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Image-based Lagrangian Particle Tracking in Bed-load Experiments

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Residual sweeping errors in turbulent particle pair diffusion in a Lagrangian diffusion model.

Nadeem A Malik¹

¹Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, P.O. Box 5046, Dhahran 31261, Saudi Arabia.

|December 19, 2017

Summary

Sweeping effects in Kinematic Simulations (KS) do not invalidate Lagrangian properties. Our analysis shows sweeping errors in turbulent pair diffusivity decrease with particle separation, remaining negligible in the inertial subrange.

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Area of Science:

Fluid dynamics
Turbulence research
Computational physics

Background:

Kinematic Simulations (KS) are used to study Lagrangian properties in turbulent flows.
Previous studies suggested sweeping effects in KS might lead to unreliable Lagrangian properties.
These conclusions often relied on an assumption of locality, which this study challenges.

Purpose of the Study:

To quantify sweeping errors in Kinematic Simulations (KS) without assuming locality.
To analyze the impact of sweeping effects on turbulent pair diffusivity.
To determine the relationship between error, particle separation, and the Kolmogorov microscale.

Main Methods:

Novel analysis of particle trajectories in a moving reference frame.
Quantification of normalized integrated error in turbulent pair diffusivity (K).
Examination of error dependence on pair separation (σl) relative to the Kolmogorov microscale (η).

Main Results:

The normalized integrated error due to sweeping decreases with increasing pair separation (σl/η).
Error approaches zero as σl/η approaches infinity and zero.
A significant intermediate range (1 < σl/η < ∞) shows negligible error.
Simulations indicate this negligible error range covers most of the simulated inertial subrange (1 < σl/η < 105).

Conclusions:

Sweeping errors in KS are not the primary cause for observed deviations from locality.
The assumption of locality is not required to understand sweeping errors in KS.
Findings are crucial for advancing pair diffusion theory and turbulence modeling.