Modeling Ocean Currents in COMSOL

Reza Malek-MadaniKevin McIlhany

U. S. Naval Academy

24 Oct, 2006

rmm@usna.edu

CCBOM• Center for Chesapeake Bay

Observation and Modeling– Mathematics– Oceanography– Physics– Ocean Engineering– Chemistry

Acoustic Wave and Current Profiler (AWAC)

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

dx/dt = u(x, y, z, t),

dy/dt = v(x, y, z, t)

Bathymetry

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

Particle Fate – in MATLAB

• 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

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

Stommel’s model

b

yAx

sin

1948 paper,Key Assumptions: 2D, Steady, Rectangular Basin, Bottom FrictionKey Features: Wind stress, CoriolisKey Findings: Boundary Layer (“Gulf Stream”)

b

yAx

sin

Boundary conditions: = 0 on all four boundaries

= stream function

Scales:

N. Atlantic Basin: 10,000 Km by 6000 KmDepth: 200 MetersCoriolis Parameter: 10^(-13)

Munk’s Model

),(2 yxfx

Zero boundary conditions

Multiphysics approach

Non –Rectangular Geometries