1. Estuarine Hydrodynamics
Arnoldo Valle-Levinson
University of Florida
Civil and Coastal Engineering Department
Gainesville, Florida

2. What is an estuary? Estuaries Coastal lagoons
Semi-enclosed coastal body of water
free communication with ocean
ocean salinity is measurably diluted by runoff

3. Types of Estuaries According to Their Origin
(Pinet, 2003)
Types of Estuaries According to Their Origin

4. (Pinet, 2003)

5. (Pinet, 2003)

6. San Francisco Bay
(Pinet, 2003)

7. Typical Estuarine Circulation

8. Types of Estuaries According to Their Stratification
(Pinet, 2003)
Competition between
tidal forcing and buoyancy forcing

9. Typical circulation in a fjord
Typical profile of net velocity
mouth
head
Typical profile of salinity (density)
depth

10. (Pinet, 2003)

11. Rio de la Plata Estuary
Argentina

12. (Pinet, 2003)

13. Axial Salinity Distributions
mouth
Axial Salinity Distributions
Chesapeake Bay
Spring of 1999

14. (Pinet, 2003)

15. Example of Well-Mixed Estuary

16. Types of Estuaries According to their water balance
Net Mass Loss
No Mass Loss

17. Inverse Estuary Normal Estuary Looking into lagoon
Red = Water going out
Blue = Water going in
Inverse Estuary
Normal Estuary

18. Salt-plug estuary
E ≥ R
M. Tomczak’s Web Site

19. Review of conservation equations
Mass and Momentum

20. Flux of mass out (kg/s) =
, w
, v
Mass per area per time
(kg/(m2 s))
Flux of mass in (kg/s) =
Flux of mass out (kg/s) =
Net Flux of mass in ‘x’ =
Net Flux of mass in ‘y’ =
Net Flux of mass in ‘z’ =

21. The change of mass per unit time going through the volume element is:
And the change of mass per unit time per unit volume is:
which is the same as: or

22. Boussinesq approximation
This is the Continuity Equation or Equation of Conservation of Mass

23. z x
Continuity Equation in Bulk Form:

24. Advective flux of salt/unit area
, w
, v
Conservation of Salt
Advective flux of salt/unit area
Diffusive flux of salt/unit area
Flux of salt into dydz =
Flux of salt out of dydz =
Net Flux of Salt in ‘x’ =

25. Salt Conservation Net Flux of Salt in ‘y’ = Net Flux of Salt in ‘z’ =
Net Salt Flux per unit volume =
Salt Conservation

26. Advection-Diffusion Equation
Conservation of Salt:
At steady state and assuming constant diffusivities:
Advection-Diffusion Equation
Further assuming motion in one direction and
integrated over the volume considered,
the statement of CONSERVATION OF SALT may be given as:
Vin Sin = Vout Sout

27. z Sb S0 x
Continuity Equation in Bulk Form:
Salt Conservation Equation in Bulk Form: VbSb = V0S0

28. Conservation of Salt:
Conservation of Heat:
Equation of State:

29. TEOS-10 Manual
“Thermodynamic properties of seawater are more accurately represented as functions of SA than of SP.”
Reference Composition Salinity SR does have units!
SR = /35 Sp (g/kg)

30. Still much work to be done on SA
Absolute Salinity SA : “ratio of the mass of dissolved material in sea water to the mass of sea water.”
----- cannot be measured in practice.
Reference Salinity SR gives our best estimate of SA
SA = SR + SA
SR = /35 Sp (g/kg)
(From TEOS-10 Manual)
Still much work to be done on SA

31. TEOS-10

32. TEOS-10

33. 90 % of Ocean Water Greater influence of salinity on density
Mean T & S for World Ocean
Greater influence of salinity on density

34. Effects of Temperature and Salinity on Density
Thermal Expansion
Saline Contraction
x 10-4 oC-1
x 10-4 S-1
Density changes by 0.2 kg/m3 for a T change of 1oC,
and by 0.8 kg/m3 for a S change of 1.

35. Conservation of Momentum (Equations of Motion)

36. Pressure gradient: Barotropic and Baroclinic
+ friction
+ tides
+ gravity
+ Coriolis
Pressure gradient: Barotropic and Baroclinic
Friction: Surface, bottom, internal
Tides: Boundary condition
Gravity: Only in the vertical
Coriolis: Only in the horizontal
REMEMBER, these are FORCES PER UNIT MASS

37. Pressure gradient: Barotropic and Baroclinic
+ friction
+ tides
+ gravity
+ Coriolis
Pressure gradient: Barotropic and Baroclinic
Friction: Surface, bottom, internal
Tides: Boundary condition
Gravity: Only in the vertical
Coriolis: Only in the horizontal
REMEMBER, these are FORCES PER UNIT MASS

38. Pressure gradient force per unit mass
Hydrostatic Pressure
Total Pressure
Pressure gradient force per unit mass
Barometric Barotropic Baroclinic
Note that even if the density is constant with depth, the horizontal pressure gradient increases with depth if there is a horizontal density gradient

39. Pressure gradient: Barotropic and Baroclinic
+ friction
+ tides
+ gravity
+ Coriolis
Pressure gradient: Barotropic and Baroclinic
Friction: Surface, bottom, internal
Tides: Boundary condition
Gravity: Only in the vertical
Coriolis: Only in the horizontal
REMEMBER, these are FORCES PER UNIT MASS

40. Gravity
[0, 0, g] = [0, 0, 9.81]
Coriolis
[-fv, fu, 0]