Evaluating the complexity of a separated laminar boundary layer flow using the flow's topological features and excess entropy

Unsteady flows are notoriously complex, yet the definition of flow complexity remains vague. A complex flow may contain numerous interacting structures, with highly unpredictable dynamic behavior. Some studies describe flow complexity from a multi-scale modeling perspective. However, limited effort has been made to evaluate a flow’s degree-of-complexity (DOC). This presentation addresses the issue using a new information theory-based framework. A separated laminar boundary layer flow is examined with time-resolved PIV. The flow evolution is divided into multiple pseudo-periods, with the velocity in each period converted into a phase trajectory. These trajectories are then categorized and symbolized based on their homological group. The resulting symbol sequence allows for the evaluation of DOC using the well-established excess entropy method. Along the streamwise direction, the flow’s complexity shows a sudden transition near the separation point. Downstream of the separation, the DOC resembles that of a random signal, indicating that the flow structures have no correlation over time.