Momentum balance in shoaling gravity waves: Comment on ’shoaling surface gravity waves cause a force and a torque on the bottom’ by K. E. Kenyon |
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| Authors: | Fabrice Ardhuin |
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| Institution: | (1) Centre Militaire d’Océanographie, Service Hydrographique et Océanographique de la Marine, Brest, France |
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| Abstract: | In a recent paper, Kenyon (2004) proposed that the wave-induced energy flux is generally not conserved, and that shoaling
waves cause a mean force and torque on the bottom. That force was equated to the divergence of the wave momentum flux estimated
from the assumption that the wave-induced mass flux is conserved. This assumption and conclusions are contrary to a wide body
of observations and theory. Most importantly, waves propagate in water, so that the momentum balance generally involves the
mean water flow. Although the expression for the non-hydrostatic bottom force given by Kenyon is not supported by observations,
a consistent review of existing theory shows that a smaller mean wave-induced force must be present in cases with bottom friction
or wave reflection. That force exactly balances the change in wave momentum flux due to bottom friction and the exchange of
wave momentum between incident and reflected wave components. The remainder of the wave momentum flux divergence, due to shoaling
or wave breaking, is compensated by the mean flow, with a balance involving hydrostatic pressure forces that arise from a
change in mean surface elevation that is very well verified by observations. |
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| Keywords: | Shoaling waves radiation stresses wave force wave scattering set-up |
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