Dynamics of vortical structures in compressible mixing layers through tracking and graph-based geometrical analyses*

We present a numerical study of the geometrical evolution of vortical structures identified by the Q-criterion in compressible temporally evolving mixing layers of varying convective Mach number (M_c = {0.3, 0.7, 1.1}, Re_ω,0 = 640, Re_θ,0 = 160) and uniform initial density. The structures are extracted from the flow field by iso-surfacing and individually tracked from instantaneous snapshots obtained throughout the direct numerical simulation. The temporal evolution and interactions among vortical structures are mapped onto a graph data structure, which is queried to conduct the geometrical analysis.

Subgraph mining is carried out on the graph conditioned on geometrical attributes of the structures to identify common pattern of structure evolution in the self-similar regime of the mixing layers. A multi-dimensional dynamic time-warping analysis is also applied on the time series of geometric signatures of the structures to search for similar temporal surface shape developments. To further characterize the inhibiting influence of compressibilty on the turbulence intensity of the mixing layer the structure shape, growth and rotation rates are investigated for the different convective Mach numbers.