Estuary Processes and Managment - River Dynamics and Integrated River Management - page 514

Initial dilution prediction —A useful dilution formula for the initial dilution of a horizontal buoyant
jet in stagnant ambient water has been given by Cederwall (1968).

53

§ ·

z

S 0.54 F 0.38 0.66 for zD . 0.5 (8.12)

¨ ¸ c o o

DF

© ¹

o

It is seen the initial dilution is dependent on the jet densimetric Froude number and the relative depth.
Eq. (8.12) has been verified by numerical models and laboratory experiments. It can be used to estimate
the initial mixing for the worst case of no ambient current.
When the effluent is discharged into an ambient current U a , the interaction of the buoyant jet with the
ambient current leads to the formation of a vortex pair (Fig. 8.55); the mixing is significantly enhanced
from that in calm water. Field and theoretical studies have shown that the moving water dilution can be
estimated by the following equations (Lee and Neville-Jones, 1987):
For buoyancy dominated near field:

0.31 BH

13 53

HU
B

3
a

S 5 (8.13)

m

Q

where, Q is the volume flux per time, B is the kinematic bouyancy flux and H is the depth.
For buoyancy dominated far field:

2 3

a

0.32 UH

HU
B

S

a

! 5 (8.13)

m

Q

Fig. 8.55 Turbulent buoyant jet in a crossflow; the horse-shoe vortex pair in the bent-over jet leads to much greater
dilution in moving water

Similar equations for estimation of initial dilution for asymptotic flow situations (e.g., pure jet or plume
in uniform crossflow, linear stratification) can be obtained from experiments by dimensional analysis or
from numerical models (Fischer et al., 1979; Lee and Chu, 2003).
For environmental risk assessment and outfall design, it is necessary to predict the impact of effluent
discharges for a wide range of discharge and ambient conditions. Typically a general mathematical model
is employed for prediction of initial mixing (e.g., Wei et al, 1998; Liu et al., 2002). The buoyant jet trajectory
and mixing can be well predicted by a validated integral model that predicts the turbulent entrainment as
a function of source characteristics, ambient velocity, and stratification. As a case study, a general
interactive modeling system called VISJET (http://www.aoe-water.hku.hk/visjet/visjet.htm) is introduced.
As can be seen in Fig. 8.56, VISJET is based on a robust near-field jet Lagrangian model JETLAG (Lee
and Cheung, 1990; Lee and Chu, 2003) that is capable of predicting the mixing of an arbitrarily inclined