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Nonlinear internal waves in the upper atmosphere. (English) Zbl 1206.86023

Summary: This article considers the large-scale dynamics generated in the upper atmosphere by the destabilization of a linear internal gravity wave and its eventual restabilization through nonlinear processes into a coherent pattern. The assumption of a strongly dissipative medium is relevant to wave propagation in the thermosphere range above 100 km. A parametric instability analysis is carried out involving the Froude, Reynolds and Prandtl numbers, and the following parameters: friction, wave incidence and disturbance periodicity. A solution of the motion is sought with the help of a multiscale technique based upon the hypothesis of large-scale flow. The leading-order amplitude equation governing this dynamics contains the Cahn-Hilliard equation, but also possesses a dispersive term depending on the Prandtl number, a large-scale damping proportional to the overall Richardson number and a quadratic term modelling the incidence effects. A numerical and analytical study of this equation is given. An internal-wave stability criterion is obtained which shows the possibility of obtaining coherent structures for large Froude numbers.

MSC:

86A10 Meteorology and atmospheric physics
76B60 Atmospheric waves (MSC2010)
76E20 Stability and instability of geophysical and astrophysical flows
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References:

[1] Afanasyev Y, J. Atmos. Sci. 58 pp 132– (2001)
[2] Andreassen O, J. Geophys. Res. 99 pp 8095– (1994)
[3] Balmforth N, J. Fluid Mech. 450 pp 131– (2002)
[4] Batchayev AM, Izvestiya, Atmospheric and Oceanic Physics 22 (1) pp 1– (1986)
[5] Bondarenko N, Atmospheric and Oceanic Physics 15 pp 711– (1979)
[6] Bouruet-Aubertot P, Dyn. Atm. Oceans 23 pp 357– (1996)
[7] Caillol P, Université Pierre et Marie Curie (2000)
[8] Caillol P, Dyn. Atmos. Oceans 32 pp 81– (2000)
[9] Campbell LJ, J. Fluid Mech. 493 pp 151– (2003) · Zbl 1059.76010
[10] Dewan EM, J. Geophys. Res. 91 pp 2742– (1986)
[11] Drazin P, Proc. R. Soc. Lond. A 356 pp 411– (1977) · Zbl 0367.76043
[12] Frisch U, Physica D 94 pp 36– (1996) · Zbl 0899.76230
[13] Fritts D, J. Atmos. Sci. 45 (12) pp 1741– (1988)
[14] Fritts DC, J. Atmos. Sci. 41 (4) pp 524– (1984)
[15] Fritts DC, Radio Sci. 20 pp 1247– (1985)
[16] Fritts DC, J. Geophys. Res. 93 pp 7015– (1988)
[17] Gerkema T, J. Marine Res. 54 pp 421– (1996)
[18] Grimshaw R, Survey in Geophys. 19 pp 289– (1998)
[19] Hines C, Quart. J. Roy. Meteor. Soc. 89 (379) pp 1– (1963)
[20] Huang HP, J. Atmos. Sci. 55 pp 611– (1998)
[21] Kato S, Dynamics of the Upper Atmosphere pp pp. 13–56– (1980)
[22] Kawasaki K, Physica A 116 (3) pp 573– (1982)
[23] Khapaev A, Izvestiya, Atmos. Oceanic Phys. 36 (1) pp 57– (2000)
[24] Klaassen G, J. Fluid Mech. 155 pp 1– (1985) · Zbl 0585.76047
[25] Klaassen G, J. Fluid Mech. 227 pp 71– (1991) · Zbl 0721.76034
[26] Klostermeyer J, Geophys. Astrophys. Fluid Dyn. 61 pp 1– (1991)
[27] Kurganskiy M, Izvestiya, Atmos. Oceanic Physics 16 (10) pp 758– (1980)
[28] Lamb H, Hydrodynamics, Dover Publications (1945)
[29] Legras B, Physica D 175 pp 139– (2003) · Zbl 1006.76036
[30] Legras B, Phys. Rev. Lett. 82 pp 4440– (1999)
[31] Lelong M, J. Atmos. Sci. 55 pp 2473– (1998)
[32] Lombard PN, Phys. Fluids 8 (12) pp 3271– (1996) · Zbl 1027.76567
[33] Manfroi A, J. Atmos. Sci. 56 pp 784– (1999)
[34] Meek C, Radio Sci. 20 pp 1363– (1985)
[35] Miyazaki T, Phys. Fluids 10 (12) pp 3168– (1998) · Zbl 1185.76904
[36] Nikitenkova SP, J. Appl. Maths. Mechs. 64 (2) pp 267– (2000)
[37] Prusa J, J. Atmos. Sci. 53 (15) pp 2186– (1996)
[38] Röttger J, Radio Sci. 25 pp 671– (1990)
[39] She Z, Phys. Lett. A 124 (3) pp 161– (1987)
[40] Sivashinsky G, Physica D 17 pp 243– (1985) · Zbl 0577.76045
[41] Smyth WD, J. Fluid Mech. 497 pp 67– (2003) · Zbl 1053.76025
[42] Sutherland B, J. Fluid Mech. 429 pp 343– (2001) · Zbl 1007.76024
[43] Thorpe SA, IMA J. Appl. Math. 260 pp 333– (1994)
[44] Tsuda T, J. Atmos. Sol. Terr. Phys. 56 pp 555– (1994)
[45] Tsuda T, J. Geophys. Res. 96 (2) pp 17265– (1991)
[46] Walterscheid RL, J. Atmos. Sci. 41 (6) pp 1062– (1984)
[47] Weinstock J, J. Atmos. Sci. 47 pp 2221– (1990)
[48] Winters KB, J. Fluid Mech. 272 pp 255– (1994) · Zbl 0846.76030
[49] Wu Y, J. Geophys. Res. 96 (5) pp 9263– (1991)
[50] Yi F, J. Atmos. Sol. Terr. Phys. 61 pp 675– (1999)
[51] Yi F, Geophys. Res. Lett. 18 (4) pp 697– (1991)
[52] Young Y, Woods Hole Oceanogr. Inst. Tech. Rep. 40 (1999)
[53] Zhang SD, J. Geophys. Res. 14 pp 4222– (2002)
[54] Zhang SD, Ann. Geophys. 18 pp 1316– (2000)
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