THE NEAR-SURFACE LAYER OF THE OCEAN
al. (1996) parameterization (3.47) than with the original Terray et al. (1996)
model (3.27). Note that no tuning coefficients are available in the original
Terray et al. (1996) model. Model (3.52) predicts lower values of dissipation
than model (3.27) in the l ayer, z > 0.4 H s ; above this layer, model (3.52) has
larger dissipation rates than (3.27).
A possible reason for this difference is the use of the wave following
versus fixed co-ordinate system. If the wave breaking energy substantially
dissipates above the trough line, and the vertical dissipation rate profile is a
nonlinear function of depth, then the difference between fixed and wavefollowing measurements can be significant. For instance, in a fixed
coordinate system it is practically impossible to study near-surface layers
with a thickness less than the surface wave height. In fact, any observational
point between the wave trough and crest will alternate between water and
air. Therefore, in order to study turbulence above the trough line, a wavefollowing coordinate system is required. We follow here Csanady’s (1984)
suggestion to analyze the near-surface data in the coordinate system
connected to the ocean surface. The Craig and Banner (1994) model is
consistent with the Csanady (1984) concept. The Terray et al. (1996) model,
which is originally fit to tower-based data, would produce a different
dissipation profile in the wave-following coordinate system.
Two other possible reasons for unresolved differences between (3.27)
and (3.52) can be related to the fact that model (3.27) is substantially based
on the fit to a tower-based data set. The standard Taylor hypothesis of a
frozen field of turbulent eddies cannot be directly applied for the turbulence
analysis of the tower-based measurements because the velocity fluctuation is
not small relative to the mean flow. Also, nonlinear components of surface
waves, which are not removed from the tower-based velocity records, might
result in an overestimation of H.
It should be noted that there is no reliable estimate of the average
dissipation rate within the wave-turbulent layer |z| < 0.6H s in the literature.
The constant dissipation rate that is set in (3.27) for |z| < 0.6 H s is not based
on any experimental data; it results from energy constraints. In Soloviev and
Lukas (2003), the dissipation data were averaged in a wave-following coordinate system and were available starting from a depth |z| = 0.1H s . These
estimates of the dissipation rate in the layer stirred by breaking surface
waves could, however, be biased because of extensive editing of the bubbledisturbed segments. This editing procedure might exclude the most energetic
turbulence events associated with breaking waves from the statistics. The
experimental dissipation profile systematically deviates from model (3.52)
for |z| < 0.6 H s (Figure 3-18a). In the layer 0.1 H s < |z| < 0.6 H s , the integral
dissipation rate,
z dz
H
³
, is about 5 times less than that predicted by model
(3.52). This suggests that during these measurements about 80% of the wave
energy dissipating in the layer stirred by breaking waves might be
186
al. (1996) parameterization (3.47) than with the original Terray et al. (1996)
model (3.27). Note that no tuning coefficients are available in the original
Terray et al. (1996) model. Model (3.52) predicts lower values of dissipation
than model (3.27) in the l ayer, z > 0.4 H s ; above this layer, model (3.52) has
larger dissipation rates than (3.27).
A possible reason for this difference is the use of the wave following
versus fixed co-ordinate system. If the wave breaking energy substantially
dissipates above the trough line, and the vertical dissipation rate profile is a
nonlinear function of depth, then the difference between fixed and wavefollowing measurements can be significant. For instance, in a fixed
coordinate system it is practically impossible to study near-surface layers
with a thickness less than the surface wave height. In fact, any observational
point between the wave trough and crest will alternate between water and
air. Therefore, in order to study turbulence above the trough line, a wavefollowing coordinate system is required. We follow here Csanady’s (1984)
suggestion to analyze the near-surface data in the coordinate system
connected to the ocean surface. The Craig and Banner (1994) model is
consistent with the Csanady (1984) concept. The Terray et al. (1996) model,
which is originally fit to tower-based data, would produce a different
dissipation profile in the wave-following coordinate system.
Two other possible reasons for unresolved differences between (3.27)
and (3.52) can be related to the fact that model (3.27) is substantially based
on the fit to a tower-based data set. The standard Taylor hypothesis of a
frozen field of turbulent eddies cannot be directly applied for the turbulence
analysis of the tower-based measurements because the velocity fluctuation is
not small relative to the mean flow. Also, nonlinear components of surface
waves, which are not removed from the tower-based velocity records, might
result in an overestimation of H.
It should be noted that there is no reliable estimate of the average
dissipation rate within the wave-turbulent layer |z| < 0.6H s in the literature.
The constant dissipation rate that is set in (3.27) for |z| < 0.6 H s is not based
on any experimental data; it results from energy constraints. In Soloviev and
Lukas (2003), the dissipation data were averaged in a wave-following coordinate system and were available starting from a depth |z| = 0.1H s . These
estimates of the dissipation rate in the layer stirred by breaking surface
waves could, however, be biased because of extensive editing of the bubbledisturbed segments. This editing procedure might exclude the most energetic
turbulence events associated with breaking waves from the statistics. The
experimental dissipation profile systematically deviates from model (3.52)
for |z| < 0.6 H s (Figure 3-18a). In the layer 0.1 H s < |z| < 0.6 H s , the integral
dissipation rate,
z dz
H
³
, is about 5 times less than that predicted by model
(3.52). This suggests that during these measurements about 80% of the wave
energy dissipating in the layer stirred by breaking waves might be
186