperbolic systems of conservation laws and the mathematical theory of shock waves. 1973, SIAM Regional Conference Series in Applied Math.
19. Montgomery P.J. Moodie T.B. Analytical and numerical results for flow and shock formation in two-layer gravity currents. J. Aust. Math. Soc. Ser. B, Appl. Math. 1998, 40:35. JAMMDU, 0334-2700, 10.1017/S0334270000012352.
20. Yih C.S. Guha C.R. Hydraulic jump in a fluid system of two-layers. Tellus 1955, 7:358. TELLAL, 0040-2826, 10.1111/j.2153-3490.1955.tb01172.x.
21. Klemp J.B. Rotunno R. Skamarock W.C. On the propagation of internal bores. J. Fluid Mech. 1997, 331:81. JFLSA7, 0022-1120, 10.1017/S0022112096003710.
22. Holland D.M. Rosales D.S. R. R. Tabak E.G. Internal hydraulic jumps and mixing in two-layer flows. J. Fluid Mech. 2002, 470:63. JFLSA7, 0022-1120, 10.1017/S002211200200188X.
23. Jiang Q. Smith R.B. Ideal shocks in 2-layer flow. Tellus 2001, 53A:129. TELLAL, 0040-2826.
24. Sommer J.L. Medvedev S.B. Plougonven R. Zeitlin V. Singularity formation during relaxation of jets and fronts toward the state of geostrophic equilibrium. Commun. Nonlinear Sci. Numer. Simul. 2003, 8:415. ZZZZZZ, 1007-5704, 10.1016/S1007-5704(03)00050-9.
25. Zeitlin V. Reznik G.M. Jelloul M.B. Nonlinear theory of geostrophic adjustment. Part 2. Two-layer and continuously stratified primitive equations. J. Fluid Mech. 2003, 491:207. JFLSA7, 0022-1120, 10.1017/S0022112003005457.
26. Pedlosky J. Geophysical Fluid Dynamics 1979, (Springer-Verlag, New York, ).
27. Vallis G.K. Atmospheric and Oceanic Fluid Dynamics 2006, 10.1017/CBO9780511790447, (Cambridge University, Cambridge, ).
28. Bouchut F. Zeitlin V. A robust well-balanced scheme for multi-layer shallow water equations. Discrete Contin. Dyn. Syst., Ser. B 2010, 13:4. ZZZZZZ, 1531-3492.
29. Gula J. Zeitlin V. Instabilities of buoyancy-driven coastal currents and their nonlinear evolution in the two-layer rotating shallow-water model. Part 1. Passive lower layer. J. Fluid Mech. 2010, 659:69. JFLSA7, 0022-1120, 10.1017/S0022112010002405.
30. Castro M.J. Macías J. Parés C. A Q-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system. Math. Modell. Numer. Anal. 2001, 35:107. MMNAAB, 0764-583X, 10.1051/m2an:2001108.
31. Bouchut F. Efficient numerical finite volume schemes for shallow water models. Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances 2007, V. Zeitlin, 10.1016/S1574-6909(06)02004-1, in edited by (Elsevier, Amsterdam, ), Chap. 4.
32. Keulegan G.H. Wave motion. Engineer Hydraulics 1950, 711-768. H. Rouse, in edited by (Wiley, New York, ), pp.
33. Stechmann S.N. Majda A.J. Gravity waves in shear and implications for organized convection. J. Atmos. Sci. 2009, 66:2579. JAHSAK, 0022-4928, 10.1175/2009JAS2976.1.