The spatiotemporal dynamics of the solar photosphere is studied by performing a proper orthogonal decomposition (POD) of line of sight velocity fields computed from high resolution data coming from the MDI/SOHO instrument. Using this technique, we are able to identify and characterize the different dynamical regimes acting in the system. Low-frequency oscillations, with frequencies in the range...

We propose an improved framework for dynamic mode decomposition (DMD) of 2-D flows for problems originating from meteorology when a large time step acts like a filter in obtaining the significant Koopman modes, therefore, the classic DMD method is not effective. This study is motivated by the need to further clarify the connection between Koopman modes and proper orthogonal decomposition (POD) ...

An adaptive method to accelerate time-dependent solvers for PDEs has been proposed [1,2,3] that adaptively combines on the fly a standard numerical solver and a low-dimensional system. The latter, in turn, combines POD (to identify modes) and Galerkin projection. To improve the computational efficiency of the method, it is essential to use a reduced number of points (instead of the whole comput...

This research combines Volterra theory and proper orthogonal decomposition (POD) into a hybrid methodology for reduced-order modeling of aeroelastic systems. The outcome of the method is a set of linear ordinary differential equations (ODEs) describing the modal amplitudes associated with both the structural modes and the POD basis functions for the fluid. For this research, the structural mode...

Radar remote sensing of the sea surface for the extraction of ocean surface wave fields requires separating wave and non-wave contributions to the sea surface measurement. Conventional methods of extracting wave information from radar measurements of the sea surface rely on filtering the wavenumber-frequency spectrum using the linear dispersion relationship for ocean surface waves. However, thi...

In our earlier paper [Numer. Funct. Anal. Optim. 31 (2010), no. 7-9, 852-869], we showed two separate data sets can be optimally approximated using balanced proper orthogonal decomposition (POD) modes derived from the data. In this work, we prove new results concerning the approximation capability of the balanced POD modes. We give exact computable expressions for the errors between the individ...

We present a new compact expansion of a random flow field into stochastic spatial modes, hence extending the proper orthogonal decomposition (POD) to noisy (noncoherent) flows. As a prototype problem, we consider unsteady laminar flow past a circular cylinder subject to random inflow characterized as a stationary Gaussian process. We first obtain random snapshots from full stochastic simulation...

The KelvinHelmholtz (KH) instability is a fundamental wave instability that is frequently observed in all kinds of shear layer (jets, wakes, atmospheric air currents etc). The study of KH-instability, coherent flow structures has a major impact in understanding the fundamentals of fluid dynamics. Therefore there is a need for methods that can identify and analyse these structures. In this Final...

In this paper, we propose a POD-based technique that is suitable for the design of reliable observers for the estimation of velocity field and contaminant flow for Navier–Stokes flow. POD modes are conccepted 7 December 2009 vailable online 13 January 2010 eywords: odel reduction roper orthogonal decomposition structed using the method snapshot. Karhunen–Loeve (Galerkin) projection to develop a...