Geophysical and astrophysical fluid dynamics beyond the traditional approximation

Reviews of Geophysics

Volumn 46, Issue 2, 2008, Pages

  Gerkema, T ^a   Zimmerman, J T F ^a,b   Maas, L R M ^a,b   Van Haren, H ^a  

^a ROYAL NETHERLANDS INSTITUTE FOR SEA RESEARCH   (Netherlands)

^b UTRECHT UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ASTROPHYSICS; CORIOLIS FORCE; EKMAN TRANSPORT; FLUID DYNAMICS; GEOPHYSICS; MESOSCALE MOTION; THERMAL CONVECTION;

EID: 66149174343     PISSN: 87551209     EISSN: None     Source Type: Journal    
DOI: 10.1029/2006RG000220     Document Type: Review

References (152)

1. Backus, G. E. (1962), The effect of the Earth's rotation on the propagation of ocean waves over long distances, Deep Sea Res. Oceanogr. Abstr., 9, 185-197.
2. Badulin, S. I., V. M. Vasilenko, and M. I. Yaremchuk (1991), Interpretation of quasi-inertial motions using Megapoligon data as an example, Izv. Atmos. Ocean. Phys., 27(6), 446-452.
3. Baines, P. G., and J. W. Miles (2000), On topographic coupling of surface and internal tides, Deep Sea Res., Part I, 47,2395-2403.
4. Beckmann, A., and S. Diebels (1994), Effects of the horizontal component of the Earth's rotation on wave-propagation on an f-plane, Geophys. Astrophys. Fluid Dyn., 76, 95-119. (Pubitemid 26463331)
5. Bjerknes, V, J. Bjerknes, H. Solberg, and T. Bergeron (1933), Physikalische Hydrodynamic, 797 pp., Springer, Berlin.
6. Bourlès, B., et al. (2003), The deep currents in the eastern equatorial Atlantic Ocean, Geophys. Res. Lett., 30(5), 8002, doi:10.1029/2002GL015095. (Pubitemid 36947055)
7. Brekhovskikh, L. M., and V. Goncharov (1994), Mechanics of Continua and Wave Dynamics, 342 pp., Springer, Berlin.
8. Bretherton, F. P. (1964), Low frequency oscillations trapped near the equator, Tellus, 16, 181-185.
9. Brillouin, M., and J. Coulomb (1933), Oscillations d'un liquide pesant dans un bassin cylindrique en rotation, 70 pp., Gauthier-Villars, Paris.
10. Burstyn, H. L. (1966), Early explanations of the role of the Earth's rotation in the circulation of the atmosphere and the ocean, Isis, 57(2), 167-187.
11. Busse, R H. (1976), A simple model of conyection in the Jovian atmosphere, Icarus, 29, 255-260. (Pubitemid 8019968)
12. Busse, F. H. (1994), Convection driven zonal flows and vortices in the major planets, Chaos, 4, 123-134.
13. Busse, F. H. (2002), Convective flows in rapidly rotating spheres and their dynamo action, Phys. Fluids, 14, 1301-1314. (Pubitemid 34439814)
14. Chandrasekhar, S. (1961), Hydrodynamic and Hydromagnetic Stability, 652 pp., Oxford Univ. Press, Oxford, UK.
15. Coleman, G. N., J. H. Ferziger, and P. R. Spalart (1990), A numerical study of the turbulent Ekman layer, J. Fluid Mech., 213, 313-348. (Pubitemid 20685095)
16. Colin de Verdière, A. (2002), Un fluide lent entre deux sphères en rotation rapide: Les théories de la circulation océanique, Ann. Math. Blaise Pascal, 9(2), 245-268.
17. Colin de Verdière, A., and R. Schopp (1994), Flows in a rotating spherical shell: The equatorial case, J. Fluid Mech., 276, 233-260.
18. Coriolis, G. (1835), Mémoire sur les équations du mouvement relatif des systèmes de corps, J. Éc. Polytech. Paris, XXIV(XV), 142-154.
19. Dellar, P. J., and R. Salmon (2005), Shallow water equations with a complete Coriolis force and topography, Phys.. Fluids, 17(10), 106601, doi:10.1063/1.2116747.
