On the control of a simplified k-e model of turbulence

TL;DR

This paper demonstrates that a simplified k-e turbulence model can be locally controlled to nullify velocity fields using distributed controls, advancing the understanding of turbulence management.

Contribution

It proves partial local null-controllability of a simplified turbulence model using combined analytical techniques, a novel step in turbulence control research.

Findings

Velocity can be driven to zero from small initial states

Control is achieved with distributed, space-supported inputs

The approach combines fixed-point, linearization, and Carleman estimates

Abstract

This paper deals with the control of a kind of turbulent flows. We consider a simplified k-e model with distributed controls, locally supported in space. We proof that the system is partially locally null-controllable, in the sense that the velocity field can be driven exactly to zero if the initial state is small enough. The proof relies on an argument where we have concatenated several techniques: fixed-point formulation, linearization, energy and Carleman estimates, local inversion, etc. Ths result can be viewed as a nontrivial step towards the control of turbulent fluids.