Flow complexity in open systems: interlacing complexity index based on mutual information

Abstract

Flow complexity is related to a number of phenomena in science and engineering, which has been approached from the perspective of chaotic dynamical systems, ergodic processes, or mixing of fluids, just to name a few. To the best of our knowledge, all existing methods to quantify flow complexity are only valid for infinite time evolutions, for closed systems or for mixing of two substances. We introduce an index of flow complexity coined interlacing complexity index (ICI), valid for a single phase flow in an open system with inlet and outlet regions, involving finite times. ICI is based on Shannon's mutual information (MI), and inspired by an analogy between inlet-outlet open flow systems and communication systems in communication theory. The roles of transmitter, receiver, and communication channel are played, respectively, by the inlet, the outlet, and the flow transport between them. A perfectly laminar flow in a straight tube can be compared to an ideal communication channel where the transmitted and received messages are identical and hence the MI between input and output is maximal. For more complex flows, generated by more intricate conditions or geometries, the ability to discriminate the outlet position by knowing the inlet position is decreased, reducing the corresponding MI. The behaviour of the ICI has been tested with numerical experiments on diverse flows cases. The results indicate that the ICI provides a sensitive complexity measure with intuitive interpretation in a diversity of conditions and in agreement with other observations, such as Dean vortices and subjective visual assessments. As a crucial component of the ICI formulation, we also introduce the natural distribution of streamlines and the natural distribution of world-lines, with invariance properties with respect to the cross section used to parameterize them, valid for any type of mass-preserving flow.

Correlation of flow complexity parameter with aneurysm rupture status

“…Usually, the intra-aneurysmal flow complexity is described by the presence of concentrated inflow jet, small impact zone, or strong vortex. These flow characteristics were quantified individually, generating a set of independent parameters, and only recently the flow complexity was described as a single index, called interlacing complexity index (Pozo et al, 2017). The interlacing complexity index measures the information lost along a sample of streamlines between two stations, by providing an average value of flow complexity over the control volume between the stations.…”

“…Out of the large number of hemodynamic parameters introduced, there is a lack of agreement on which index is the main indicator of rupture status, except the complex hemodynamic environment which is presented as a collection of hemodynamic parameters. Recently, the complexity of the flow was quantified as a single parameter inspired by communication theory and named interlacing complexity index . The index measures the “loss of information” in propagating from “inlet” to “outlet” in a communication system.…”

“…Recently, the complexity of the flow was quantified as a single parameter inspired by communication theory and named interlacing complexity index. 17 The index measures the "loss of information" in propagating from "inlet" to "outlet" in a communication system. The parameter is a reliable complexity index that requires a careful delineation of the two stations of the control volume and depends on generating enough streamlines or world-lines to produce an accurate index.…”

A New Decision Process for Choosing the Wind Resource Assessment Workflow with the Best Compromise between Accuracy and Costs for a Given Project in Complex Terrain

“…This method of defining "complex terrain" is used widely in the industry by WAsP users, but is limited to a binary classification (either "complex" or "not complex"). There have been some attempts to assess flow complexity objectively using streamlines and other features, for example, [7], but these methods are computationally demanding or require functionality that is not available in wind energy sector tools.…”

Dynamical complexity measure to distinguish organized from disorganized dynamics

“…The past decades have witnessed a considerable growth of the science of complexity, devoted to understand the emerging behavior of collective systems, regardless of their physical, biological, or social nature [1][2][3][4][5][6][7]. Much of the research has focused on defining multiple metrics to classify and quantify complex dynamics involving many variables [8].…”