Open-boundary modal analysis: Interpolation, extrapolation, and filtering

Increasingly accurate remote sensing techniques are available today, and methods such as modal analysis are used to transform, interpolate, and regularize the measured velocity fields. Until recently, the modes used did not incorporate flow across an open boundary of the domain. Open boundaries are an important concept when the domain is not completely closed by a shoreline. Previous modal analysis methods, such as those of Lipphardt et al. ( 2000), project the data onto closed-boundary modes, and then add a zero-order mode to simulate flow across the boundary. Chu et al. ( 2003) propose an alternative where the modes are constrained by a prescribed boundary condition. These methods require an a priori knowledge of the normal velocity at the open boundary. This flux must be extrapolated from the data or extracted from a numerical model of a larger-scale domain, increasing the complexity of the operation. In addition, such methods make it difficult to add a threshold on the length scale of open-boundary processes. Moreover, the boundary condition changes in time, and the computation of all or some modes must be done at each time step. Hence real-time applications, where robustness and efficiency are key factors, were hardly practical. We present an improved procedure in which we add scalable boundary modes to the set of eigenfunctions. The end result of open-boundary modal analysis (OMA) is a set of time and data independent eigenfunctions that can be used to interpolate, extrapolate and filter flows on an arbitrary domain with or without flow through segments of the boundary. The modes depend only on the geometry and do not change in time.