Analysis of cyclic events in turbulent flows using recurrence plots

Abstract

A new technique for extracting information about cyclic and periodic features in turbulent-flow fields is proposed. This is based on a combination of proper orthogonal decomposition, applied to DNS and LES flow data, and the use of ‘recurrence plots’, the latter being a tool often adopted for analysing dynamical systems outside the field of fluid mechanics. The principal premise underpinning the technique is that the properties of a flow, viewed as a dynamical system, can be characterised by the temporal coefficients of the related proper orthogonal decomposition analysis of the flow. While such an analysis, on its own, yields useful information on the mode shapes, ordered according to their energy content, and on the temporal variation of these modes, it is not suited to the identification of ‘cyclicity’, here understood to be recurrent, as opposed to periodic, events that characterise drastic changes in the flow when this is viewed as a dynamical system. Following illustration with reference to a classical dynamical system, the Lorenz set, the method is applied to four turbulent flows: a three-dimensional transitional mixing layer, a flow separating from a ducted two-dimensional hump, that same flow controlled by means of a synthetic slot jet, and a flow separating from a three-dimensional ducted hill.