Spatio–temporal dynamic mode decomposition in a shear layer flow

Abstract

Dynamic mode decomposition is a useful method for extracting temporal information of coherent structures in unsteady flows. However, this method cannot simultaneously extract temporal and spatial development information, including wave number and spatial growth rate, which is essential in fully developed flows. Thus, using the idea of spatio–temporal dynamic mode decomposition from Le Clainche & Vega, we established an algorithm for spatio–temporal dynamic mode decomposition through element rearrangement, matrix blocking, and re-decomposition techniques, based on the traditional dynamic mode decomposition. This method can calculate the spatio–temporal modes of an unsteady function whose space dimension exceeds two. Each spatio–temporal mode is characterized by temporal growth rate, angular frequency, spatial growth rate, and wave number, thereby expanding the dimension of acquiring information of unsteady flow fields. The feasibility and effectiveness of this method are verified by a function of time and space. The application of spatio–temporal dynamic mode decomposition in a typical unsteady shear layer flow shows that this method can capture the dominant coherent structure in the flow field and accurately acquire its spatio–temporal evolution information.