Controlling wake turbulence

Moving Surface Boundary-Layer Control on the Wake of Flow around a Square Cylinder

Abstract: In this paper, the entire process of the flow around a fixed square cylinder and the moving surface boundary-layer control (MSBC) at a low Reynolds number was numerically simulated [...]

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.

Drag reduction of wake flow by shear-driven rotation

This paper proposes a control strategy in which immersed bodies are driven to rotate not by external forces but by the flow itself. Due to the asymmetric distribution of the shear stress exerted on the surfaces, two side-by-side arranged cylinders rotate about their axes to produce moving fluid-solid boundaries. It is shown that the drag and the lift coefficients are significantly reduced in comparison with the stationary cylinder system. Different from the slip-boundary technique, the drag-reduction mechanism is explained in terms of a pressure-recovery effect introduced by the rotating surfaces.

Stabilization of vortices in the wake of a circular cylinder using harmonic forcing

We explore whether vortex flows in the wake of a fixed circular cylinder can be stabilized using harmonic forcing. We use Föppl's point vortex model augmented with a harmonic point source-sink mechanism which preserves conservation of mass and leaves the system Hamiltonian. We discover a region of Lyapunov-stable vortex motion for an appropriate selection of parameters. We identify four unique parameters that affect the stability of the vortices: the uniform flow velocity, vortex equilibrium positions, forcing amplitude, and forcing frequency. We assess the robustness of the controller using a Poincaré section.

Elimination of vortex streets in bluff-body flows

We present an effective technique for suppressing the vortex-induced vibrations of bluff bodies by eliminating the von Kármán street formed in their wake. Specifically, we find that small amounts of combined windward suction and leeward blowing around the body modify the wake instability and lead to suppression of the fluctuating lift force. Three-dimensional simulations and stability analysis are employed to quantify our findings for the flow past fixed and flexibly mounted circular cylinders.

Controlling spatio-temporal chaos in the scenario of the one-dimensional complex Ginzburg-Landau equation

We discuss some issues related with the process of controlling space-time chaotic states in the one-dimensional complex Ginzburg-Landau equation. We address the problem of gathering control over turbulent regimes with the use of only a limited number of controllers, each one of them implementing, in parallel, a local control technique for restoring an unstable plane-wave solution. We show that the system extension does not influence the density of controllers needed in order to achieve control.

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.

Controllability of flow turbulence

In this paper, we study the controllability of real-world flow turbulence governed by the two-dimensional Navier-Stokes equations, using strategies developed in chaos control. A case of control/synchronization of turbulent dynamics is observed when only one component of the velocity field vector is unidirectionally coupled to a target state, while the other component is uncoupled. Unlike previous results, it is shown that the dynamics of the whole velocity field cannot be completely controlled/synchronized to the target, even in the limit of long time and strong coupling strength. It is further revealed that the controlled component of the velocity field can be fully controlled/synchronized to the target, but the other component, which is not directly coupled to the target, can only be partially controlled/synchronized to the target. By extending an auxiliary method to distributed dynamic systems, the partial synchronization of two turbulent orbits in the present study can be categorized in the domain of generalized synchronization of spatiotemporal dynamics.

Tailoring wavelets for chaos control

Chaos is a class of ubiquitous phenomena and controlling chaos is of great interest and importance. In this Letter, we introduce wavelet controlled dynamics as a new paradigm of dynamical control. We find that by modifying a tiny fraction of the wavelet subspaces of a coupling matrix, we could dramatically enhance the transverse stability of the synchronous manifold of a chaotic system. Wavelet controlled Hopf bifurcation from chaos is observed. Our approach provides a robust strategy for controlling chaos and other dynamical systems in nature.

Synchronization and information processing by an on-off coupling

This paper proposes an on-off coupling process for chaos synchronization and information processing. An in depth analysis for the net effect of a conventional coupling is performed. The stability of the process is studied. We show that the proposed controlled coupling process can locally minimize the smoothness and the fidelity of dynamical data. A digital filter expression for the on-off coupling process is derived and a connection is made to the Hanning filter. The utility and robustness of the proposed approach is demonstrated by chaos synchronization in Duffing oscillators, the spatiotemporal synchronization of noisy nonlinear oscillators, the estimation of the trend of a time series, and restoration of the contaminated solution of the nonlinear Schrödinger equation.