Turbulent Boundary Layers Analysed Using Causally Coherent Structures
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Turbulent flows constitute complex dynamical systems, with relevance ranging from pollutant dispersion in the atmospheric boundary layer to airflow in the human respiratory system. Unlike low-dimensional chaotic systems, such as the Lorenz model, turbulence is inherently high-dimensional, strongly nonlinear and multiscale, rendering the identification of causal relationships particularly challenging. Both interventional [1] and non-interventional [2] causality detection approaches have been explored in the past. While interventional methods require carefully designed perturbations that are often difficult or infeasible to implement in experiments, non-interventional approaches rely solely on observational data and are therefore well suited to both simulations and laboratory measurements. In this work, we use a non-interventional approach and introduce the novel concept of causally coherent structures (CCSs) considering zero-pressure-gradient turbulent boundary layers [3,4]. Specifically, the extraction of causally coherent patterns in turbulent flows is carried out using information-theoretic measures. Information-theoretic metrics are employed to identify causal interactions within the turbulent dynamics, highlighting their advantages over conventional correlation-based analyses, which do not necessarily imply causation. In particular, we examine the sensitivity of Shannon transfer entropy [5] to key hyper-parameters and how this sensitivity varies with wall-normal location and temporal history. Building on this analysis, we introduce a novel framework to identify CCSs in the space–time parameter space of turbulent boundary layers, allowing their wall-normal organisation and symmetry properties to be quantified. The proposed approach provides a general methodology that can be extended to other complex dynamical systems.
