An improved criterion to select dominant modes from dynamic mode decomposition

Dynamic mode decomposition (DMD) has been extensively utilized to analyze the coherent structures in many complex flows. Although specific flow patterns with dominant frequency and growth rate can be captured, extracting dominant DMD modes for flow reconstruction and dynamic modeling still needs a priori knowledge on flow physics, especially for some transient states of unstable flows. In this paper, a criterion to select dominant modes from DMD technique is developed. The unsteady flow can be described by the superposition of each normalized DMD mode multiplied by its time coefficient. The dominance of each DMD mode can be ordered by time integration of its time coefficient. Compared with standard DMD approach, which decides the dominance of DMD modes from the order of amplitude or mode norm, this criterion considers the evolution of each mode within the whole sampling space, and ranks them according to their contribution to all samples. The proposed mode selection strategy is evaluated by test cases including both equilibrium and transient states of a cylinder at Reynolds number of 60 and a transient state of a NACA0012 airfoil buffeting in transonic flow. Results indicate that using this criterion, dominant DMD modes can be identified and flow dynamics in unstable or transient systems can be reconstructed accurately with fewer modes. Besides, this approach has better convergence against mode number and lower sensitivity to the initial condition than standard DMD method.