1. Modeling Ocean Currents in COMSOL Reza Malek-Madani Kevin McIlhany U. S. Naval Academy 24 Oct, 2006 rmm@usna.edu

2. CCBOM Center for Chesapeake Bay Observation and Modeling –Mathematics –Oceanography –Physics –Ocean Engineering –Chemistry Acoustic Wave and Current Profiler (AWAC)

3. Velocity Vector Field, Chesapeake Bay, Dec 27, 1999, Courtesy of Tom Gross, NOAA, Coastal Survey Division http://chartmaker.ncd.noaa.gov/csdl/op/images/UVanim.gif

4. dx/dt = u(x, y, z, t), dy/dt = v(x, y, z, t)

5. Bathymetry

6. Deformation –in MATLAB (N. Brasher, RMM, G. Fowler )

7. Particle Fate – in MATLAB

8. How do the errors in the velocity field affect the errors in the dynamical systems computations and the particle fates? Are the statistics of the particle trajectories stable and realizable relative to the statistics of the velocity field? Are stable and unstable manifolds of the system dx/dt = u, dy/dt = v computable if u and v are known only locally in time (90 day date length) and in space (incomplete data collection)? New hydrodynamic model

9. Goals and Strategy Goals: –Obtain velocity field for the dynamics of the Chesapeake Bay, based on real wind and planetary forcing, and –Apply dynamical systems tools to the velocity field to understand transport and mixing in the Bay. Strategy: First consider reduced models. –Qualitative Models: Simple geometry – Emphasis on PDEs - Stommel, Munk, Veronis, 2 1/2 layer model, Navier-Stokes, nonlinear Ellipitic PDEs –Complex Geometries: 2D and 3D boundaries of the Chesapeake Bay. Eigenvalue and Poisson Solvers –Comparison With Quoddy (NOAA) model

10. Stommel’s model 1948 paper, Key Assumptions: 2D, Steady, Rectangular Basin, Bottom Friction Key Features: Wind stress, Coriolis Key Findings: Boundary Layer (“Gulf Stream”) Boundary conditions:  = 0 on all four boundaries y = stream function Scales: N. Atlantic Basin: 10,000 Km by 6000 Km Depth: 200 Meters Coriolis Parameter: 10^(-13)

11. Munk’s Model Zero boundary conditions Multiphysics approach

12. Non –Rectangular Geometries