Tetrahedron deformation and alignment of perceived vorticity and strain in a turbulent flow

Details Tetrahedron deformation and alignment of perceived vorticity and strain in a turbulent flow Tetrahedron deformation and alignment of perceived vorticity and strain in a turbulent flow

2012-04-26

arxiv.org/abs/1204.5857v1

Physics

Fluid Dynamics

Scientific paper

We describe the structure and dynamics of turbulence by the scale dependent perceived velocity gradient tensor as supported by following four tracers, i.e. fluid particles, that initially form a regular tetrahedron. We report results from experiments in a von K\'arm\'an swirling water flow and from numerical simulations of the incompressible Navier-Stokes equation. We analyze the dynamics of the perceived rate of strain tensor and perceived vorticity for initially regular tetrahedron of size $r_0$ from the dissipative to the integral scale. The experimental data at higher Reynolds number suggest the existence of a self-similar regime in the inertial range, where the perceived vorticity aligns with the largest eigenvalue of the perceived rate of strain tensor over durations of order $t_0$, where $t_0$ is the turbulence time scale of the flow for scale $r_0$. For smaller Reynolds numbers we found the dynamics to be scale dependent.

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