Nonlinear extensions to operator-based causality analysis

Causality analysis in fluid dynamics remains challenging due to the high dimensionality and nonlinearity of the underlying dynamics. Data-driven techniques, such as Granger causality analysis and transfer entropy often require large datasets, and yield results sensitive to variable choice and correlation, limiting interpretability and accuracy. Here, we seek to exploit the knowledge and structure of the governing equations to develop more robust causality analysis tools. We first discuss Linear Operator-based Causality Analysis (LOCA), where causal interactions can be inferred from the linearized governing equations. Building on this foundation, we next introduce a nonlinear extension to this methodology that incorporates quadratic interactions, allowing us to isolate and quantify the individual causal contributions of both linear and nonlinear terms. We apply this method upon flow over bluff body arrays to demonstrate and compare its performance with alternative causal analysis tools.