Dynamical equations and turbulent closures in geophysics

Continuum Mechanics and Thermodynamics

Volumn 10, Issue 1, 1998, Pages 1-28

  Sander, Johannes ^a  

^a UNIVERSITY OF BERN   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032221665     PISSN: 09351175     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001610050078     Document Type: Review

References (136)

1. Ahmadi G, Abu-Zaid S (1991) A thermodynamically consistent stress transport model for rotating turbulent flows. Geophys. Astrophys. Fluid Dyn. 61: 109-125
2. Andreas EL (1987) Spectral measurements in a disturbed boundary layer over snow. J. Atmosph. Sci. 44: 1912-1939
3. Anis A, Moum JN (1995) Surface wave-turbulence interactions: Scaling ∈(z) near the sea surface. J. Phys. Oceanogr. 25: 2025-2045
4. Appenzeller C, Davies HC, Norton WA (1996) Fragmentation of stratospheric intrusions. J. Geophys. Res. 101: 1435-1456
5. Bardina J, Ferzinger JH, Rogallo RS (1985) Effect of rotation on isotropic turbulence: computation and modelling. J. Fluid Mech. 154: 321-336
6. Barnier B, Crépon M, Le Provost C (1989) Horizontal ocean circulation forced by deep-water formation. Part 2: A quasi-geostrophic simulation. J. Phys. Oceanogr. 19: 1794-1808
7. Bauer G, Diebels S, Hutter K (1994) Nonlinear internal waves in ideal rotating basins. Geophys. Astrophys. Fluid Dyn. 78: 21-46
8. Baumert H, Burchard H, Kleine E (1997) On second-moment closures for marine turbulence: A review. In: Marine Turbulence Revisited, edited by J. C. J. Nihoul Proc. 29th Int. Liège Coll. on Ocean Hydrodyn., Liège
9. Berezin YA, Hutter K, Zhukov VP (1991) Large-scale vortical structure, supported by small-scale turbulent motions. Helicity as a cause for inverse energy cascade. Continuum Mech. Thermodyn. 3: 127-146
10. Boubnov BM, Golitsyn GS (1986) Experimental study of convective structures in rotating fluids. J. Fluid Mech. 167: 503-531
11. Boubnov BM, Golitsyn GS (1990) Temperature and velocity field regimes of convective motions in a rotating plane fluid layer. J. Fluid Mech. 219: 215-239
12. Boussinesq J (1903) Théorie Analytique de la Chaleur. Volume 2 Gauthier-Villars Paris
13. Brandt P, Rubino A, Alpers W, Backhaus JO (1997) Internal waves in the Strait of Messina studied by a numerical model and synthetic aperture radar images from the ERS 1/2 satellites. J Phys. Oceanogr. 27: 648-663
14. Bryan K (1969) A numerical method for the study of the circulation of the world ocean. J. Comput. Phys. 4: 347-376
15. Businger JA (1981) Equations and concepts. In: Atmospheric turbulence and air pollution modelling, edited by F. T. M. Nieuwstadt and H. van Dop pp. 1-36, D. Reidel Dordrecht
16. Canuto VM, Minotti F (1993) Stratified turbulence in the atmosphere and oceans: A new subgrid model. J. Atmosph. Sci. 50: 1925-1935
17. Cauchy AL (1828) Exercices de Mathématiques. Volume 3 Chapter Sur l'équilibre et le mouvement d'un système de points materiels, Paris: Gauthier Villar
18. Champagne FH, Harris VG, Corrsin S (1970) Experiments on nearly homogeneous turbulent shear flow. J. Fluid Mech. 41: 81-139
19. Chandrasekhar S (1953) The instability of a layer of fluid heated below and subject to Coriolis force. Proc. Roy. Soc. A 217: 306-327
