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where u orb
rms
is the rms orbital velocity and
α
0
.
4 is Heisenberg's constant ( Ve r o n &
Melville , 1999 ). The larger the dissipation rate
dis , the higher will be the Kolmogorov
interval of the spectrum V
(
f
)
.
dis is the dissipation rate per unit of volume, and to obtain the total dissipation in
the water column per unit of area D a , one needs to integrate
Term
dis (
z
)
over the water depth z
=
=
from the surface z
0tothebottom z
d :
d
0 dis (
D a =
z
)
dz
.
(5.67)
dis (
)
To perform the integration, either continuous measurements of the
profile or its
parameterisation as a function of depth are required. Knowledge of the parameterisation
is obviously preferable as it enables estimation of the total dissipation on the basis of a
single-depth measurement of the spectrum (5.66) .
There is, however, no general agreement on the parameterisation of the vertical dissipa-
tion distribution
z
dis (
z
)
. In the classical theory of the boundary layer over a solid wall,
dis
is a simple inverse function of distance z to the wall:
z 1
dis (
z
)
(5.68)
(see e.g. Landau & Lifshitz , 1987 ). Early measurements in the boundary layer beneath the
wavy surface found the
dis -depth distribution to be consistent with this wall-layer theory
( Arsenyev et al. , 1975 ; Dillon et al. , 1981 ; Oakey & Elliott , 1982 ; Jones , 1985 ; Soloviev
et al. , 1988 ). More recently, however, both by direct and indirect means it was shown that,
at least at strong wind forcing, the dissipation
dis close to the water surface may exceed
the wall-layer values by up to two orders of magnitude ( Agrawal et al. , 1992 ; Melville ,
1994 ; Drennan et al. , 1996 ; Terray et al. , 1996 ). Terray et al. ( 1996 ) and Drennan et al.
( 1996 ) parameterised the vertical dissipation profile as
const
z
<
H ,
dis (
z
) =
(5.69)
z 2
z
H .
Based on considerations of the expected total wind input which should match the total
dissipation, it was found that H approximately scales with significant wave height H s as
H
=
0
.
6 H s
(5.70)
( Terray et al. , 1996 ; Drennan et al. , 1996 ). Later refined studies of Soloviev & Lukas
( 2003 ) and Gemmrich & Farmer ( 2004 ) confirmed the existence of enhanced near-surface
turbulence due to breaking, but pointed out that the scaling H of the constant-dissipation
level is still an issue.
At Lake George (see Section 3.5 about the Lake George experiment), turbulence spec-
tra V
were measured by acoustic Doppler velocimeters (ADV) as described by Young
et al. ( 2005 ) in greater detail. Under reasonably strong wind forcing, such spectra exhibited
distinct Kolmogorov intervals as shown in Figure 5.36 . A vertical profile of these turbu-
lence spectra is plotted in the figure. The ADV was traversed down from the surface in
(
f
)
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