Investigation of Cointegration Relationships in Turbulent Flows

Abstract

Turbulence has often been called one of the last unsolved problems of classical physics and impacts a wide variety of fields in nature and engineering. An important area of focus in turbulence research is the discovery and scaling laws in turbulence which facilitate reduced order representations that are useful for efficient computational predictions of turbulent flows. In this work we seek to utilize the method of cointegration, a tool typically utilized in econometrics for the study of non-stationary time series, to search for and quantify new relationships amongst a variety of physical quantities in (nonstationary or inhomogeneous) turbulent flows. The primary research questions of this work are: (i) Do cointegration relationships exist in non-stationary and/or non-homogeneous turbulent flows?, (ii) If so, what are the cointegration relationships?, (iii) What collections of signals show strong evidence of cointegration relationships? and (iv) What is the utility of cointegration analysis in investigation of turbulent flows? To address these questions, we analyze flow data (available from publicly accessible databases) obtained from direct numerical simulations of two test cases: (a) turbulent channel flow and (b) buoyancy driven flow in a periodic box.