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Non-normal stability analysis of a shear current under surface gravity waves

Published online by Cambridge University Press:  31 July 2008

D. AMBROSI  and
M. ONORATO
D. AMBROSI
Affiliation:
Dip. di Matematica, Politecnico di Torino, corso Duca degli Abruzzi 24, 10129 Torino, Italy
M. ONORATO
Affiliation:
Dip. di Fisica Generale, Università di Torino, via Pietro Giuria 1, 10125 Torino, Italy
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Abstract

The stability of a horizontal shear current under surface gravity waves is investigated on the basis of the Rayleigh equation. As the differential operator is non-normal, a standard modal analysis is not effective in capturing the transient growth of a perturbation. The representation of the stream function by a suitable basis of bi-orthogonal eigenfunctions allows one to determine the maximum growth rate of a perturbation. It turns out that, in the considered range of parameters, such a growth rate can be two orders of magnitude larger than the maximum eigenvalue obtained by standard modal analysis.

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 609 , 25 August 2008 , pp. 49 - 58
Copyright
Copyright © Cambridge University Press 2008

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