20. Chawla SS, Verma AR (1983) Free convection from a disk rotating in a vertical plane. J. Fluid Mech. 126: 307-313
21. Chen R, Fernando HJS, Boyer DL (1989) Formation of isolated vortices in a rotating convecting fluid. J. Geophys. Res. 94: 18445-18453
22. Chou PY (1945) On the velocity correlations and the solution of the equations of turbulent motions. Quart. Appl. Math. 3: 38-54
23. Craig PD, Banner ML (1994) Modeling wave-enhanced turbulence in the ocean surface layer. J. Phys. Oceanogr. 24: 2546-2559
24. Crow SC (1968) Viscoelastic properties of fine-grained incompressible turbulence. J. Fluid Mech. 33: 1-20
25. Curry JH, Herring JR, Loncaric J, Orszag ST (1984) Order and disorder in two-and three-dimensional Bènard convection. J. Fluid Mech. 147: 1-38
26. Daly BJ, Harlow FH (1970) Transport equations in turbulence. Phys. Fluids 13: 2634-2649
27. Davies HC, Schär C, Wernli H (1991) The palette of fronts and cyclones within a baroclinic wave development. J. Atmosph. Sci. 48: 1666-1689
28. de Saint-Venant B (1843) Note à joindre au mémoire sur la dynamique des fluides. Comptes Rendus des Séance de l'Académie des Sciences 17: 1240-1243
29. Deardorff JW (1970) A three-dimensional numerical investigation of the idealized planetary boundary layer. Geophysical Fluid Dynamics 1: 377-410
30. Deardorff JW (1972) Numerical investigation on neutral and unstable planetary boundary layers. J. Atmosph. Sci. 29: 91-115
31. Deardorff JW (1973a) Three-dimensional numerical modeling of the planetary boundary layer. In: Workshop in Micrometeorology, edited by D. A. Haugen Chapter 7, pp. 271-311, Am. Met. Soc. Boston, Mass.
32. Deardorff JW (1973b) The use of subgrid transport equations in a three-dimensional model of atmospheric turbulence. J. Fluids Eng. 95: 429-438
33. Diebels S, Schuster B, Hutter K (1994) Nonlinear internal waves over variable topography. Geophys. Astrophys. Fluid Dyn. 76: 165-192
34. Durst F, Friedrich R, Launder BE, Schmidt FW, Schumann U, Whitelaw JH (Eds.) (1997) Turbulent Shear Flow. Volume 10. Springer Verlag Berlin
35. Dutton JA, Fichtl GH (1969) Approximate equations of motion for gases and liquids. J. Atmosph. Sci. 26: 241-254
36. Eady ET (1949) Long waves and cyclone waves. Tellus 1: 33-52
37. Eckart C, Ferris HG (1956) Equations of motion of the ocean and atmosphere. Rev. Modern Phys. 28: 48-52
38. Euler L (1750, publ. 1752) Dècouverte d'un nouveau principe de mécanique. Mémoires de l'Académie des Sciences de Berlin 6: 185-217 Reprinted in: Leonhardi Euleri Opera Omnia, ed. J. O. Fleckenstein, auctoritate et impensis Societatis Scientiarum Naturalium Helveticae, (Schweizerische Naturforschende Gesellschaft), Lausanne, 1957, Ser. II, Vol. 5, 81-108, Orell Füssli, Zürich.
39. Euler L (1750, publ. 1752) Dècouverte d'un nouveau principe de mécanique. Mémoires de l'Académie des Sciences de Berlin 6: 185-217 Reprinted in: Leonhardi Euleri Opera Omnia, ed. J. O. Fleckenstein, auctoritate et impensis Societatis Scientiarum Naturalium Helveticae, (Schweizerische Naturforschende Gesellschaft), Lausanne, 1957, Ser. II, Vol. 5, 81-108, Orell Füssli, Zürich.
