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

TL;DR

This paper investigates how perceived vorticity and strain in turbulent flows align and evolve over time, using experiments and simulations to reveal scale-dependent dynamics and self-similar regimes in turbulence.

Contribution

It introduces a scale-dependent analysis of perceived velocity gradients in turbulence, combining experimental and numerical methods to explore vorticity-strain alignment dynamics.

Findings

Perceived vorticity aligns with the intermediate eigenvector of perceived strain.

Vorticity tends to align with the strongest eigenvector over time.

Self-similar alignment dynamics observed at high Reynolds numbers.

Abstract

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 statistics and the dynamics of the perceived rate of strain tensor and vorticity for initially regular tetrahedron of size $r_0$ from the dissipative to the integral scale. Just as for the true velocity gradient, at any instant, the perceived vorticity is also preferentially aligned with the intermediate eigenvector of the perceived rate of strain. However, in the perceived rate of strain eigenframe fixed at a given time $t=0$, the perceived vorticity evolves in time such as to align with the strongest eigendirection at $t=0$. This also applies to the true velocity gradient. The experimental data at the higher Reynolds number suggests the existence of a self-similar regime in the inertial range. In particular, the dynamics of alignment of the perceived vorticity and strain can be rescaled by $t_0$, the turbulence time scale of the flow when the scale $r_0$ is in the inertial range. For smaller Reynolds numbers we found the dynamics to be scale dependent.