20. Denbo, D. W., and E. D. Skyllingstad (1996), An ocean large-eddy simulation model with application to deep convection in the Labrador Sea, J. Geophys. Res., 101(C1), 1095-1110. (Pubitemid 126678269)
21. Dengler, M., and D. Quadfasel (2002), Equatorial deep jets and abyssal mixing in the Indian Ocean, J. Phys. Oceanogr., 32, 1165-1180. (Pubitemid 34526807)
22. Dintrans, B., and M. Rieutord (2000), Oscillations of a rotating star: A non-perturbative theory, Astron. Astrophys., 354, 86-98.
23. Dintrans, B., M. Rieutord, and L. Valdettaro (1999), Gravitoinertial waves in a rotating stratified sphere or spherical shell, J. Fluid Mech., 398, 271-297. (Pubitemid 129657156)
24. d'Orgeville, M., B. L. Hua, and H. Sasaki (2007), Equatorial deep jets triggered by a large vertical scale variability within the western boundary layer, J. Mar. Res., 65, 1-25.
25. Dubois, E. (1885), Résumé analytique de la théorie des marées telle qu'elle est établie dans la Mécanique Céleste de Laplace, Rev. Marit. Colon., 85, 116-154, 419-460, 687-710.
26. Durran, D. R., and C. Bretherton (2004), Comments on "The roles of the horizontal component of the Earth's angular velocity in nonhydrostatic linear models," J. Atmos. Sci., 61, 1982-1986.
27. Eckart, C. (1960), Hydrodynamics of Oceans and Atmospheres, 290 pp., Pergamon, New York.
28. Ekman, V. W. (1905), On the influence of the Earth's rotation on ocean currents, Ark. Mat. Astron. Fys., 2(11), 1-52.
29. Ekman, V. W. (1932), Studien zur Dynamik der Meeresströmungen, Gerlands Beitr. Geophys., 36, 385-438.
30. Emanuel, K. A. (1979), Inertial instability and mesoscale convective systems. part I: Linear theory of inertial instability in rotating viscous fluids, J. Atmos. Sci., 36, 2425-2449.
31. Etling, D. (1971), Einfluβ der thermischen Schichtung auf der Stabilität einer Ekman'schen Grenzschichtströmung, Beitr. Phys. Atmos., 44, 168-186.
32. Firing, E. (1987), Deep zonal currents in the central equatorial Pacific, J. Mar. Res., 45, 791-812. (Pubitemid 18547334)
33. Fotheringham, P., and R. Hollerbach (1998), Inertial oscillations in a spherical shell, Geophys. Astrophys. Fluid Dyn., 89, 23-43. (Pubitemid 128650741)
34. Friedlander, S., and W. L. Siegmann (1982), Internal waves in a rotating stratified fluid in an arbitrary gravitational field, Geophys. Astrophys. Fluid Dyn., 19, 267-291.
35. Fritts, D. C, and M. J. Alexander (2003), Gravity wave dynamics and effects in the middle atmosphere, Rev. Geophys., 41(1), 1003, doi:10.1029/2001RG000106. (Pubitemid 36971555)
36. Fruman, M. D. (2005), Equatorial symmetric instability, 178 pp., Ph.D. thesis, Univ. of Toronto, Toronto, Ont., Canada.
37. Galperin, B., A. Rosati, L. H. Kantha, and G. L. Mellor (1989), Modeling rotating stratified turbulent flows with application to oceanic mixed layers, J. Phys. Oceanogr., 19, 901-916.
38. Garrett, C., and L. St. Laurent (2002), Aspects of deep ocean mixing, J. Oceanogr., 58, 11-24. (Pubitemid 34609347)
39. Garwood, R. W. (1991), Enhancements to deep turbulent entrainment, in Deep Convection and Deep Water Formation in the Oceans, edited by P. C. Chu and J. C. Gascard, pp. 197-213, Elsevier, Amsterdam.
40. Garwood, R. W., P. C. Gallacher, and P. Muller (1985a), Wind direction and equilibrium mixed layer depth: General theory, J. Phys. Oceanogr., 15, 1325-1331.
