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Inertial Range Scaling in Rotations of Long Rods in Turbulence
Fluid Dynamics · Submitted 19 Apr 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim For particles with length in the inertial range, we derive a scaling relationship for the mean square rotation rate, $< \dot{p}_i \dot{p}_i > \propto l^{-4/3}$ and show that measurements approach this scaling.
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The abstract, sentence by sentence
We measure the rotational statistics of neutrally buoyant rods with lengths $2.8 < l/\eta <72.9 $ in turbulence. For particles with length in the inertial range, we derive a scaling relationship for the mean square rotation rate, $< \dot{p}_i \dot{p}_i > \propto l^{-4/3}$ and show that measurements approach this scaling. Deviations from the proposed scaling are explained as the effect of dissipation range scales. The correlation time of the Lagrangian autocorrelation of rod rotation rate scales as the turn over time of eddies of the size of the rod. Measuring rotational dynamics of single long rods provides a new way to access the spatial structure of the flow at different length scales.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We measure the rotational statistics of neutrally buoyant rods with lengths $2.8 < l/\eta <72.9 $ in turbulence. | contribution 0.60 | 0.97 | 0.04 | asserted 1.00 |
| s1 | For particles with length in the inertial range, we derive a scaling relationship for the mean square rotation rate, $< \dot{p}_i \dot{p}_i > \propto l^{-4/3}$ and show that measurements approach this scaling. | result 0.99 | 0.95 | 0.70 | asserted 1.00 |
| s2 | Deviations from the proposed scaling are explained as the effect of dissipation range scales. | interpretation 0.99 | 0.76 | 0.09 | asserted 1.00 |
| s3 | The correlation time of the Lagrangian autocorrelation of rod rotation rate scales as the turn over time of eddies of the size of the rod. | result 1.00 | 0.83 | 0.12 | asserted 1.00 |
| s4 | Measuring rotational dynamics of single long rods provides a new way to access the spatial structure of the flow at different length scales. | interpretation 0.91 | 0.54 | 0.32 | asserted 0.85 |
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Original abstract
We measure the rotational statistics of neutrally buoyant rods with lengths $2.8 < l/\eta <72.9 $ in turbulence. For particles with length in the inertial range, we derive a scaling relationship for the mean square rotation rate, $< \dot{p}_i \dot{p}_i > \propto l^{-4/3}$ and show that measurements approach this scaling. Deviations from the proposed scaling are explained as the effect of dissipation range scales. The correlation time of the Lagrangian autocorrelation of rod rotation rate scales as the turn over time of eddies of the size of the rod. Measuring rotational dynamics of single long rods provides a new way to access the spatial structure of the flow at different length scales.
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