Abstract
This paper is a result of the author’s struggle to understand the momentum balance in Longuet-Higgins’ (1969) fluctuating horizontal stress mechanism. A surface stress oscillating in phase with a gravity wave will cause the wave to grow. If no other external forces than the fluctuating stress act on the surface then there is no average transfer of momentum across the surface and yet clearly the momentum of the wave is increasing. After some time it became clear that we have to be careful in defining what a fluctuating stress means. We can distinguish two limiting cases:
Case A: The fluctuating stress is purely viscous, and all viscosity effects in the fluid motion are taken care of.
Case B: The fluctuating stress is purely inviscid, and the fluid is also inviscid.
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References
Elliott, J. A. 1972:Microscale pressure fluctuations near waves being generated by wind. J. Fluid Mech. 54, 427
Garrett, C. and Smith, J. 1976:On the interaction between long and short surface waves. J. Phy. Oceanogr. J5, 925
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Longuet-Higgins, M.S. 1969: On the action of a variable stress at the surface of water waves. Physics of Fluids 12, 737
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© 1978 Plenum Press, New York
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Hasselmann, D. (1978). Energy and Momentum Flux to Nonresonant Forced Waves. In: Favre, A., Hasselmann, K. (eds) Turbulent Fluxes Through the Sea Surface, Wave Dynamics, and Prediction. Springer, Boston, MA. https://doi.org/10.1007/978-1-4612-9806-9_30
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DOI: https://doi.org/10.1007/978-1-4612-9806-9_30
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-9808-3
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