41. Garwood, R. W., P. Muller, and P. C. Gallacher (1985b), Wind direction and equilibrium mixed layer depth in the tropical Pacific Ocean, J. Phys. Oceanogr., 15, 1332-1338.
42. Gates, W. L. (2004), Derivation of the equations of atmospheric motions in oblate spherical coordinates, J. Atmos. Sci., 61, 2478-2487. (Pubitemid 39520329)
43. Gerkema, T. (2006), Internal-wave reflection from uniform slopes: Higher harmonics and Coriolis effects, Nonlinear Processes Geophys., 13, 265-273. (Pubitemid 44048090)
44. Gerkema, T, and V. I. Shrira (2005a), Near-inertial waves on the "nontraditional" β plane, J. Geophys. Res., 110, C01003, doi:10.1029/2004JC002519.
45. Gerkema, T, and V. I. Shrira (2005b), Near-inertial waves in the ocean: Beyond the 'traditional approximation,' J. Fluid Mech., 529, 195-219.
46. Gerkema, T, and V. I. Shrira (2006), Non-traditional reflection of internal waves from a sloping bottom, and the likelihood of critical reflection, Geophys. Res. Lett., 33, L06611, doi:10.1029/2005GL025627.
47. Gerkema, T, F. P. A. Lam, and L. R. M. Maas (2004), Internal tides in the Bay of Biscay: Conversion rates and seasonal effects, Deep Sea Res., Part II, 51, 2995-3008. (Pubitemid 39588365)
48. Grimshaw, R. (1975a), Internal gravity waves: Critical layer absorption in a rotating fluid, J. Fluid Mech., 70, 287-304.
49. Grimshaw, R. H. J. (1975b), A note on the β-plane approximation, Tellus, 27,351-356.
50. Guillot, T. (2005), The interiors of giant planets: Models and outstanding questions, Annu. Rev. Earth Planet. Sci., 33, 493-530. (Pubitemid 40849794)
51. Haeusser, T. M., and S. Leibovich (1997), Amplitude and mean drift equations for the oceanic Ekman layer, Phys. Rev. Lett., 79(2), 329-332. (Pubitemid 127647511)
52. Haeusser, T. M., and S. Leibovich (2003), Pattern formation in the marginally unstable Ekman layer, J. Fluid Mech., 479, 125-144. (Pubitemid 36440316)
53. Harlander, U., and L. R. M. Maas (2006), Characteristics and energy rays of equatorially trapped, zonally symmetric internal waves, Meteorol. Z., 15(4), 439-450. (Pubitemid 44304745)
54. Heimpel, M., and J. Aurnou (2007), Turbulent convection in rapidly rotating spherical shells: A model for equatorial and high latitude jets on Jupiter and Saturn, Icarus, 187, 540-557.
55. Heimpel, M., J. Aurnou, and J. Wicht (2005), Simulation of equatorial and high-latitude jets on Jupiter in a deep convection model, Nature, 438, 193-196. (Pubitemid 41599866)
56. Hendershott, M. C. (1981), Long waves and ocean tides, in Evolution of Physical Oceanography, edited by B. A. Warren and C. Wunsch, pp. 292-341, MIT Press, Cambridge, Mass.
57. Hollerbach, R., and R. R. Kerswell (1995), Oscillatory internal shear layers in rotating and processing flows, J. Fluid Mech., 298, 327-339. (Pubitemid 26463376)
58. Hua, B. L., D. W. Moore, and S. le Gentil (1997), Inertial nonlinear equilibration of equatorial flows, J. Fluid Mech, 331,345-311.
59. Hughes, B. (1964), Effect of rotation on internal gravity waves, Nature, 201, 798-801.
60. Huthnance, J. M. (1978), Inertial waves and an initial-value problem for a thin spherical rotating fluid shell, J. Fluid Mech, 86, 273-288.
61. Hylleraas, E. A. (1939), Über die Schwingungen eines stabil geschichteten, durch Meridiane begrenzten Meeres, Astrophys. Nor., III(6), 139-164.
62. Ingersoll, A. P., and D. Pollard (1982), Motion in the interiors and atmospheres of Jupiter and Saturn-Scale analysis, anelastic equations, barotropic stability-criterion, Icarus, 52, 62-80.
