Time development of small disturbances to plane Couette Flow

Shepherd, T. G. ORCID: https://orcid.org/0000-0002-6631-9968 (1985) Time development of small disturbances to plane Couette Flow. Journal of the Atmospheric Sciences, 42 (17). pp. 1868-1872. ISSN 1520-0469 doi: 10.1175/1520-0469(1985)042<1868:TDOSDT>2.0.CO;2

Abstract/Summary

The question of linear sheared-disturbance evolution in constant-shear parallel flow is here reexamined with regard to the temporary-amplification phenomenon noted first by Orr in 1907. The results apply directly to Rossby waves on a beta-plane, and are also relevant to the Eady model of baroclinic instability. It is shown that an isotropic initial distribution of standing waves maintains a constant energy level throughout the shearing process, the amplification of some waves being precisely balanced by the decay of the others. An expression is obtained for the energy of a distribution of disturbances whose wavevectors lie within a given angular wedge and an upper bound derived. It is concluded that the case for ubiquitous amplification made in recent studies may have been somewhat overstated: while carefully-chosen individual Fourier components can amplify considerably before they decay. a general distribution will tend to exhibit little or no amplification.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/32996
Identification Number/DOI	10.1175/1520-0469(1985)042<1868:TDOSDT>2.0.CO;2
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Publisher	American Meteorological Society
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