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

Mean density anomaly Mean principal-axis flow

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:

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.

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.

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

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

Along estuary: pressure gradient balanced by friction

S0

S0 Mean density anomaly Mean principal-axis flow