63. Ioannou, P. J., and R. S. Lindzen (1993a), Gravitational tides in the outer planets. I. Implications of classical tidal theory, Astrophys. J., 406, 252-265.
64. Ioannou, P. J., and R. S. Lindzen (1993b), Gravitational tides in the outer planets. II. Interior calculations and estimation of the tidal dissipation factor, Astrophys. J, 406, 266-278.
65. Israeli, M. (1972), On trapped oscillations of rotating fluids in spherical shells, Stud. Appl. Math., L1, 219-237.
66. Joyce, T. M., R. Lukas, and E. Firing (1988), On the hydrostatic balance and equatorial geostrophy, Deep Sea Res., Part A, 35, 1255-1257.
67. Kasahara, A. (2003a), The roles of the horizontal component of the Earth's angular velocity in nonhydrostatic linear models, J. Atmos. Sci., 60, 1085-1095. (Pubitemid 38362744)
68. Kasahara, A. (2003b), On the nonhydrostatic atmospheric models with inclusion of the horizontal component of the Earth's angular velocity, J. Meteorol. Soc. Jpn., 81(5), 935-950. (Pubitemid 38127171)
69. Kasahara, A. (2004), Reply, J. Atmos. Sci, 61, 1987-1991.
70. Kasahara, A., and J. M. Gary (2006), Normal modes of an incompressible and stratified fluid model including the vertical and horizontal components of Coriolis force, Tellus, Ser. A, 58, 368-384.
71. Kerswell, R. R. (1995), On the internal shear layers spawned by the critical regions in oscillatory Ekman boundary layers, J. Fluid Mech, 298, 311-325. (Pubitemid 26463375)
72. Laplace, P.-S. (1798), Traité de mécanique céleste, vol.1, 368 pp., Crapelet, Paris.
73. Laplace, P.-S. (1878), Oeuvres complètes de Laplace, vol.1, 395 pp., Gauthier-Villars, Paris.
74. Lavrovskii, E. K., I. P. Semenova, L. N. Slezkin, and V. V. Fominykh (2000), Mediterranean lenses as liquid gyroscopes in the ocean, Dokl Phys., 45(11), 606-609. (Pubitemid 33211985)
75. LeBlond, P. H., and L. A. Mysak (1978), Waves in the Ocean, 602 pp., Elsevier, Amsterdam.
76. Leibovich, S., and S. K. Lele (1985), The influence of the horizontal component of Earth's angular velocity on the instability of the Ekman layer, J. Fluid Mech, 150, 41-87. (Pubitemid 15479950)
77. Longuet-Higgins, M. S. (1964), Planetary waves on a rotating sphere, Proc. R. Soc. London, Ser. A, 279, 446-473.
78. Lukas, R., and E. Lindstrom (1991), The mixed layer of the western equatorial Pacific Ocean, J. Geophys. Res., 96, 3343-3357.
79. Luyten, J. R., and J. C. Swallow (1976), Equatorial undercurrents, Deep Sea Res. Oceanogr. Abstr., 23, 999-1001.
80. Maas, L. R. M. (2001), Wave focusing and ensuing mean flow due to symmetry breaking in rotating fluids, J. Fluid Mech, 437, 13-28. (Pubitemid 32596294)
81. Maas, L. R. M. (2005), Wave attractors: Linear yet nonlinear, Int. J. Bifurcation Chaos, 15(9), 2757-2782. (Pubitemid 41545732)
82. Maas, L. R. M., and U. Harlander (2007), Equatorial wave attractors and inertial oscillations, J. Fluid Mech, 570, 47-67. (Pubitemid 46040007)
83. Maas, L. R. M., and F. P. A. Lam (1995), Geometric focusing of internal waves, J. Fluid Mech, 300, 1-41. (Pubitemid 26463837)
84. Maniopoulou, A., and N. Andersson (2004), The traditional approximation in general relativity, Mon. Not. R. Astron. Soc., 351, 1349-1358. (Pubitemid 38919833)
85. Marshall, J., and F. Schott (1999), Open-ocean convection: Observations, theory, and models, Rev. Geophys., 37, 1-64. (Pubitemid 29280563)
86. Marshall, J., C. Hill, L. Perelman, and A. Adcroft (1997), Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling, J. Geophys. Res., 102(C3), 5733-5752. (Pubitemid 127684302)
87. McWilliams, J. C, and E. Huckle (2006), Ekman layer rectification, J. Phys. Oceanogr., 36, 1646-1659. (Pubitemid 44550286)
