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Figure 5.38 Dimensional profile of dissipation dis (denoted as in this figure) versus distance to
the surface z , obtained from the turbulence spectra shown in Figure 5.36 . The line of best fit and its
correlation coefficient are shown. Figure is reproduced from Young & Babanin ( 2006a ) © American
Meteorological Society. Reprinted with permission
an amount, however, is never greater than 50%, usually much less ( Melville et al. , 1992 ),
and therefore a reasonable match indicated by (5.73) has to be expected.
In order to verify which of the parameterisations (5.68) or (5.69) is to be used for the
integration (5.67) in the general case, Babanin et al. ( 2005 ) estimated and compared B a ,
D a
and I a . For that, a set of records for which the wind input I a was directly recorded ( Donelan
et al. , 2006 ) was chosen for the analysis. Bottom friction B a was measured by means of
physical modelling of the respective wave conditions in a laboratory flume with the bottom
covered with Lake George mud ( Babanin et al. , 2005 ), and the ADV-obtained
dis were
integrated over the depth using both (5.68) and (5.69) .
The vertical profile of
dis for the Figure 5.36 spectra is shown in Figure 5.38 . The profile
is very close to quadratic and therefore parameterisation (5.69) was first used to estimate
the dissipation D a .
The corresponding total dissipation T a (5.73) is plotted versus the total wind input I a in
Figure 5.39 . The data separate into two groups. For records with wind speed U 10 <
s
(five points on the left), the total dissipation is significantly overestimated. It is, however,
somewhat underestimated for the winds U 10 >
7
.
5m
/
7
.
5m
/
s (points on the right).
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