DIFFUSION OF TURBIDITY BY SHEAR
EFFECT AND TURBULENCE IN THE
SOUTHERN BIGHT OF THE NORTH SEA
JACQUES C. J. NIHOUL
lnstirul tie Mathimatiquu. Unfoersity of Likgu, Belgium
1. INTRODUCTION
Concerned with the alarming state of pollution in the North Sea. the
Belgian Government initiated in 1971 extensive experimental and theoretical investigations of the Southern Bight (51 ' N-53" N).
The Southern Bight is an irregular shallow area where very strong tidal
currents (up to 1 m/s) are encountered. Observations indicated that the
water column is fairly well mixed and that the shear eflect (associated with
the tidal currents) plays an essential rok in the dispersion of pollutants
(Nihoul, 1972).
The appellation sheur eflect is widely used to denote similar but not
identical phenomena. In this context, it is meant in the following sense:
space average concentrations (say over the depth or over the cross section)
are governed by equations whioh are derived from the threedimensional
ones by space integration. In this process, the quadratic convection terms
give two contributions, the first of which represents tbe advection by the
mean motion while the second contains the mean product of deviations
around the means and contributes to the dispersion.
This effect has been described by several authors in pipes. channels, and
estuaries where, after integration over the cross-section, the flow-steady or
oscillating-is essentially in one direction (Taylor, 1953, 1954; Elder, 1959;
Bowden, 1965).
In the shallow waters of the Southern Bight, it is generally sufficient :o
consider the mean concentrations over the depth but, out at sea, no further
averaging is possible and the dispersion mechanism is fundamentally two
dimensional. Thus the models valid for estuarine ditfusion must be generalized to account for the rotation of the tidal velocity vector (Nihoul, 1972).
In addition, to study and control the dumping of industrial wastes, the
model must include the sedimentation of the solid suspensions. Some of the
331
EFFECT AND TURBULENCE IN THE
SOUTHERN BIGHT OF THE NORTH SEA
JACQUES C. J. NIHOUL
lnstirul tie Mathimatiquu. Unfoersity of Likgu, Belgium
1. INTRODUCTION
Concerned with the alarming state of pollution in the North Sea. the
Belgian Government initiated in 1971 extensive experimental and theoretical investigations of the Southern Bight (51 ' N-53" N).
The Southern Bight is an irregular shallow area where very strong tidal
currents (up to 1 m/s) are encountered. Observations indicated that the
water column is fairly well mixed and that the shear eflect (associated with
the tidal currents) plays an essential rok in the dispersion of pollutants
(Nihoul, 1972).
The appellation sheur eflect is widely used to denote similar but not
identical phenomena. In this context, it is meant in the following sense:
space average concentrations (say over the depth or over the cross section)
are governed by equations whioh are derived from the threedimensional
ones by space integration. In this process, the quadratic convection terms
give two contributions, the first of which represents tbe advection by the
mean motion while the second contains the mean product of deviations
around the means and contributes to the dispersion.
This effect has been described by several authors in pipes. channels, and
estuaries where, after integration over the cross-section, the flow-steady or
oscillating-is essentially in one direction (Taylor, 1953, 1954; Elder, 1959;
Bowden, 1965).
In the shallow waters of the Southern Bight, it is generally sufficient :o
consider the mean concentrations over the depth but, out at sea, no further
averaging is possible and the dispersion mechanism is fundamentally two
dimensional. Thus the models valid for estuarine ditfusion must be generalized to account for the rotation of the tidal velocity vector (Nihoul, 1972).
In addition, to study and control the dumping of industrial wastes, the
model must include the sedimentation of the solid suspensions. Some of the
331