Alignment and rotation of spheroids in unsteady vortex flow
Peer reviewed, Journal article
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Preferential orientations of inertialess nonspherical particles are examined through three qualitatively different stages of a time-evolving Taylor–Green vortex flow. Despite an unexpected decorrelation between the vorticity vector and the direction of Lagrangian stretching, experienced by material fluid elements over a substantial time interval, prolate spheroids aligned with the Lagrangian stretching direction, whereas oblate spheroids aligned with the Lagrangian compression direction. We, therefore, infer that spheroidal tracers orient themselves relative to the Lagrangian history of the velocity gradients, defined by the left Cauchy–Green deformation tensor, rather than with the fluid vorticity vector. This preferential alignment persists all throughout the statistically unsteady flow field and even in the inviscid and nonturbulent early stage of the time-dependent vortex flow. This explains the observed preferential spinning of rods and tumbling of disks, similar to that in homogeneous isotropic turbulence, even at the early stage when the flow is anisotropic and laminar. These preferred modes of particle rotation prevail all through the evolving flow despite a surprisingly long time interval, during which the fluid vorticity decorrelates from the direction of Lagrangian stretching.