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Restricted Euler dynamics along trajectories of small inertial particles in turbulence

Published online by Cambridge University Press:  06 March 2017

Perry L. Johnson Open the ORCID record for Perry L. Johnson [Opens in a new window]  and
Charles Meneveau
Perry L. Johnson*
Affiliation:
Department of Mechanical Engineering and Center for Environmental and Applied Fluid Mechanics, The Johns Hopkins University, Baltimore, MD 21218, USA
Charles Meneveau
Affiliation:
Department of Mechanical Engineering and Center for Environmental and Applied Fluid Mechanics, The Johns Hopkins University, Baltimore, MD 21218, USA
*
†Email address for correspondence: [email protected]
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Abstract

The fate of small particles in turbulent flows depends strongly on the velocity gradient properties of the surrounding fluid, such as rotation and strain rates. For non-inertial (fluid) particles, the restricted Euler model provides a simple low-dimensional dynamical system representation of Lagrangian evolution of velocity gradients in fluid turbulence, at least for short times. Here, we derive a new restricted Euler dynamical system for the velocity gradient evolution of inertial particles, such as solid particles in a gas, or droplets and bubbles in turbulent liquid flows. The model is derived in the limit of small (sub-Kolmogorov-scale) particles and low Stokes number. The system exhibits interesting fixed points, stability and invariant properties. Comparisons with data from direct numerical simulations show that the model predicts realistic trends such as the tendency of increased straining over rotation along heavy particle trajectories and, for light particles such as bubbles, the tendency of reduced self-stretching of the strain rate.

JFM classification

Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Turbulent Flows: Turbulence theory Turbulent Flows: Turbulent Flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 816 , 10 April 2017 , R2
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Copyright
© 2017 Cambridge University Press 

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