1. Estuarine models: what is under the hood?
Correlation skill
0 psu
Bottom salinity
34 psu

2. Lin and Kuo 2003

3. Variables
Sediment concentration: C
Velocities: u, v, w
Water level: 
Water density: 
Salinity and temperatures: S, T
Basic variables: 7 (excludes sediment concentration)
Equations needed: 7

4. Process Differential Equations Boundary conditions Topology/
bathymetry + +
Numerical
algorithm
Discretization
(grid)
Algebraic
equations
Code &
computer
Post-processing
Solution
(variables are known
at grid locations)
Skill assessment

5. Topology/bathymetry

6. Discretization Refined grid (“hi-res”) fDB16 # nodes: 27416
# elements:
#  levels
min element area: m^2
max element area: m^2
Refined grid
(“hi-res”)
fDB16

7. Grays River: example of cascading grids

8. Grays river: detail

9. Introduction to governing equations
Continuity
Depth-averaged form:
Salt and heat conservation

10. Introduction to governing equations
Conservation of momentum
(from Newton’s 2nd law: f=ma)

11. Introduction to governing equations
Equation of state
 =  (s, T, p)
Turbulence closure equations

12. Conservation of mass - water
Consider a control volume of infinitesimal size dz dy dx
Let density =
Let velocity =
Mass inside volume =
Mass flux into the control volume =
Mass flux out of the control volume =

13. Conservation of mass-water
Conservation of mass states that
Rate of change of mass inside the system =
Mass flux into of the system – Mass flux out the system
Thus
and, after differentiation by parts

14. Conservation of mass - water
Rearranging,
For incompressible fluids, like water
and, thus

15. Conservation of mass of a solute
Consider a 1D system with stationary fluid and a solute that is diffusing dz dy dx
Let flux of mass per unit area entering the system =
Let flux of mass per unit area leaving the system =
Let concentration (mass /unit volume) of solute inside the control volume = C

16. Conservation of mass of a solute - diffusion
Conservation of mass states that
Mass flux of solute leaving the system – mass flux of solute entering the system =
rate of change of solute in the system
Thus or or

17. Conservation of mass of a solute - diffusion
How do we quantify qD ?
In a static fluid, flux of concentration (q), occurs due to random molecular motion
It is not feasible to reproduce molecular motion on a large scale.
Thus, we wish to represent the molecular motion by the macroscpoic property of the solute (its concentration, C)
Also, from observation we know
In a fluid of constant C (well mixed liquid), there is no net flux of concentration
Solute moves from a region of high concentration to regions of low concentration
Over some finite time scale, the solute does not show any preferential direction of motion

18. Conservation of mass of a solute - diffusion
Based on these observations, Adolph Fick (1855) hypothesized that
(molecular processes are represented by an empirical coefficient analogous to diffusivity)
or in three dimensions
Fick’s law
Diffusion coefficient
Applying Fick’s law to the 1D mass conservation equation for a solute, we get or