How far does turbulence spread?

TL;DR

This study uses direct numerical simulations to investigate how turbulence, injected locally in a channel flow, spreads spatially, revealing that at high Reynolds numbers turbulence propagates through self-advection rather than molecular diffusion, leading to a new state where transport and cascade are equally significant.

Contribution

It demonstrates that turbulence spreading at high Reynolds numbers is governed by self-advection, not molecular diffusion, and introduces a new turbulent state where transport and cascade are equally important.

Findings

Turbulent energy density peaks at the forcing location and decreases with distance.

At high Reynolds numbers, the energy profile becomes Reynolds-independent.

Turbulence spreads via self-advection, not molecular diffusion.

Abstract

How locally injected turbulence, spreads in space is investigated with direct numerical simulations. We consider a turbulent flow in a long channel generated by a forcing that is localised in space. The forcing is such that it does not inject any mean momentum in the flow. We show that at long times a statistically stationary state is reached where the turbulent energy density in space fluctuates around a mean profile that peaks at the forcing location and decreases fast away from it. We measure this profile as a function of the distance from the forcing region for different values of the Reynolds number. It is shown, that as the Reynolds number is increased, it converges to a Reynolds-independent profile implying that turbulence spreads due to self-advection and not molecular diffusion. In this limit therefore, turbulence plays the simultaneous role of cascading the energy to smaller scales and transporting it to larger distances. The two effects are shown to be of the same order of magnitude. Thus a new turbulent state is reached where turbulent transport and turbulent cascade are equally important and control its properties.