Controllability of flow turbulence

Some observations regarding steady laminar flows past bluff bodies

Steady laminar flows past simple objects, such as a cylinder or a sphere, have been studied for well over a century. Theoretical, experimental and numerical methods have all contributed fundamentally towards our understanding of the resulting flows. This article focuses on developments during the past few decades, when mostly numerical and asymptotical advances have provided insights also for steady, although unstable, high-Reynolds-numbers flow regimes.

Network approach to the pinning control of drift-wave turbulence

Network of coupled oscillators has long been employed as an important approach to explore the complicated dynamics in spatially extended systems. Here we show how this approach can be used to the analysis of turbulence pinning control. Specifically, by use of a model of two-dimensional drift-wave plasma turbulence, we investigate how the performance of the turbulence control is influenced by the spatial distribution of the pinning strength. It is found that the dynamics of pinned turbulence can be well captured by a simple model of networked modes, based on which the dependence of the control performance on the pinning distribution can be analytically obtained. In particular, the model predicts that as the distribution of the pinning strength becomes more nonuniform, the performance of turbulence control will be gradually decreased. This theoretical prediction is in good agreement with the results of numerical simulations, including the sinusoidal and localized pinning distributions. Our studies provide a new viewpoint to the mechanism of mode couplings in drift-wave turbulence, as well as be constructive to the design of new schemes for controlling turbulence in realistic systems.

Synchronization of chaos in fully developed turbulence

We investigate chaos synchronization of small-scale motions in the three-dimensional turbulent energy cascade, via pseudospectral simulations of the incompressible Navier-Stokes equations. The modes of the turbulent velocity field below about 20 Kolmogorov dissipation lengths are found to be slaved to the chaotic dynamics of larger-scale modes. The dynamics of all dissipation-range modes can be recovered to full numerical precision by solving small-scale dynamical equations with the given large-scale solution as an input, regardless of initial condition. The synchronization rate exponent scales with the Kolmogorov dissipation time scale, with possible weak corrections due to intermittency. Our results suggest that all sub-Kolmogorov length modes should be fully recoverable from numerical simulations with standard, Kolmogorov-length grid resolutions.

Regulating drift-wave plasma turbulence into spatiotemporal patterns by pinning coupling

Using the technique of pinning coupling in chaos control, we investigate how the two-dimensional drift-wave plasma turbulence described by the Hasegawa-Mima equation can be regulated into different spatiotemporal patterns. It is shown both analytically and numerically that, depending on the pattern structure of the target, the pinning strength necessary for regulating the turbulence could have a large variation. More specifically, with the increase of the wave number of the target, the critical pinning strength is found to be increased by a power-law scaling. Moreover, in both the transition and transient process of the pinning regulation, the modes of the turbulence are found to be suppressed in a hierarchical fashion, that is, by the sequence of mode wave number. The findings give insight into the dynamics of drift-wave turbulence, as well as indicative to the design of new control techniques for real-world turbulence.

Taming turbulence in the complex Ginzburg-Landau equation

Taming turbulence in the complex Ginzburg-Landau equation (CGLE) by using a global feedback control method and choosing traveling-wave solutions as our target state is investigated. The problem of optimal control for the smallest driving strength is studied by systematically comparing the stabilities of all traveling waves. Within the Benjamin-Feir-Newell unstable parameter region (c2<-c1 -1, a critical control curve is determined, which is located at c2=alphacbeta1 , with alpha approximately -4.0 and beta approximately -0.87. It characterizes the transition of chosen traveling-wave target state from long wavelength to short one. This finding is of great significance for taming turbulence in the CGLE and some other spatiotemporal systems as well.

Transition zone in controlling spatiotemporal chaos

The controllability of spatiotemporal chaos is investigated. Contrary to our common sense that there is only one transition point (i.e., a critical control strength) for successful control, we find that actually a transition zone exists, connecting two transition points for the local and global stabilities of the controlled state, respectively. Within the zone, the controllable probability increases from zero to one for random initial conditions. This behavior is found to be very generic and is expected to have a severe consequence in realistic applications in the control of spatiotemporal chaos.

Sporadic feedback control of flow turbulence

In this work we consider the problem of flow turbulence control in a two-dimensional Navier-Stokes equation. We suggest a control strategy which sporadically applies global feedback to a single velocity component of the velocity field. It is found that this control strategy can significantly enhance the control efficiency when the optimal fraction for the control period is suitably chosen, both larger and smaller control time fractions may reduce the control precision. The physical mechanism underlying this interesting and strange behavior is heuristically analyzed, based on mode-mode interactions.