40. Fernando HJS, Boyer DL, Chen R-R (1989) Turbulent thermal convection in rotating and stratified fluids. Dyn. Atmos. Oceans 13: 95-121
41. Fernando HJS, Chen R-R, Boyer DL (1991) Effects of rotation on convective turbulence. J. Fluid Mech. 228: 513-547
42. Ferziger JH (1996) Large eddy simulation. In: Direct numerical simulation of turbulent flows, edited by T. B. Gatski, M. Y. Hussaini, and J. L. Lumley pp. 109-154, Oxford University Press
43. Ferziger JH, Perić M (1996) Computational methods for fluid dynamics. Springer Heidelberg
44. Galperin B, Rosati A, Kantha LH, Mellor GL (1989) Modelling rotating stratified turbulent flows with application to oceanic mixed layers. J. Phys. Oceanogr. 19: 901-916
45. Germane M, Piomelli U, Moin P, Cabot WH (1991) A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A3: 1760-1765
46. Gibson CH (1980) Fossil temperature, salinity, and vorticity turbulence in the ocean. In: Marine Turbulence, edited by J. C. J. Nihoul Volume 28 of Elsevier Oceanography Series Proc. 11th Int. Liège Coll. on Ocean Hydrodyn.
47. Gibson CH, Stegen GR, Williams RB (1970) Statistics of the fine structure of turbulent velocity and temperature fields measured at high Reynolds numbers. J. Fluid Mech. 41: 153-167
48. Gibson MM, Launder BE (1977) On the calculation of horizontal, turbulent, free shear flows under gravitational influence. J. Heat Transfer 98: 81-87
49. Greenspan HP (1969) The theory of rotating fluids. Cambridge Monographs on Mechanics and applied Mathematics, University Press Cambridge
50. Haidvogel DB, Beckmann A (1997) Numerical models of the coastal ocean. In: The Sea, J. Wiley New York, in press
51. Hanjalić K (1994) Advanced turbulence closure models: a view of current status and future prospects. Int. J. Heat Fluid Flow 15: 178-203
52. Hanjalić K, Launder BE (1972) A Reynolds stress model of turbulence and its application to thin shear flow. J. Fluid Mech. 52: 609-638
53. Hathaway DH, Sommerville RCJ (1983) Three dimensional simulations of convection in layers with tilted rotation vectors. J. Fluid Mech. 126: 75-89
54. Hinze JO (1959) Turbulence (2nd ed.). McGraw-Hill New York Re-issued 1987
55. Hopfinger EJ (1987) Turbulence in stratified fluids: A review. J. Geophys. Res. 92: 5287-5303
56. Hopfinger EJ, Browand FK, Gagne Y (1982) Turbulence and waves in a rotating tank. J. Fluid Mech. 125: 505-534
57. Hutter K (1983) Theoretical Glaciology. Mathematical approaches to geophysics, D. Reidel Dordrecht, Holland
58. Hutter K, Svendsen B, Rickenmann D (1996) Debris flow modeling: a review. Continuum Mech. Thermodyn. 8: 1-35
59. Jacquin L, Leuchter O, Cambon C, Mathieu J (1990) Homogeneous turbulence in the presence of rotation. J. Fluid Mech. 220: 1-52
60. Jöhnk K, Svendsen B (1996) A thermodynamic formulation of the equations of motion and buoyancy frequency for Earth's fluid outer core. Continuum Mech. Thermodyn. 8: 75-101
61. Jones H, Marshall J (1993) Convection with rotation in a neutral ocean: a study of open-ocean deep convection. J. Phys. Oceanogr. 23: 1009-1039
