On the properties of steady states in turbulent axisymmetric flows

TL;DR

This study experimentally investigates steady states in turbulent axisymmetric flows, revealing how mean velocity fields depend on viscosity and forcing, and providing evidence of flow Beltramization at higher Reynolds numbers.

Contribution

It offers the first experimental evidence of Beltramization and nonlinear depletion in non-homogeneous, non-isotropic turbulent flows, confirming theoretical predictions.

Findings

Velocity-vorticity alignment increases with Reynolds number

Mean velocity fields depend on viscosity and forcing

Flow exhibits Beltramization at high Reynolds numbers

Abstract

We experimentally study the properties of mean and most probable velocity fields in a turbulent von K\'arm\'an flow. These fields are found to be described by two families of functions, as predicted by a recent statistical mechanics study of 3D axisymmetric flows. We show that these functions depend on the viscosity and on the forcing. Furthermore, when the Reynolds number is increased, we exhibit a tendency for Beltramization of the flow, i.e. a velocity-vorticity alignment. This result provides a first experimental evidence of nonlinearity depletion in non-homogeneous non-isotropic turbulent flow.