1. Freshwater input
Salty water inflow
(near the bottom)
Along the Estuary: Pressure Gradient balanced by Friction (Pritchard, 1956)

4. Mean density anomaly
Mean principal-axis flow

5. Pressure gradient vs. vertical mixing
expanding the pressure gradient:
The momentum balance then
becomes:
We can write:
O.D.E. with general solution
obtained from integrating twice:

6. General solution:
c1and c2 are determined with boundary conditions:
This gives the solution:
Third degree polynomial proportional to depth and inversely proportional to friction.
Requires knowledge of I, G, and wind stress.

7. Integrating u(z) and making it equal to R, we obtain:
We can express I in terms of River Discharge R, G ,and wind stress if we restrict the
solution to:
i.e., the river transport per unit width
provides the water added to the
system.
Integrating u(z) and making it equal to R, we obtain:
Which makes:
Note that the effects of G and R are in the same direction, i.e., increase I.
The wind stress tends to oppose I.

8. Substituting
into:
We get:
Density-induced: sensitive to H and Az; third degree polynomial - two inflection points
River induced: sensitive to H; parabolic profile
Wind-induced: sensitive to H (dubious) and Az; parabolic profile

10. If we take no bottom stress at z = -H (instead of u(-H) = 0):

14. Along estuary: pressure gradient balanced by friction

15. S0

16. S0
Mean density anomaly
Mean principal-axis flow