unaccounted for because of bubble disturbances. Though we are using here
the averaging technique of Baker and Gibson (1987) that accounts for the
turbulence intermittency, it nevertheless may not completely compensate for
editing bubble-disturbed segments. For the same reason, the confidence
intervals might also be underestimated close to the ocean surface.
Figure 3-18b shows the same graphs but for the average dissipation rate
profile for moderate and high wind speed conditions (U 15 = 7 m s
-1 - 19.2 m
s
-1 ). The experimental profile in Figure 3-18b extends to deeper layers than
in Figure 3-18a. The interpretation of Figure 3-18b is, however, hindered
because of larger uncertainty in the significant wave height data than in
Figure 3-18a. In the experiment of Soloviev and Lukas (2003 this
uncertainty rapidly increases with the decrease of the wind speed.
The main features of the CB94 model can be summarized as follows:
1) Prandtl-type mixing length specification;
2) A turbulent kinetic energy equation representing a balance between
parameterized versions of diffusion, dissipation and shear generation;
3) The Kolmogorov-type eddy viscosity (proportional to the mixing)
length and the square root of turbulent kinetic energy;
4) Dimensionless constants (N, B, Sq, S M ) are determined from fluid
dynamics problems that are not related directly to wave enhanced
turbulence.
5) A surface turbulent kinetic energy input, due to the waves, set
proportional to the cube of the friction velocity.
We should make one final remark here about the CB94 model, which is
based on the turbulence closure scheme of Mellor and Yamada (1982).
There have been reports that this closure scheme does not work well in flows
with negligible shear-production (Umlauf and Burchard, 2001). Though the
flow in spilling wave breakers is not shear free because of intense air
entrainment leading to the formation of a bore-like structure (Section 1.6.4),
the length scale hypothesis (3.33) may not necessarily hold in this case. In
the next section we consider the model of Benilov and Ly (2002), which
intends to address this problem.
3.3.3 Benilov and Ly (2002) wave-turbulent model
The CB94 model treats breaking waves as a surface source for the
turbulent kinetic energy. Benilov and Ly (2002; hereafter BL02) considered
breaking waves as a volume source of energy. They incorporated wave
kinetic energy b w into the turbulent kinetic energy budget equation (1.24)
following ideas of Kitaigorodskii et al. (1983):
Chapter 3: NEAR-SURFACE TURBULENCE
187
)
the averaging technique of Baker and Gibson (1987) that accounts for the
turbulence intermittency, it nevertheless may not completely compensate for
editing bubble-disturbed segments. For the same reason, the confidence
intervals might also be underestimated close to the ocean surface.
Figure 3-18b shows the same graphs but for the average dissipation rate
profile for moderate and high wind speed conditions (U 15 = 7 m s
-1 - 19.2 m
s
-1 ). The experimental profile in Figure 3-18b extends to deeper layers than
in Figure 3-18a. The interpretation of Figure 3-18b is, however, hindered
because of larger uncertainty in the significant wave height data than in
Figure 3-18a. In the experiment of Soloviev and Lukas (2003 this
uncertainty rapidly increases with the decrease of the wind speed.
The main features of the CB94 model can be summarized as follows:
1) Prandtl-type mixing length specification;
2) A turbulent kinetic energy equation representing a balance between
parameterized versions of diffusion, dissipation and shear generation;
3) The Kolmogorov-type eddy viscosity (proportional to the mixing)
length and the square root of turbulent kinetic energy;
4) Dimensionless constants (N, B, Sq, S M ) are determined from fluid
dynamics problems that are not related directly to wave enhanced
turbulence.
5) A surface turbulent kinetic energy input, due to the waves, set
proportional to the cube of the friction velocity.
We should make one final remark here about the CB94 model, which is
based on the turbulence closure scheme of Mellor and Yamada (1982).
There have been reports that this closure scheme does not work well in flows
with negligible shear-production (Umlauf and Burchard, 2001). Though the
flow in spilling wave breakers is not shear free because of intense air
entrainment leading to the formation of a bore-like structure (Section 1.6.4),
the length scale hypothesis (3.33) may not necessarily hold in this case. In
the next section we consider the model of Benilov and Ly (2002), which
intends to address this problem.
3.3.3 Benilov and Ly (2002) wave-turbulent model
The CB94 model treats breaking waves as a surface source for the
turbulent kinetic energy. Benilov and Ly (2002; hereafter BL02) considered
breaking waves as a volume source of energy. They incorporated wave
kinetic energy b w into the turbulent kinetic energy budget equation (1.24)
following ideas of Kitaigorodskii et al. (1983):
Chapter 3: NEAR-SURFACE TURBULENCE
187
)