336
JACQUES C: . J. NWOUL
a physical point of view. If the sedimentation velocity is important, the
particles-although a high friction velocity may prevent their deposition
and maintain them in suspension-will tcnd to concentrate in a region
closer to the bottom whcre the velocity is smaller than the mean velocity.
The second term in the b!?-hand side of Eq. (16) thus overeetimatcs the real
advcction of those p a r t h and this is corrected by the first part of the shear
effect. (Of course the argument does not apply if the concentration becomes
too large since the whok model is b m d 011 the hypothesis of weak
in homogenei ties.)
The second term in the right-hand side of Eq. (26) may be interpreted as a
dispersion term and appears as a natural generalization to variable depth
and twodimensional horizontal flows of Bowden's results (Bowden, 1965).
Combining Eqs. (16) and (26) and introducing a horizontal eddy diffusivity p, one obtains
This equation has been used extensively in modelling the dispersion of
pollutants in the Southern Bight. The velocity 1 and depth H are either
measured or calculated by a separate numerical model combining the effects
of winds and tides. The ooeffkicnts yI, yl, and fi can bt estimated theoretically but they are as w i l y determined by nupwrbl simulation if, as often,
observations are available for refmnae. Tba calculated values agree well
with the theoretical predictions.
Examining the sacond term in the right-band side of Eq. (30). one can see
that the shear &wt produces a diffusion in the direction of the instantaneous velocity with an apparent diffusivity of the order of uH. The isotropic
turbulent dispersion represented by the laet tMm of Eq. (30) is usually much
smaller as the eddy dithreivity p can be two orders of magnitude smaller than
uH. After one or two tidal periods, thera result0 an enhanced dispersion in
the direction of the maximum tidal velocity. Rapid variations of depth and
strong winds can of coursc modify the situation but the tendency remains
and the patches of pollutants haw very often an elongated shnpe with a
maximum dispersion roughly in the dimtion of the maximum current.
This prediction of the model well veriflad by thc observations (Nihoul,
1971).
One of the consequences of the cogent influewe of the shear effect is that
the second-order operator in Eq. (30) is nearly parabolic; the dominant
JACQUES C: . J. NWOUL
a physical point of view. If the sedimentation velocity is important, the
particles-although a high friction velocity may prevent their deposition
and maintain them in suspension-will tcnd to concentrate in a region
closer to the bottom whcre the velocity is smaller than the mean velocity.
The second term in the b!?-hand side of Eq. (16) thus overeetimatcs the real
advcction of those p a r t h and this is corrected by the first part of the shear
effect. (Of course the argument does not apply if the concentration becomes
too large since the whok model is b m d 011 the hypothesis of weak
in homogenei ties.)
The second term in the right-hand side of Eq. (26) may be interpreted as a
dispersion term and appears as a natural generalization to variable depth
and twodimensional horizontal flows of Bowden's results (Bowden, 1965).
Combining Eqs. (16) and (26) and introducing a horizontal eddy diffusivity p, one obtains
This equation has been used extensively in modelling the dispersion of
pollutants in the Southern Bight. The velocity 1 and depth H are either
measured or calculated by a separate numerical model combining the effects
of winds and tides. The ooeffkicnts yI, yl, and fi can bt estimated theoretically but they are as w i l y determined by nupwrbl simulation if, as often,
observations are available for refmnae. Tba calculated values agree well
with the theoretical predictions.
Examining the sacond term in the right-band side of Eq. (30). one can see
that the shear &wt produces a diffusion in the direction of the instantaneous velocity with an apparent diffusivity of the order of uH. The isotropic
turbulent dispersion represented by the laet tMm of Eq. (30) is usually much
smaller as the eddy dithreivity p can be two orders of magnitude smaller than
uH. After one or two tidal periods, thera result0 an enhanced dispersion in
the direction of the maximum tidal velocity. Rapid variations of depth and
strong winds can of coursc modify the situation but the tendency remains
and the patches of pollutants haw very often an elongated shnpe with a
maximum dispersion roughly in the dimtion of the maximum current.
This prediction of the model well veriflad by thc observations (Nihoul,
1971).
One of the consequences of the cogent influewe of the shear effect is that
the second-order operator in Eq. (30) is nearly parabolic; the dominant