Scalar dispersion in a multi-scale generated turbulent flow

Combined PLIF and PIV experiments were performed in the near-wake region of a multi-scale array of three different length scales. We document, and measured terms of the multi-scale triple-decomposed energy budget and show the importance of non-linear interactions between the primary shedding structures in multi-scale generated turbulence. We subsequently observe a cascade of scalar bursting events, in which the scalar is transported a large distance in the transverse direction over a short period of time. These bursts unfolded spatially, such that they were observed between the small and medium wakes and the medium and large wakes. These bursts were also observed in the wake of a single-scale array of objects of comparable blockage to the multi-sale array, but there was no cascade of bursts identified and they all occurred in the same spatial location. Combined, these findings verify the space-scale unfolding (SSU) mechanism originally postulated in Laizet & Vassilicos (2012). By performing the multi-scale triple decomposition of Baj et al. (2015) we show that the dominant mode in the scalar transport is that associated to the fundamental shedding of the larger of the two intersecting wakes. We thus conclude that the SSU mechanism is subtly different to that originally postulated by Laizet & Vassilicos (2012). Those authors originally attributed the SSU mechanism to the coherence of the overall, Reynolds-decomposed velocity fluctuation u′. Here we show that the dominant effect is in fact the coherent part of the fluctuating velocity concordant with the fundamental shedding frequency of the larger of the two interacting wakes. Downstream of the wake intersection point this particular coherent scalar flux component is the major contributor to the overall scalar flux. INTRODUCTION Many turbulent flows are triggered by the instability of large-scale coherent motions embedded within the flow, such as the von Kármán vortex street of a cylinder wake. Given the high energy content within these coherent motions Hussain & Reynolds (1970) proposed a triple decomposition of the velocity field in which the classical Reynolds-decomposed fluctuating velocity is further decomposed into a coherent and stochastic part, u = u+u′ = u+ ũ+u′′. In many cases, however, turbulence is triggered at a number of length scales simultaneously (e.g. flows through a forest or a cityscape). It is reasonable to expect that at each of these levels some sort of flow regularisation is enforced, resulting in coherence being introduced into the flow on top of the stochastic turbulent motion. In this regard, features of singleand multi-scale generated turbulence can diverge as the former lacks the dynamical interplay of the embedded multi-scale coherent motions. Indeed, recently, multi-scale generated turbulence has been shown to have some beneficial properties in terms of mixing performance relative to turbulence generated by a single length scale only (Goh et al., 2013; Cafiero et al., 2014; Laizet & Vassilicos, 2015). Since coherence is introduced at multiple length scales (and hence frequencies) simultaneously in multi-scale generated turbulence the single-scale triple decomposition of Hussain & Reynolds (1970) is insufficient to describe the dynamical interplay between these scales. For this reason Baj et al. (2015) developed a multi-scale triple decomposition, based on the optimal mode decomposition (Wynn et al., 2013), where the velocity is decomposed as u(x, t) = u(x)+∑ l ũl(x, t)+u′′(x, t) (1) in which there are a number of coherent motions ũl with corresponding phase signals φ l(t). Note that the coherent modes ũl have a temporal dependence on both the phase signal φ l(t) as well as a slowly varying amplitude signal A(t); see Baj & Buxton (2017) for more details. We now extend this analysis to examine the dispersion of passive scalar in a multi-scale generated flow. Laizet & Vassilicos (2012) postulated the existence of the “spacescale unfolding” (SSU) mechanism, in which the spatial unfolding of the various sized wakes of a multi-scale array leads to an enhancement of the scalar transport and stirring