Time development of small disturbances to plane Couette Flow
Shepherd, T. G. (1985) Time development of small disturbances to plane Couette Flow. Journal of the Atmospheric Sciences, 42 (17). pp. 1868-1872. ISSN 1520-0469
To link to this item DOI: 10.1175/1520-0469(1985)042<1868:TDOSDT>2.0.CO;2
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.