88. Miles, J. W. (1974), On Laplace's tidal equations, J. Fluid Mech, 66,241-260.
89. Miropol'sky, Y. Z. (2001), Dynamics of Internal Gravity Waves in the Ocean, 406 pp., Kluwer, Dordrecht.
90. Müller, D. (1992), Angular momentum budget of shallow waters on a rotating sphere, Phys. Rev. A, 45, 5545-5555.
91. Müller, R. (1989), A note on the relation between the "traditional approximation" and the metric of the primitive equations, Tellus, Ser. A, 41, 175-178.
92. Needler, G. T, and P. H. LeBlond (1973), On the influence of the horizontal component of the Earth's rotation on long period waves, Geophys. Fluid Dyn., 5, 23-46.
93. Ogilvie, G. I., and D. N. C. Lin (2004), Tidal dissipation in rotating giant planets, Astrophys. J., 610, 477-509. (Pubitemid 39196103)
94. Phillips, N. A. (1966), The equations of motion for a shallow rotating atmosphere and the "traditional approximation," J. Atmos. Sci., 23, 626-628.
95. Phillips, N. A. (1968), Reply, J Atmos. Sci., 25, 1155-1157.
96. Phillips, N. A. (1970), Reply, J. Atmos. Sci., 27, 506.
97. Phillips, O. M. (1966), The Dynamics of the Upper Ocean, 261 pp., Cambridge Univ. Press, Cambridge, UK.
98. Pickart, R. S., D. J. Torres, and R. A. Clarke (2002), Hydrography of the Labrador Sea during active convection, J. Phys. Oceanogr., 32, 428-457.
99. Pingree, R. D., and A. L. New (1991), Abyssal penetration and bottom reflection of internal tidal energy into the Bay of Biscay, J. Phys. Oceanogr., 21, 28-39.
100. Price, J. F., and M. A. Sundermeyer (1999), Stratified Ekman layers, J. Geophys. Res., 104(C9), 20,467-520,494.
101. Proudman, J. (1948), The applicability of Laplace's differential equations of the tides, Int. Hydrogr. Rev., 25(2), 122-129.
102. Raymond, W. H. (2000), Equatorial meridional flows: Rotationally induced circulations, Pure Appl. Geophys., 157, 1767-1779.
103. Raymond, W. H. (2001), Kelvin waves: Rotationally induced circulations, Dyn. Atmos. Oceans, 34, 23-43. (Pubitemid 32646565)
104. Rhines, P. B. (1975), Waves and turbulence on a beta-plane, J. Fluid Mech, 69, 417-443.
105. Richards, K., and H. Banks (2002), Characteristics of interleaving in the western equatorial Pacific, J. Geophys. Res., 107(C12), 3231, doi: 10.1029/2001JC000971. (Pubitemid 36610927)
106. Richardson, P. L., and D. M. Fratantoni (1999), Float trajectories in the deep western boundary current and deep equatorial jets of the tropical Atlantic, Deep Sea Res., Part II, 46, 305-333. (Pubitemid 29163250)
107. Riemenschneider, U., and V. A. Sheremet (2006), Ball release experiments on a centrifuge: Misalignment between the buoyancy force and the axis of rotation, J. Fluid Mech, 564, 435-454. (Pubitemid 44420007)
108. Rieutord, M., and L. Valdettaro (1997), Inertial waves in a rotating spherical shell, J. Fluid Mech, 341, 77-99. (Pubitemid 27405441)
109. Rieutord, M., B. Georgeot, and L. Valdettaro (2001), Inertial waves in a rotating spherical shell: Attractors and asymptotic spectrum, J. Fluid Mech, 435, 103-144. (Pubitemid 32526777)
110. Saint-Guily, B. (1970), On internal waves. Effects of the horizontal component of the Earth's rotation and of a uniform current, Dtsck Hydrogr. Z, 25(1), 16-23.
