The persistence of trip-induced spanwise periodicity in developing turbulent boundary layers

The present work investigates spanwise periodic modes introduced at the inception point (trip) of a developing turbulent boundary layer. Empirical evidence suggests that these modes can be persistent, and the idea here is to exploit this apparent persistence/amplification of weak lateral variations in turbulent boundary layers, to explore whether the downstream evolution can be substantially modified. Preliminary results, where micro vortex generators are used to introduce the spanwise modes at the trip, indicate the presence of spanwise alternating modes. These modes appear to strengthen after some distance downstream of their introduction for certain configurations (this strengthening can occur almost 350 blade heights downstream of the trip). Further, the spanwise wavelength of the trip seems to play a critical role in determining the downstream development and subsequent evolution of the turbulent boundary layer towards a canonical state. Collectively, these findings suggest that three-dimensionality introduced at the trip may be a viable approach to perturb the evolution of developing turbulent boundary layers over a large streamwise development length. Introduction A turbulent boundary layer forming on a flat plate appears to exhibit a lateral instability during its development that can sustain and amplify initially weak spanwise perturbations. For example, persistent lateral variations have been observed within developing turbulent boundary layers, even in carefully fabricated, well-controlled wind tunnel facilities with nominally uniform freestream conditions (Klebano ff & Tidstrom, 1959; Watmu ff, 1998). These modes are thought to arise due to subtle imperfections in the upstream screens used for flow conditioning (Bradshaw, 1965; Furuyaet al., 1979; Pooket al., 2016). Townsend (1976, pp. 328-331) demonstrated analytically that small lateral variations in turbulent boundary layers tend to be selectively amplified up to a critical amplitude as the boundary layer develops, with the most amplified or dominant wavelengths tending to be those that are on the order of the boundary layer thickness ( δ). In the case of the studies mentioned above, it is thought that these lateral variations may be introduced from weak flow imperfections in the free-stream. However, these spanwise variations could also be introduced or exacerbated by surface roughness (Gong et al., 1996; Mejia-Alvarez & Christensen, 2013; Reynolds et al., 2007). To investigate this phenomenon, the present work examines the downstream persistence of lateral variations introduced at the inception point (or trip) in a developing zero pressure gradient turbulent boundary layer. In doing so we hope to shed light on the ability of the developing turbulent boundary layer to selectively amplify approximatelyδ-scaled spanwise variations—as proposed by Townsend (1976)—out of pre-existing heterogeneity (this could be heterogeneity in the free-stream, in the trip, or in the surface stress conditions). A further aim here is to investigate the viability of controlling or perturbing the evolution of the developing turbulent boundary layer through embedded spanwise perturbations. A number of studies have investigated the evolution of the turbulent boundary layer under di fferent tripping conditions. For example, Schlatter & Örlü (2011), using direct numerical simulations of developing turbulent boundary layers, have shown that relatively minor modifications to the trip parameters can produce noncanonical development up to surprisingly high Reynolds numbers. Marusicet al. (2015) demonstrated similar results experimentally, finding non-canonical development to even higher Reynolds numbers (however, in these cases the trip perturbation was rather aggressive). Here, we plan to exploit the ability of a relatively modest spanwise perturbation to excite persistent δ-scaled spanwise modes, to attain both a further reaching and e fficient modification to the evolution of a turbulent boundary layer. This idea is largely underpinned by the suggestion of Castillo & Johansson (2002) who noted that upstream conditions could impose a profound influence on the downstream development. Based on these findings they proposed that flow control initiated from upstream manipulations could provide a viable avenue of research for turbulent boundary layer control. For the preliminary results discussed here, spanwise periodic disturbances are introduced at the trip of a turbulent boundary layer using a series of micro vortex generators (MVGs). By systematically changing the MVG wavelength and mapping how the mean velocity changes with the development distance, we investigate the ability of a turbulent boundary layer to self-sustain certain spanwise periodic modes. Experimental Set-up The experiments are performed in the High Reynolds Number Boundary Layer Wind Tunnel (HRNBLWT) at the University of Melbourne (Nickelset al., 2005). Figure 1 shows an overall view of the experimental campaign, which employs both hot-wire anemometry and particle image velocimetry (PIV) measurements. Typically, the boundary layer in the facility is tripped using a strip of 40 grit sand paper (SP40); and this will correspond to our reference case. Spanwise-periodic modes are introduced using a series of MVGs