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Rain-induced attenuation of deep-water waves

Published online by Cambridge University Press:  29 April 2013

William L. Peirson*
Affiliation:
Water Research Laboratory, School of Civil and Environmental Engineering, The University of New South Wales, Manly Vale, NSW 2093, Australia
José F. Beyá
Affiliation:
Water Research Laboratory, School of Civil and Environmental Engineering, The University of New South Wales, Manly Vale, NSW 2093, Australia Escuela de Ingeniería Civil Oceánica, Facultad de Ingeniería, Universidad de Valparaíso, Av. Brasil 1786 of. 30, Valparaíso, Chile
Michael L. Banner
Affiliation:
School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia
Joaquín Sebastián Peral
Affiliation:
AREVA Wind GmbH Am Lunedeich 156 D-27572 Bremerhaven, Germany
Seyed Ali Azarmsa
Affiliation:
Faculty of Marine Sciences, Tarbiat Modares University, PO Box: 14115-111, Tehran, Iran
*
Email address for correspondence: w.peirson@unsw.edu.au

Abstract

A laboratory investigation has been undertaken to quantify water wave attenuation rates as a function of rainfall rate. Vertical artificial rainfall is shown to generate weak near-surface velocity fluctuations that decline systematically away from the free surface and are independent of rainfall rate across the range of rainfall rates investigated (40–$170~\mathrm{mm} ~{\mathrm{h} }^{- 1} $). In the absence of rain, the observed attenuation of gravity waves is at levels consistent with classical viscous theory, but with a systematic finite-amplitude effect observed above a mean steepness of 0.10. Wave attenuation rates were found to be independent of the mean wave steepness and identical when artificial rainfall rates of 108 and $141~\mathrm{mm} ~{\mathrm{h} }^{- 1} $ were applied. Reassessment of complementary theoretical and experimental studies of individual droplets impacting on undisturbed water surfaces indicates that above a weak threshold rainfall rate of $30~\mathrm{mm} ~{\mathrm{h} }^{- 1} $, the surface irradiation becomes so frequent that droplet-generated violent surface motions directly interact with the incoming droplets. Present evidence is that a matching of time scales develops between the incoming surface irradiation and surface water motions generated by antecedent droplets as the rainfall rate increases. Consequently, at high rainfall rates, a highly dissipative surface regime is created that transmits little of the incident rainfall kinetic energy to the aqueous layers below. Rainfall-induced wave attenuation rates are compared with measurements of other wave attenuation processes to obtain a hierarchy of strength in both the laboratory and the field. Comparison is also made with wave attenuation theories that incorporate momentum and energy flux considerations. Rain-induced wave attenuation rates are weak or very strong depending on whether they are expressed in terms of energy scaling obtained from above or below the surface respectively, due to the high dissipation rate that occurs in the vicinity of the interface.

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Papers
Copyright
©2013 Cambridge University Press 

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