62. Joule JP (1850) On the mechanical equivalent of heat. Phil. Trans. Roy. Soc. London 140: 61-82. Reprinted in: The scientific papers of J. P. Joule, London, 1963, Vol. 1, 298-328, Dawsons, Pall Mall
63. Joule JP (1850) On the mechanical equivalent of heat. Phil. Trans. Roy. Soc. London 140: 61-82. Reprinted in: The scientific papers of J. P. Joule, London, 1963, Vol. 1, 298-328, Dawsons, Pall Mall
64. Kolmogorov AN (1941) Local structure of turbulence in an incompressible fluid at very high Reynolds numbers. Dokl. Akad. Nauk SSSR 30: 299-303
65. Launder BE, Reece GJ, Rodi W (1975) Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 68: 537-566
66. Launder BE, Tselepidakis DP (1994) Application of a new second-moment closure to turbulent channel flow rotating in orthogonal mode. Int. J. Heat Fluid Flow 15: 2-10
67. Launder BE, Tselepidakis DP, Younis BA (1987) A second-moment closure study of rotating channel flow. J. Fluid Mech. 183: 63-75
68. Leonard A (1974) Energy cascade in large eddy simulations of turbulent fluid flows. Adv. Geophys. 18A: 237-248
69. Leonard A (1996) Direct numerical simulation of turbulent flows. In: Simulation and modeling of turbulent flows, edited by T. B. Gatski, M. Y. Hussaini , and J. L. Lumley pp. 79-108, Oxford University Press
70. Lumley JL (1970) Toward a turbulent constitutive relation. J. Fluid Mech. 41: 413-434
71. Lumley JL, Khajeh-Nouri B (1974) Computational modeling of turbulent transport. Adv. Geophys. 18A: 169-192
72. Mahrt L (1986) On the shallow motion approximations. J. Atmosph. Sci. 43: 1036-1044
73. Manabe S, Stouffer RJ (1994) Multiple-century response of a coupled ocean-atmosphere model to an increase of atmospheric carbon dioxide. J. Climate 7: 5-23
74. Marchuk GI, Kochergin VP, Klimok VI, Sukhorukov VA (1977) On the dynamics of the ocean surface mixed layer. J. Phys. Oceanogr. 7: 865-875
75. Marshall J, Hill C, Perelman L, Adcroft A (1997) Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling. J. Geophys. Res. 102: 5733-5752
76. Mason PJ (1989) Large-eddy simulation of the convective atmospheric boundary layer. J. Atmosph. Sci. 46: 1492-1516
77. Mason PJ, Brown AR (1994) The sensitivity of large-eddy simulations of turbulent shear flow to subgrid models. Boundary Layer Met. 70: 133-150
78. Maxworthy T, Narimousa S (1991) Vortex generation by convection in a rotating fluid. Ocean Modell. 92: 5-8 Hooke Inst. Oxford Univ., Oxford, England
79. Maxworthy T, Narimousa S (1994) Unsteady, turbulent convection into a homogeneous, rotating fluid, with oceanographic applications. J. Phys. Oceanogr. 24: 865-887
80. Mayer JR (1842) Bemerkungen über die Kräfte der unbelebten Natur. Annalen der Chemie und Pharmacie 42: 233-240 Repr. in Mechanik der Wärme, Ostwalds Klassiker der exakten Wissenschaften, Volume 180, 1997, Verlag H. Deutsch, Thun, Frankfurt a. M.
81. Mayer JR (1842) Bemerkungen über die Kräfte der unbelebten Natur. Annalen der Chemie und Pharmacie 42: 233-240 Repr. in Mechanik der Wärme, Ostwalds Klassiker der exakten Wissenschaften, Volume 180, 1997, Verlag H. Deutsch, Thun, Frankfurt a. M.