111. Savonije, G. J., and J. C. B. Papaloizou (1997), Non-adiabatic tidal forcing of a massive, uniformly rotating star-II. The lowfrequency, inertial regime, Mon. Not. R. Astron. Soc., 291, 633-650. (Pubitemid 127687454)
112. Savonije, G. J., J. C. B. Papaloizou, and F. Alberts (1995), Nonadiabatic tidal forcing of a massive, uniformly rotating star, Mon. Not. R. Astron. Soc., 277, 471-496.
113. Schopp, R., and A. Colin de Verdière (1997), Taylor columns between concentric spheres, Geophys. Astrophys. Fluid Dyn., 86, 43-73. (Pubitemid 127655077)
114. Semenova, I. P., and L. N. Slezkin (2003), Dynamically equilibrium shape of intrusive vortex formations in the ocean, Fluid Dyn., 38(5), 663-669. (Pubitemid 38149674)
115. Send, U., C. Eden, and F. Schott (2002), Atlantic equatorial deep jets: Space-time structure and cross-equatorial fluxes, J. Phys. Oceanogr., 32, 891-902. (Pubitemid 34476032)
116. Sheremet, V. A. (2004), Laboratory experiments with tilted convective plumes on a centrifuge: A finite angle between the buoyancy force and the axis of rotation, J. Fluid Mech, 506, 217-244. (Pubitemid 38673023)
117. Solberg, H. (1928), Integrationen der atmosphärischen Störungsgleichungen. Erster Teil: Wellenbewegungen in rotierenden, inkompressiblen Flüssigkeitsschichten, Geofys. Publ., V(9), 1120.
118. Solberg, H. (1936), Über die freien Schwingungen einer homogenen Flüssigkeitsschicht auf der rotierenden Erde I, Astrophys. Nor., 1(7), 237-340.
119. Stem, M. E. (1963), Trapping of low frequency oscillations in an equatorial 'boundary layer,' Tellus, 15, 246-250.
120. Stewartson, K. (1971), On trapped oscillations of a rotating fluid in a thin spherical shell, Tellus, 23, 506-510.
121. Stewartson, K. (1972a), On trapped oscillations of a rotating fluid in a thin spherical shell II, Tellus, 24, 283-287.
122. Stewartson, K. (1972b), On trapped oscillations in a slightly viscous rotating fluid, J. Fluid Mech., 54, 749-761.
123. Stewartson, K., and J. A. Rickard (1969), Pathological oscillations of a rotating fluid, J. Fluid Mech., 5, 577-592.
124. Straneo, F, M. Kawase, and S. C. Riser (2002), Idealized models of slantwise convection in a baroclinic flow, J. Phys. Oceanogr., 32, 558-572.
125. Taylor, G. I. (1923), Experiments on the motion of solid bodies in rotating fluids, Proc. R. Soc. London, Ser. A, 104, 213-218.
126. Thuburn, J., N. Wood, and A. Staniforth (2002a), Normal modes of deep atmospheres. I: Spherical geometry, Q. J. R. Meteorol. Soc., 128, 1771-1792.
127. Thuburn, J., N. Wood, and A. Staniforth (2002b), Normal modes of deep atmospheres. II: f-F-plane geometry, Q. J. R. Meteorol. Soc., 128, 1793-1806.
128. Tolstoy, I. (1963), The theory of waves in stratified fluids including the effects of gravity and rotation, Rev. Mod. Phys., 35(1), 207230.
129. Tritton, D. J. (1978), Turbulence in rotating fluids, in Rotating Fluids in Geophysics, edited by P. H. Roberts and A. M. Soward, pp. 105-138, Academic, London.
130. van Aken, H. M., L. R. M. Maas, and H. van Haren (2005), Observations of inertial wave events near the continental slope off Goban Spur, J. Phys. Oceanogr., 35, 1329-1340. (Pubitemid 41373001)
131. van der Toorn, R., and J. T. F. Zimmerman (2008), On the spherical approximation of the geopotential in Geophysical Fluid Dynamics and the use of a spherical coordinate system, Geophys. Astrophys. Fluid Dyn, in press.
