Multifractal analysis of a lobed mixer flowfield utilizing the proper orthogonal decomposition

We use the theory of multifractal measures to throw a fresh perspective on the data analysis of velocity time traces in a lobed mixer flow. A lobed mixer is a device that enhances mixing through secondary flows and streamwise vorticity. A specially designed rake of hot wires with high spatial resolution was used to collect the streamwise velocity data. Through the use of the proper orthogonal decomposition, a basic knowledge of the coherent structures, on an energy weighted basis, was studied. The instantaneous velocity traces that are necessary for calculating the generalized fractal dimensions are reproduced from the ensemble average measurements taken from the proper orthogonal decomposition. We compute the generalized fractal dimensions D(q) and the f(alpha) multifractal spectrum of several proper eigenmodes for data samples from the velocity time trace of several hot-wire probes at different energy levels. This is a marked departure from previous multifractal theory applications to self-similar cascades that mainly dealt with the dissipation fields of turbulent kinetic energy. In the course of this exposition it will be pointed out that in certain cases a single dimension D1 may suffice to capture the entire spectrum of scaling exponents for the velocity time trace. We verify that in such cases the location of the hot-wire probes imply a lack of intermittency.