Modeling Ocean Currents in COMSOL Reza Malek-Madani Kevin McIlhany U. S. Naval Academy 24 Oct, 2006...
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Modeling Ocean Currents in COMSOL
Reza Malek-MadaniKevin McIlhany
U. S. Naval Academy
24 Oct, 2006
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CCBOM• Center for Chesapeake Bay
Observation and Modeling– Mathematics– Oceanography– Physics– Ocean Engineering– Chemistry
Acoustic Wave and Current Profiler (AWAC)
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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
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dx/dt = u(x, y, z, t),
dy/dt = v(x, y, z, t)
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Bathymetry
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Deformation –in MATLAB (N. Brasher, RMM, G. Fowler)
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Particle Fate – in MATLAB
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• 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
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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
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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)
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Munk’s Model
),(2 yxfx
Zero boundary conditions
Multiphysics approach
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Non –Rectangular Geometries
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