Lagrangian coherent superstructures in buoyancy driven turbulence

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Large-scale coherent flow structures, termed superstructures (SSs), play a key role in stratified turbulent flows by controlling the overall rate of mass and momentum transport. However, progress in our understanding of the mechanics of SSs has been hampered by arbitrariness in the detection methods of these coherent flow structures and hence leading to contrasting classifications of the results or even misinterpretations of physical mechanisms. As a result, little is known about how SSs determine global transport and mixing rates of the whole flow. The aim of this project is to develop 3D Lagrangian coherent structure identification methods and apply them to experimental particle tracking and numerical simulation data of shear flows with stable and unstable stratification to determine the role of these structures for the global exchange of mass and momentum. In Phase I of the project, we have shown how Lagrangian coherent structures (LCSs) control the mass transfer in stably stratified gravity currents. For the first time, we extracted rotational 3D LCSs using the co-called Lagrangian-averaged vorticity deviation (LAVD) method from experimental 3D particle tracking data. We have achieved this using a novel extraction algorithm and several simultaneous observation volumes stitched together. This approach has revealed the boundaries of LCSs composed of fluid elements that exhibit the same mean material rotation, thereby allowing only negligible radial filamentation for the boundary. The detected LCSs populating the strongly stratified gravity current boundary were predominantly large, spanwise oriented SSs, reminiscent of Kelvin-Helmholtz rollers. These SSs suppress mixing in their immediate vicinity, while organizing entrainment of mass by deflecting streamlines that cross the boundary of the gravity current at their rear and front sides. We have performed a similar analysis of mass transfer in numerical simulations of the planetary boundary layer that will be finalized in the last stage of Phase I. In the present Phase II proposal, we will complete the development of fully 3D Lagrangian coherent structure methods so that they can be applied broadly to experimental and numerical data of turbulent flows: beyond material barriers to momentum transport, we will also seek material barriers to vorticity transport and we will generalize the stably stratified flow analysis by extending it to the unstably stratified regime. We will extend the experimental analysis to explore the unstably stratified regime and investigate moderately high Reynolds number regimes in line with a primary goal of the SPP for Phase II. This effort will provide a new understanding of fluxes of mass, heat and momentum governed by superstructures across a wide range of flows that are of major relevance in nature and practical applications.