Field and Numerical Studies of Near-Bed Aggregate Dynamics
189
4
Relating the Diffusion-Advection Equation to the Hydrodynamic Regime
The hydrodynamic regime is defined according to the law of the wall. For each
experiment the velocity profile in the BBL is defined by the current velocity at
100 cm above the seafloor (u IOO ), by"no slip" at the sediment-water interface and
by the sediment roughness height (zo)' Depending on the mean velocity (u) the
friction velocity U*, which is required in the following, can be calculated by:
(2)
According to Newberger and Caldwell (1981), two approaches have been used
to describe the distribution of A(z) in the BBL. In one case, the coefficient Ac(z)
was set to a constant value for all model layers (Table 1, experiment 1). The subscript c indicates a constant diffusion coefficient over the total model height.
However, their results suggest that A(z) should be linearly proportional to the
friction velocity and the height above the seafloor. Thus, the hydrodynamic regime is taken into account and the formulation for A(z) is
A(z) = u.z k,
following the standard textbooks on boundary layer hydrodynamics.
Table la Ranges for variables used in the numerical experiments
without particle interaction included. In all experiments, aggregates were distributed among three aggregate size classes of
0.000066,0.000128 and 0.000234 m in diameter for the according
settling velocities of 30, 50 and 80 mday-1 (Gibbs 1985). In all nine
cases, the initial conditions of each size class were 50 g m- 3 distributed homogeneously from 0-1 m above the seafloor amounting to
a total mass of 50 g in each aggregate size class. In all experiments
Zo was set at 0.001 (m).
Hydrodynamic
Hydrodynamic
Hydrodynamic
parameter
regime 1
regime 2
ulOO (m S-l)
0.1
0.5
Alc,ld(z) (m 2 s- 1 )
0.0-0.042
0.0-1.250
u. (m S-l)
0.006
0.03
Height of the
23.7
118.7
boundary layer (m)
Dissipation energy, 9.0 x 10- 11 _4.6 X 10- 5 1.1 x 10- 8 -0.0058
E, (m 3 S-2)
Kolmogorov length, 0.0006-0.0161
0.00018-0.0048
A (z), (m)
(3)
189
4
Relating the Diffusion-Advection Equation to the Hydrodynamic Regime
The hydrodynamic regime is defined according to the law of the wall. For each
experiment the velocity profile in the BBL is defined by the current velocity at
100 cm above the seafloor (u IOO ), by"no slip" at the sediment-water interface and
by the sediment roughness height (zo)' Depending on the mean velocity (u) the
friction velocity U*, which is required in the following, can be calculated by:
(2)
According to Newberger and Caldwell (1981), two approaches have been used
to describe the distribution of A(z) in the BBL. In one case, the coefficient Ac(z)
was set to a constant value for all model layers (Table 1, experiment 1). The subscript c indicates a constant diffusion coefficient over the total model height.
However, their results suggest that A(z) should be linearly proportional to the
friction velocity and the height above the seafloor. Thus, the hydrodynamic regime is taken into account and the formulation for A(z) is
A(z) = u.z k,
following the standard textbooks on boundary layer hydrodynamics.
Table la Ranges for variables used in the numerical experiments
without particle interaction included. In all experiments, aggregates were distributed among three aggregate size classes of
0.000066,0.000128 and 0.000234 m in diameter for the according
settling velocities of 30, 50 and 80 mday-1 (Gibbs 1985). In all nine
cases, the initial conditions of each size class were 50 g m- 3 distributed homogeneously from 0-1 m above the seafloor amounting to
a total mass of 50 g in each aggregate size class. In all experiments
Zo was set at 0.001 (m).
Hydrodynamic
Hydrodynamic
Hydrodynamic
parameter
regime 1
regime 2
ulOO (m S-l)
0.1
0.5
Alc,ld(z) (m 2 s- 1 )
0.0-0.042
0.0-1.250
u. (m S-l)
0.006
0.03
Height of the
23.7
118.7
boundary layer (m)
Dissipation energy, 9.0 x 10- 11 _4.6 X 10- 5 1.1 x 10- 8 -0.0058
E, (m 3 S-2)
Kolmogorov length, 0.0006-0.0161
0.00018-0.0048
A (z), (m)
(3)