Abstract
A Lagrangian perspective has yielded many new insights in our quest to reveal the intricacies of turbulent flows. Much of this progress has been possible by following the trajectories of idealised, inertialess objects (tracers) traversing through the flow. Their spins and tumbles provide a glimpse into the underlying local velocity gradients of the turbulent field. While it is known that the spinning and tumbling rates of anisotropic particles are modified in turbulence – compared with those in a random flow field – a quantitative explanation for this has remained elusive. Now, Pujara et al. (J. Fluid Mech., vol. 922, 2021, R6) have made an attempt to predict the split between spinning and tumbling rates by accessing the particle's alignment with the local vorticity. Their analysis of filtered turbulent fields reveals a Lagrangian scale invariance, whereby key quantities relating to the particle's rotational statistics are preserved from the dissipative to the integral scale.
Highlights
Almost all of the turbulent flows around us contain tiny particles suspended in them
If the particles were to randomly orient themselves in the turbulent field, their mean-square tumbling rate can be analytically obtained as p2 = 1/τη2[1/6 + 1/10((AR2 − 1)/(AR2 + 1))2], where AR is the aspect ratio of the spheroid, and τη is the dissipative time scale (Parsa et al 2012; Chevillard & Meneveau 2013)
This prediction is at striking odds with both experiments and simulations of spheroids advected through isotropic turbulence (Parsa et al 2012; Byron et al 2015; Ni et al 2015)
Summary
Almost all of the turbulent flows around us contain tiny particles suspended in them. If the particles were to randomly orient themselves in the turbulent field, their mean-square tumbling rate can be analytically obtained as p2 = 1/τη2[1/6 + 1/10((AR2 − 1)/(AR2 + 1))2], where AR is the aspect ratio of the spheroid, and τη is the dissipative time scale (Parsa et al 2012; Chevillard & Meneveau 2013) This prediction is at striking odds with both experiments and simulations of spheroids advected through isotropic turbulence (Parsa et al 2012; Byron et al 2015; Ni et al 2015). Their results suggest the existence of an underlying scale invariance for the rotational statistics within the Lagrangian framework
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