132. van Haren, H. (2005), Sharp near-equatorial transitions in inertial motions and deep-ocean step-formation, Geophys. Res. Lett., 32, L01605, doi: 10.1029/2004GL021630.
133. van Haren, H. (2006), Asymmetric vertical internal wave propagation, Geophys. Res. Lett., 33, L06618, doi:10.1029/ 2005GL025499.
134. van Haren, H., and C. Millot (2004), Rectilinear and circular inertial motions in the western Mediterranean Sea, Deep Sea Res., Part I, 51, 1441-1455.
135. Van Haren, H., and C. Millot (2005), Gyroscopic waves in the Mediterranean Sea, Geophys. Res. Lett., 32, L24614, doi: 10.1029/2005GL023915. (Pubitemid 43239968)
136. van Haren, H., L. R. M. Maas, and H. van Aken (2002), On the nature of internal wave spectra near a continental slope, Geophys. Res. Lett., 29(12), 1615, doi:10.1029/2001GL014341. (Pubitemid 35376475)
137. Vasavada, A. R., and A. P. Showman (2005), Jovian atmospheric dynamics: An update after Galileo and Cassini, Rep. Prog. Phys., 68, 1935-1996. (Pubitemid 41024594)
138. Verkley, W. T. M. (1990), On the beta plane approximation, J. Atmos. Sci., 47, 2453-2460.
139. Veronis, G. (1959), Cellular convection with finite amplitude in a rotating fluid, J. Fluid Mech., 5, 401-435.
140. Veronis, G. (1963a), On the approximations involved in transforming the equations of motion from a spherical surface to the βplane. II. Barorropic systems, J. Mar. Res., 21, 110-124.
141. Veronis, G. (1963b), On the approximations involved in transforming the equations of motion from a spherical surface to the βplane. II. Baroclinic systems, J. Mar. Res., 21(3), 199-204.
142. Veronis, G. (1968), Comments on Phillips' proposed simplification of the equations of motion for a shallow rotating atmosphere, J. Atmos. Sci., 25, 1154-1155.
143. Walter, M., C. Mertens, and M. Rhein (2005), Mixing estimates from a large-scale hydrographie survey in the North Atlantic, Geophys. Res. Lett., 32, L13605, doi:10.1029/2005GL022471.
144. Walton, I. C. (1975), On waves in a thin rotating spherical shell of slightly viscous fluid, Mathematika, 22, 46-59.
145. Wangsness, R. K. (1970), Comments on "The equations of motion for a shallow rotating atmosphere and the 'traditional approximation' ," J. Atmos. Sci., 27, 504-506.
146. White, A. A., and R. A. Bromley (1995), Dynamically consistent, quasi-hydrostatic equations for global models with a complete representation of the Coriolis force, Q. J. R. Meteorol. Soc., 121, 399-418.
147. White, A. A., B. J. Hoskins, I. Roulstone, and A. Staniforth (2005), Consistent approximate models of the global atmosphere: Shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic, Q. J. R. Meteorol. Soc., 131, 2081-2107. (Pubitemid 41568776)
148. Wippermann, F. (1969), The orientation of vortices due to instability of the Ekman-boundary layer, Beitr. Phys. Atmos., 42, 225244.
149. Wirth, A., and B. Barnier (2006), Tilted convective plumes in numerical experiments, Ocean Modell, 12, 101-111. (Pubitemid 41799922)
150. Wirth, A., and B. Barnier (2008), Mean circulation and structures of tilted ocean deep convection, J. Phys. Oceanogr., 38, 803-816.
151. Yano, J., O. Talagrand, and P. Drossart (2005), Deep two-dimensional turbulence: An idealized model for atmospheric jets of the giant outer planets, Geophys. Astrophys. Fluid Dyn., 99, 137-150. (Pubitemid 40659702)
152. Zikanov, 0., D. N. Slinn, and M. R. Dhanak (2003), Large-eddy simulations of the wind-induced turbulent Ekman layer, J. Fluid Mech., 495, 343-368.