1 CORIE circulation modeling system Simulation databases Daily forecasts Codes: SELFE, ELCIRC 3D baroclinic Unstructured grids

2 POM 1/ ROMS 2 MICOM 3 MOM 4 FVCOM 5 SEOM 6 ADCIRC /QUODDY 7 UnTRIM/ ELCIRC 8 SELFE 9 Horizontal gridStru. Unstr. Vertical representation  - or S- coord isopycnicz-coordS-coord  -coord z-coord  -coord Numerical algorithmFD FVSEFEFD/FVFE/FV Continuity wave or primitive equations PE GWCEPE Wetting and dryingNo YesNo2D ADCIRC only Yes Mode splittingYes No Advection treatmentEul ELM 1.Princeton Ocean Model (POM) (Mellor and Blumberg) 2.Regional Ocean Modeling System, Haidvogel et al. (Rutgers Univ.) 3.Miami Isopycnic Model, Bleck et al. (University of Miami) 4.Modular Ocean Model, Bryan and Cox, GFDL 5.Finite Volume Community Ocean Model, C. Chen (University of Massacusetts) 6.Spectral Element Ocean Model, Levin et al. (Rutgers Univ.) 7.Advanced Circulation, Luettich et al. (Univ. of UNC, Waterway Experiment Station of Army Corp of Engineers): QUODDY, Lynch et al. (Dartmouth College) 8. Unstructured Tidal River Inter-tidal Mudflat, Casulli (Univ. of Trento, Italy); Eulerian-Lagrangian Circulation, Zhang, Baptista & Myers (OHSU) 9. Semi-implicit Eulerian-Lagrangian Finite Element, Zhang and Baptista (OHSU)

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

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

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

6 Consider a control volume of infinitesimal size dx dy dz Mass inside volume = Let density = Let velocity = Mass flux into the control volume = Mass flux out of the control volume = Conservation of mass - water Adapted from Arun Chawla’s class notes for EBS575/675 Introduction to Fluid Dynamics

7 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 Conservation of mass Adapted from Arun Chawla’s class notes for EBS575/675 Introduction to Fluid Dynamics and, after differentiation by parts

8 Rearranging, For incompressible fluids, like water and, thus Conservation of mass Adapted from Arun Chawla’s class notes for EBS575/675 Introduction to Fluid Dynamics

9 Consider a 1D system with stationary fluid and a solute that is diffusing 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 Conservation of mass of a solute dx dy Adapted from Arun Chawla’s class notes for EBS575/675 Introduction to Fluid Dynamics

10 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 Conservation of mass of a solute Adapted from Arun Chawla’s class notes for EBS575/675 Introduction to Fluid Dynamics

11 How do we quantify q ? 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 Conservation of mass of a solute Adapted from Arun Chawla’s class notes for EBS575/675 Introduction to Fluid Dynamics

12 Based on these observations, Adolph Fick (1855) hypothesized that 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 (molecular processes are represented by an empirical coefficient analogous to viscosity) Conservation of mass of a solute Adapted from Arun Chawla’s class notes for EBS575/675 Introduction to Fluid Dynamics