Energy dissipation across the wave spectrum - Breaking and Dissipation of Ocean Surface Waves - page 296

Ardhuin et al. ( 2009a ) investigated propagation of swell across the oceans by means of
space-borne synthetic aperture radar data. They measured energy e- folding scales along
wave-propagation distances 3000 to 30000 km and provided unique material for investi-
gating and estimating dissipation of wave energy in field conditions due to causes other
than breaking.
Ardhuin et al. ( 2009a ) conducted their analysis based on what they call the linear energy
e- folding scale

α such that

dF ( f ,θ,φ) = α RF ( f ,θ,φ). (7.60)

Here, R is the radius of Earth, F is the wave frequency-directional spectrum, which also
depends on

, the separation angle from the source storm of the swell on the Earth's sphere.
They compare the measurements with academic linear decay

φ

α i which corresponds to an
idealistic scenario of swell propagating over the global oceans, without even viscosity
included. Such a scenario would be observed in the case of no energy lost by the wave
field, i.e. the decay is due to the spatial expansion of the energy front only.
The first obvious energy sink in any fluid motion is that due to viscosity. The viscosity
of water, however, is too small to have any significance in dissipating the energy of dom-
inant wind-generated waves directly (e.g. Lamb , 1932 , although indirectly its role is very
important in promoting wave-induced turbulence as will be discussed later in this section).
For the swell, Ardhuin et al. ( 2009a ) found that indeed dissipation of the small-amplitude
swells can be explained by the viscous dissipation with measured

α corresponding to the

scales of 20000 km or more.
However, for a swell steepnesses of

H
λ

s = > 0 . 005 (7.61)

α is not constant and depends on steepness. As a result, decay of swell energy is always

larger, sometimes by several orders of magnitude, than that expected from the theory for
molecular viscosity, under ambient temperature and pressure. “Steep swells lose a signifi-
cant fraction of their energy, up to 65% over a distance as short as 2800 km”. In terms used
in this topic, steepness (7.61) can be converted into

= ak > ≈ 0 . 016 (7.62)

and is a threshold indicator in the swell-attenuation behaviour.
Other mechanisms of ocean-wave decay unrelated to breaking, i.e. such that can persist
both in the presence and absence of breaking, are due to interactions of waves with turbu-
lence, both in the water and in the air (see e.g. and The WISE Group , 2007 ). These can
either be background turbulence or wave-induced turbulence, that is turbulence that owes
its existence to the mean wave motion itself.
In the laboratory, it is possible to investigate wave motion and propagation in a turbulence-
free water environment (e.g. Babanin , 2006 ; Babanin & Haus , 2009 ; Dai et al. , 2010 ), but