Do coherent structures organize scalar mixing in a turbulent boundary layer?

Abstract

A scalar emanating from a point source in a turbulent boundary layer does not mix homogeneously, but is organized in large regions with little variation of the concentration: uniform concentration zones. We measure scalar concentration using laser-induced fluorescence and, simultaneously, the three-dimensional velocity field using tomographic particle image velocimetry in a water tunnel boundary layer. We identify uniform concentration zones using both a simple histogram technique, and more advanced cluster analysis. From the complete information on the turbulent velocity field, we compute two candidate velocity structures that may form the boundaries between two uniform concentration zones. One of these structures is related to the rate of point separation along Lagrangian trajectories and the other one involves the magnitude of strong shear in snapshots of the velocity field. Therefore, the first method allows for the history of the flow field to be monitored, while the second method only looks at a snapshot. The separation of fluid parcels in time was measured in two ways: the exponential growth of the separation as time progresses (related to finite-time Lyapunov exponents and unstable manifolds in the theory of dynamical systems), and the exponential growth as time moves backward (stable manifolds). Of these two, a correlation with the edges of uniform concentration zones was found for the past Lyapunov field but not with the time-forward future field. The magnitude of the correlation is comparable to that of the regions of strong shear in the instantaneous velocity field.

Objective momentum barriers in wall turbulence

“…Furthermore, the objective nature of this work provides frame-indifferent structures that are experimentally verifiable (e.g. Eisma et al 2021), unlike the predictions from non-objective criteria. The vortices and MTB identified are resilient under fluid advection, providing a new way in which to track the evolution of individual or clusters of structures.…”

“…2016; Eisma et al. 2021). LCSs and OECSs are, however, constructed as boundaries of coherent structures in passive tracer advection rather than minimizers of momentum transport, as would be required for a physical UMZ interface analogue.…”

“…While correlations may exist between measured scalar concentrations and the features of these non-objective diagnostics (e.g. Westerweel et al 2009;Eisma, Westerweel & van de Water 2021), there can be no causal relationship. Several formal modifications of these vortex diagnostics have been proposed to make them objective, but only the approach of Liu, Gao & Liu (2019a); Liu et al (2019b) would be generally applicable, as found by Haller (2021).…”

“…Haller 2015;Serra et al 2017;Beron-Vera et al 2018;Serra et al 2020). Some of these approaches have been used to identify vortices away from turbulent/non-turbulent interfaces (TNTIs) in gravity current experiments (Neamtu-Halic et al 2019), as well as to look at boundary layer structures in PIV studies (Green, Rowley & Haller 2007;Pan, Wang & Zhang 2009;Wilson, Tutkun & Cal 2013;He et al 2016;Eisma et al 2021). LCSs and OECSs are, however, constructed as boundaries of coherent structures in passive tracer advection rather than minimizers of momentum transport, as would be required for a physical UMZ interface analogue.…”

“…Westerweel et al. 2009; Eisma, Westerweel & van de Water 2021), there can be no causal relationship. Several formal modifications of these vortex diagnostics have been proposed to make them objective, but only the approach of Liu, Gao & Liu (2019 a ); Liu et al.…”