82. McComb WD (1990) The physics of fluid turbulence. Clarendon Press Oxford
83. Mellor GL (1973) Analytic prediction of the properties of stratified planetary surface layers. J. Atmosph. Sci. 30: 1061-1069
84. Mellor GL, Herring HJ (1973) A survey of mean turbulent field closure models. AIAA J. 11: 590-599
85. Mellor GL, Yamada T (1982) Development of a turbulent closure model for geophysical fluid problems. Rev. Geophys. Space Phys. 20: 851-875
86. Mihaljan JM (1962) A rigorous exposition of the Boussinesq approximations applicable to a thin layer of fluid. Astropnys. J. 136: 1126-1133
87. Miller MJ, White AA (1984) On the non-hydrostatic equations in pressure and sigma coordinates. Quart. J. Roy. Met. Soc. 110: 515-533
88. Moeng C-H (1984) A large eddy-simulation model for the study of planetary boundary-layer turbulence. J. Atmosph. Sci. 41: 2052-2062
89. Muschinski A (1992) Statistische Beschreibung turbulenter Strömungen mittels einer lokalen Interpretation der Heisenbergschen Turbulenztheorie. Ph. D. thesis University of Hannover Berichte des Instituts für Meteorologie und Klimatologie, Bd. 41
90. Nakagawa Y, Frenzen P (1955) A theoretical and experimental study of cellular convection in rotating fluids. Tellus 7: 1-21
91. Nataf H-C, Hager BH (1984) Convection experiments in a centrifuge and the generation of plumes in a very viscous fluid. Ann. Geophysicae 2: 303-310
92. Navier LMH (1822) Mémoire sur les lois du mouvement des fluides. Mémoires de l'Académie des Sciences de l'Institut de France 6: 389-440 Annee 1823, publ. Paris 1827
93. Nieuwstadt FTM, Brost RA (1986) The decay of convective turbulence. J. Atmosph. Sci. 43: 532-546
94. Oberbeck A (1888) Über die Bewegungserscheinungen der Atmosphaere. Sitzungsberichte königl. Preuss. Akad. Wissenschaften, Berlin 1: 383-395 [Engl. transl. repr. in: Selected papers on the theory of thermal convection, with special application to the Earth's planetary atmosphere. B. Saltzman, Ed., New York, 162-183, 1962]
95. Oberbeck A (1888) Über die Bewegungserscheinungen der Atmosphaere. Sitzungsberichte königl. Preuss. Akad. Wissenschaften, Berlin 1: 383-395 [Engl. transl. repr. in: Selected papers on the theory of thermal convection, with special application to the Earth's planetary atmosphere. B. Saltzman, Ed., New York, 162-183, 1962]
96. Ottino JM (1989) The kinematics of mixing: stretching, chaos and transport. University Press Cambridge
97. Panetta RL (1993) Zonal jets in wide baroclinically unstable regions: Persistence and scale selection. J. Atmosph. Sci. 50: 2073-2106
98. Phillips OM (1966) The dynamics of the upper ocean. Cambridge Monographs on Mechanics and Applied Mathematics, University Press Cambridge
99. Polzin KL, Toole JM, Schmitt RW (1997) Spatial variability of turbulent mixing in the abyssal ocean. Science 276: 93-96
100. Prandtl L (1945) Über ein neues Formelsystem für die ausgebildete Turbulenz. Nachr. Akad. Wiss. Göttingen, Math.-Phys. Kl. 6: 6-19
101. Raasch S (1990) Two numerical case studies of horizontal roll vortices in near-neutral inversion capped planetary boundary layers. Contrib. Atmos. Phys. 63: 205-222
102. Raasch S, Etling D (1991) Numerical simulation of rotating turbulent thermal convection. Contrib. Atmos. Phys. 64(3) 185-199
103. Reynolds O (1883) An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Phil. Trans. Roy. Soc. London A 174: 935-982
104. Reynolds O (1895) On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Phil. Trans. Roy. Soc. London (A) 186, part I: 123-164
105. Richardson LF (1922) Weather prediction by numerical process. University Press Cambridge
106. Rodi W (1978) Turbulence models and their application in hydraulics: A state of the art review. SFB 80/T/127 University Karlsruhe
107. Rodi W (1987) Examples of calculation methods for flow and mixing in stratified fluids. J. Geophys. Res. 92: 5305-5328
108. Rossby HT (1969) A study of Bénard convection with and without rotation. J. Fluid Mech. 36: 309-335
