Controlling flow turbulence

This paper investigates the viability and effectiveness of using a technique developed for low-dimensional chaotic systems to control flow turbulence governed by the Navier-Stokes equations. By using a global pinning coupling strategy, we show that turbulence can be controlled to desirable time-varying target states, including a spatially extended periodic state and a turbulent one. Exponential convergence to the target state is found and the exponential rate scales linearly to the coupling strength. The linear scaling law breaks down when localized pinning control is applied. A wavelet multiscale technique is utilized for the characterization of both the effectiveness of the present control strategy and the inverse energy transfer in two-dimensional turbulence.