Biorthogonal decomposition analysis and reconstruction of spatiotemporal chaos generated by coupled wakes

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Abstract
Very often in hydrodynamics, the description of the complexity of flows can only be achieved by the use of simple models. These models, obtained usually by phenomenological arguments, need in general the knowledge of some parameters. The challenge is then to determine the values of these parameters from experiments. Here, our concern is the description of a coupled wakes experiment using a complex Ginzburg-Landau equation (GLE). Our analysis is based on a proper decomposition of experimental spatiotemporal chaotic flow fields, followed by a projection of the GLE onto the proper directions. We show that our method is able to recover the parameters of the model which permit us to reconstruct the spatiotemporal chaos observed in the experiment. As it is based on a general projection principle, this method is general and could be applied to other systems.