On the Effect of Wind and Turbulence on Ocean Swell
Fabrice Ardhuin
Centre Militaire Océanographique, Service Hydrographique et Océanographique de la Marine
Brest, France
Alastair D. Jenkins
Bjerknes Centre for Climate Research
Bergen, Norway
ABSTRACT
A quantitave review of processes contributing to the evolution of swell
is proposed, combining direct interactions of swell with the wind and
upper ocean turbulence, and interaction with shorter wind waves. The
interaction with short waves is based on the extension of Hasselmann’s
(1971) theory for short wave modulation by long wave to the presence
of variable wind stresses. Quantitative estimations of the various effects
are performed based on the wave modulation model of Hara et al.
(2003) and the wind-over-wave coupling model of Kudryavtsev and
Makin (2004). It is found that the observations of swell decay in the
Pacific (Snodgrass et al., 1963) are quantitatively consistent with the
effects of wind stress modulation and direct wind to wave momentum
transfer.
KEY WORDS: Waves, turbulence, wind, swell, modulation.
INTRODUCTION
The problem of swell forecasting on the coast of Morocco (Gelci,
1949) led Gelci et al (1957) to develop the first numerical spectral
wave models. Half a century later, the forecasting of wind seas has
made enormous progress but swells are still the least well predicted part
of the wave spectrum (Rogers, 2002). Although these long period
waves may be well generated in numerical wave models, what happens
next is still much of a mystery. At the same time it is now well
recognized that swells play an important role in air-sea interactions
(e.g. Drennan et al., 1999; Grachev et al. 2003) and should impact the
remote sensing of ocean properties. These new applications, along with
the traditional problem of wave and surf forecasting, warrant a closer
inspection of the theory and practical aspects of swell evolution.
It was recognized very early that viscosity had a negligible effect on
waves of periods of about 10 s and longer (Lamb, 1932), so that, once
generated, swells were supposed to dissipate slowly due to the action of
the wind, as represented by Jeffrey’s (1925) sheltering theory
(Sverdrup and Munk, 1947). These ideas have been gradually
abandoned and traded for eddy viscosity analogies (Bowden, 1950;
Groen and Dorrestein, 1950) that are used today in some operational
wave forecasting models (e.g. Tolman and Chalikov, 1996). The
magnitude and the frequency dependence of the associated wave
damping are calibrated using buoy and altimeter data, and no theory is
available to predict these parameters. Other wave models wishfully
assume that swell dissipates in the same way as the wind sea (WAMDI,
1988; Komen et al., 1994).
The validation studies on the spectral shape and magnitude of the
dissipation are very few. Snodgrass et al. (1966) have demonstrated
that swells of periods larger than 16 s are hardly attenuated when
crossing the Pacific from south to north, although attenuation of shorter
period waves was observed. There is also qualitative evidence of waves
blown flat by strong opposing winds, without any satisfactory theory or
good observations (Jenkins 2002). We therefore take advantage of
recent developments in wave-turbulence interaction theory (Teixeira
and Belcher, 2002; Ardhuin and Jenkins, manuscript submitted to J.
Phys. Ocenogr.) and observation of short wave modulations by long
waves (Hara et al., 2003) to review and combine the existing theories,
including the much ignored 30-year old theory on swell-short wave
modulations by Hasselmann (1971), and evaluate their relevance for
swell forecasting.
The paper unfolds as follows. First the theory recent result for wave-
turbulence interaction is recalled, followed by an extension of
Hasselmann’s (1971) theory for short wave modulation, including now
the modulation of the wind forcing. Next, a semi-empirical
parameterization is proposed for the short wave modulation, and the
different effects are evaluated numerically for typical wind conditions.
Perspectives for validation are discussed with our conclusions.
WAVE-TURBULENCE INTERACTION
Using rapid distortion theory, Teixeira and Belcher (2002) found that
waves propagating in a turbulent field produced turbulent kinetic
energy locally at the rate of
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Proceedings of The Fifteenth (2005) International Offshore and Polar Engineering Conference
Seoul, Korea, June 19-24, 2005
Copyright © 2005 by The International Society of Offshore and Polar Engineers
ISBN 1-880653-64-8 (Set); ISSN 1098-6189 (Set)