×

zbMATH — the first resource for mathematics

A mechanism of formation of multiple zonal jets in the oceans. (English) Zbl 1181.76071
Summary: Multiple alternating zonal jets observed in the ocean are studied with an idealized quasigeostrophic model of flow in a zonal channel. The jets are maintained by the eddies generated by the imposed, supercritical background flow. The formation, nonlinear dynamics and equilibration of the jets are explained in terms of linear stability arguments and nonlinear self-interactions of the linear eigenmodes. In the proposed mechanism, energy of the background flow is released to the primary instability mode with long meridional and short zonal length scales. This mode undergoes secondary, transverse instability that sets the meridional scale of the emerging multiple zonal jets. This instability channels energy into several weakly damped zonal eigenmodes that amplify the jets. The emerging jets feed back on the instabilities through the partial meridional localization of the most unstable eigenmodes.

MSC:
76E20 Stability and instability of geophysical and astrophysical flows
76U05 General theory of rotating fluids
86A05 Hydrology, hydrography, oceanography
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Balk, Phys. Rev. Lett. A 146 pp 217– (1990) · doi:10.1016/0375-9601(90)90168-N
[2] DOI: 10.1002/qj.49708235202 · doi:10.1002/qj.49708235202
[3] DOI: 10.1126/science.1131375 · doi:10.1126/science.1131375
[4] DOI: 10.1175/JPO2698.1 · doi:10.1175/JPO2698.1
[5] DOI: 10.1029/2006GL025865 · doi:10.1029/2006GL025865
[6] McWilliams, Fundamentals of Geophysical Fluid Dynamics pp 249– (2006) · Zbl 1233.86003
[7] DOI: 10.1016/0377-0265(77)90002-1 · doi:10.1016/0377-0265(77)90002-1
[8] McIntyre, J. Meteorol. Soc. Jpn 60 pp 37– (1982)
[9] DOI: 10.1029/2008GL033267 · doi:10.1029/2008GL033267
[10] DOI: 10.1029/2005GL022728 · doi:10.1029/2005GL022728
[11] DOI: 10.1175/1520-0469(1978)0352.0.CO;2 · doi:10.1175/1520-0469(1978)0352.0.CO;2
[12] DOI: 10.1016/S0167-2789(01)00384-0 · Zbl 0983.86002 · doi:10.1016/S0167-2789(01)00384-0
[13] DOI: 10.1175/1520-0485(1993)0232.0.CO;2 · doi:10.1175/1520-0485(1993)0232.0.CO;2
[14] DOI: 10.1175/1520-0469(1999)0562.0.CO;2 · doi:10.1175/1520-0469(1999)0562.0.CO;2
[15] DOI: 10.1175/1520-0485(1994)0242.0.CO;2 · doi:10.1175/1520-0485(1994)0242.0.CO;2
[16] DOI: 10.1175/1520-0469(1997)0542.0.CO;2 · doi:10.1175/1520-0469(1997)0542.0.CO;2
[17] DOI: 10.1175/JAS4000.1 · doi:10.1175/JAS4000.1
[18] DOI: 10.1063/1.2173285 · Zbl 1185.76763 · doi:10.1063/1.2173285
[19] DOI: 10.1175/1520-0485(2004)0342.0.CO;2 · doi:10.1175/1520-0485(2004)0342.0.CO;2
[20] DOI: 10.1175/JAS4009.1 · doi:10.1175/JAS4009.1
[21] DOI: 10.1175/JAS4013.1 · doi:10.1175/JAS4013.1
[22] DOI: 10.1175/1520-0485(1996)0262.0.CO;2 · doi:10.1175/1520-0485(1996)0262.0.CO;2
[23] DOI: 10.1017/S0022112005004416 · Zbl 1074.76024 · doi:10.1017/S0022112005004416
[24] Starr, Physics of Negative Viscosity Phenomena pp 256– (1968)
[25] DOI: 10.1063/1.1752928 · Zbl 1186.76124 · doi:10.1063/1.1752928
[26] Pedlosky, Geophysical Fluid Dynamics pp 710– (1987) · doi:10.1007/978-1-4612-4650-3
[27] DOI: 10.1175/1520-0469(2004)0612.0.CO;2 · doi:10.1175/1520-0469(2004)0612.0.CO;2
[28] DOI: 10.1175/1520-0485(1975)0052.0.CO;2 · doi:10.1175/1520-0485(1975)0052.0.CO;2
[29] DOI: 10.1016/0167-2789(96)00102-9 · Zbl 0900.76191 · doi:10.1016/0167-2789(96)00102-9
[30] DOI: 10.1017/S0022112007006179 · Zbl 1116.76033 · doi:10.1017/S0022112007006179
[31] DOI: 10.1175/1520-0485(1975)0052.0.CO;2 · doi:10.1175/1520-0485(1975)0052.0.CO;2
[32] DOI: 10.1175/1520-0469(1993)0502.0.CO;2 · doi:10.1175/1520-0469(1993)0502.0.CO;2
[33] DOI: 10.1357/0022240054307894 · doi:10.1357/0022240054307894
[34] DOI: 10.1017/S0022112083000518 · Zbl 0556.76039 · doi:10.1017/S0022112083000518
[35] Ivanov, Geophys. Res. Lett. 36 (2008)
[36] DOI: 10.1357/002224000321511214 · doi:10.1357/002224000321511214
[37] DOI: 10.1175/1520-0469(1998)0552.0.CO;2 · doi:10.1175/1520-0469(1998)0552.0.CO;2
[38] DOI: 10.1175/JPO3111.1 · doi:10.1175/JPO3111.1
[39] DOI: 10.1029/2006JC003735 · doi:10.1029/2006JC003735
[40] DOI: 10.1175/1520-0469(2004)0612.0.CO;2 · doi:10.1175/1520-0469(2004)0612.0.CO;2
[41] DOI: 10.1175/2008JPO3853.1 · doi:10.1175/2008JPO3853.1
[42] DOI: 10.1175/1520-0485(1999)0292.0.CO;2 · doi:10.1175/1520-0485(1999)0292.0.CO;2
[43] Hogg, Deep-Sea Res. 46 pp 335– (1999) · doi:10.1016/S0967-0645(98)00097-6
[44] DOI: 10.1175/1520-0469(1988)0452.0.CO;2 · doi:10.1175/1520-0469(1988)0452.0.CO;2
[45] DOI: 10.1175/2007JPO3835.1 · doi:10.1175/2007JPO3835.1
[46] DOI: 10.1029/2006EO200001 · doi:10.1029/2006EO200001
[47] DOI: 10.1175/1520-0469(1980)0372.0.CO;2 · doi:10.1175/1520-0469(1980)0372.0.CO;2
[48] DOI: 10.1029/2008GL035998 · doi:10.1029/2008GL035998
[49] DOI: 10.1029/2004GL019691 · doi:10.1029/2004GL019691
[50] DOI: 10.1029/2005GL024645 · doi:10.1029/2005GL024645
[51] DOI: 10.1175/2008JAS2611.1 · doi:10.1175/2008JAS2611.1
[52] DOI: 10.1017/S0022112075001504 · Zbl 0366.76043 · doi:10.1017/S0022112075001504
[53] DOI: 10.1175/2007JPO3856.1 · doi:10.1175/2007JPO3856.1
[54] DOI: 10.1175/JAS4016.1 · doi:10.1175/JAS4016.1
[55] DOI: 10.1175/2007JAS2227.1 · doi:10.1175/2007JAS2227.1
[56] DOI: 10.1029/2005GL025368 · doi:10.1029/2005GL025368
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.