Reconstruction of three-dimensional flow fields from two-dimensional data

Abstract

The objective of this work is to develop a procedure that allows for reconstructing three-dimensional flow fields from two-dimensional information contained in some representative planes, conveniently distributed throughout the domain. The reconstructing tool is based on two recent methods developed by two of the authors, namely the higher order dynamic mode decomposition and the spatio-temporal Koopman decomposition (STKD). The latter method decomposes a given spatio-temporal flow field as a series expansion in Fourier-like modes (including both wavenumbers/frequencies and spatial/temporal growth rates) in time and some distinguished longitudinal spatial coordinates, and spatial modes depending on the remaining transverse spatial coordinates. To obtain the (unknown) three-dimensional reconstruction, the STKD method is first applied to the (known) two-dimensional data in the considered planes. This application of STKD yields both the wavenumbers/frequencies and the spatial/temporal growth rates appearing in the three-dimensional reconstruction. Imposing that the three-dimensional reconstruction coincides with the two-dimensional data in the given set of planes, a system of linear equations results that permits computing the various ingredients appearing in the three-dimensional STKD expansion.The performance of the method is tested in the three-dimensional wake of a circular cylinder at Reynolds number (based on the cylinder diameter and the incoming free-stream velocity) equal to 280. The resulting flow is highly non-linear and quasi-periodic, with two fundamental temporal frequencies, associated with the well-known modes A and B. The method can be applied using experimental or numerical data, allowing to identify the full three-dimensional flow field and its main characteristics from limited information.