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The Quarterly Journal of Mechanics and Applied Mathematics 1993 46(1):117-130; doi:10.1093/qjmam/46.1.117
© 1993 by Oxford University Press
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ENERGY FLUX AND GROUP VELOCITY IN CURRENTS OF UNIFORM VORTICITY

I. BREVIK1 and R. SOLLIE{dagger},2

( 1Division of Applied Mechanics, University of Trondheim N-7034 Trondheim-NTH, Norway
2Department of Physics, Florida State University Tallahassee, Florida 32306, USA )

{dagger} Present address: IKU, SINTEF Group, N-7034 Trondheim, Norway.

Linear water waves superimposed on an opposing current varying linearly down to a depth h are investigated. Fluxes of mass, momentum, and energy are calculated. Of main interest is the expression for the energy flux and its possible decomposition into terms in such a way that the contribution from wave energy is clearly shown. Such a decomposition would link the kinematic group-velocity concept to the dynamic concept of velocity of propagation of wave energy. We write the energy flux in a form that generalizes the simple expression found by Brink-Kjaer for the case of a linear current extending down to the bottom. In this expression the term corresponding to the group velocity appears quite naturally, as the energy flux of ‘pure wave energy’.


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