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2002 LAPCOD Meeting
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Open-Boundary Modal Analysis: A Complete Functional Basis to Interpolate, Extrapolate and Filter Experimental Eulerian Data
F. Lekien, C. Coulliette, J. Marsden, R. Bank
California Institute of Technology
lekien@caltech.edu(Abstract received 11/01/2002 for session B)
ABSTRACT
Developments in dynamical systems theory have brought a wide range of methods that can be used to analyze and predict Lagrangian behavior in geophysical flows. However, it requires the ocean to be described as a dynamical system, that is, a fairly smooth differential equation. Increasingly accurate remote sensing techniques are available today and it is both appealing and unavoidable to be able to use the measured velocities directly to describe a dynamical system. Modal analysis has been used in the past 30 years to extrapolate and filter noisy and incomplete data sets. Up to recently, the modes used did not correctly allow flow across an open boundary of the domain. Open boundaries are an important concept when the domain is not completely closed by a shoreline, which is typical of coastal HF radar data. Previous modal analysis methods project the data only onto closed-boundary modes, and then used an ad hoc procedure to add a zero-order mode to allow flow across the boundary. This approach has many shortcomings, the primary one being that the projection is non-optimal. Numerically speaking, the approach we highlight also has many advantages, such as solving for the eigenfunctions on an unstructured (triangular) grid, which does not require the boundary to be either a staircase or a spline, as is typical with other modal analysis methods. We present the theory and a practical use of Open-boundary Modal Analysis (OMA), a complete set of eigenfunctions that can be used to interpolate, extrapolate and filter flows on an arbitrary domain with or without flow through a segment of the boundary. Finally, we demonstrate that other typical modal analysis methods reduce to OMA in the limit of a completely closed domain.
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2002 LAPCOD Meeting, Key Largo, Florida, December 12-16, 2000