109. Rotta JC (1951) Statistische Theorie nichthomogener Turbulenz. Z. Physik 129: 547-572
110. Rouse H, Ince S (1957) History of Hydraulics. Iowa Institute of Hydraulic Research State University of Iowa
111. Sadiki A, Hutter K (1996) On the frame dependence and form invariance of the transport equations for the Reynolds stress tensor and the turbulent heat flux vector: its consequences on closure models in turbulence modelling. Continuum Mech. Thermodyn. 8: 341-349
112. Sander J, Hutter K (1991) On the development of the theory of the solitary wave. a historical essay. Acta Mechanica 86: 111-152
113. Sander J, Wolf-Gladrow D, Olbers D (1995) Numerical studies of open ocean deep convection. J. Geophys. Res. 100: 20579-20600
114. Saunders PM (1973) The instability of a baroclinic vortex. J. Phys. Oceanogr. 3: 61-65
115. Schär C, Smith RB (1993a) Shallow-water flow past isolated topography. Part I: vorticity production and wake formation. J. Atmosph. Sci. 50: 1737-1400
116. Schär C, Smith RB (1993b) Shallow-water flow past isolated topography. Part II: transition to vortex shedding. J. Atmosph. Sci. 50: 1401-1412
117. Schemm CE, Lipps FB (1976) Some results from a simplified three-dimensional numerical model of atmospheric turbulence. J. Atmosph. Sci. 33: 1021-1041
118. Schlichting H (1965) Grenzschicht Theorie (5th ed.). Verlag G. Braun Karlsruhe
119. Schmidt H, Schumann U (1989) Coherent structure of the convective boundary layer derived from large-eddy simulations J. Fluid Mech. 200: 511-562
120. Semtner AJ, Chervin RM (1992) Ocean general circulation from a global eddy-resolving model. J. Geophys. Res. 97: 5493-5550
121. Shao L, Michard M, Bertoglio JP (1991), Effects of solid body rotation on the transport of turbulence. In: Eighth Symposium on Turbulent Shear Flows Volume 2, Munich
122. Speziale CG, Gatski TB, Mhuiris NMG (1990) A critical comparison of turbulence models for homogeneous shear flows in a rotating frame. Phys. Fluids A 2(9) 1678-1684
123. Spiegel EA, Veronis G (1960) On the Boussinesq approximation for a compressible fluid. Astrophys. J. 131: 442-447
124. Stewart I (1992) Numerical methods: Warning - handle with care! Nature 355: 16-17
125. 2 emission rates on the stability of the thermohaline circulation. Nature 388: 862-865
126. Stokes GG (1845) On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic solids. Trans. Cambridge Phil. Soc. 8: 287-305 Reprinted in: Mathematical and Physical Papers (1880) 1: 75-129, Cambridge, University Press
127. Stokes GG (1845) On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic solids. Trans. Cambridge Phil. Soc. 8: 287-305 Reprinted in: Mathematical and Physical Papers (1880) 1: 75-129, Cambridge, University Press
128. Stokes GG (1850) On the effect of the internal friction of fluids on the motion of pendulums. Trans. Cambridge Phil. Soc. 9: 8 Reprinted in: Mathematical and Physical Papers (1880) 3: 1-141, Cambridge, University Press
129. Stokes GG (1850) On the effect of the internal friction of fluids on the motion of pendulums. Trans. Cambridge Phil. Soc. 9: 8 Reprinted in: Mathematical and Physical Papers (1880) 3: 1-141, Cambridge, University Press
130. Stull RB (1988) An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers Dordrecht, The Netherlands
131. Svensson U (1979) The structure of the turbulent Ekman layer. Tellus 31: 340-350
132. Szabó I (1987) Geschichte der mechanischen Prinzipien. Birkhäuser Basel
133. Thunis P, Bornstein R (1996) Hierachy of mesoscale flow assumptions and equations. J. Atmosph. Sci. 53: 381-397
134. Turcotte DL, Torrance KE, Hsui AT (1973) Convection in the Earth's mantle. In: Methods in computational physics, edited by B. A. Bolt Volume 13 pp. 431-454, Academic Press New York
135. Veronis G (1958) Cellular convection with finite amplitude in a rotating fluid. J. Fluid Mech. 5: 401-435
136. Woods JD (1980) Do waves limit turbulent diffusion in the ocean? Nature 288: 219-224