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We construct a discrete shell-model for two-dimensional turbulence that takes into account local and nonlocal interactions between velocity modes in Fourier space. In real space, its continuous limit is described by the one-dimensional…
Intermittency is one of central obstacles for understanding small-scale dynamics in the fully developed hydrodynamic turbulence. The modern approach is largely based on the multifractal theory of Parisi and Frisch which is, however,…
Boundary feedback control design is studied for 1D hyperbolic systems with an in-domain disturbance and a boundary feedback controller under the effect of actuator saturation. Nonlinear semigroup theory is used to prove well-posedness of…
In this paper we study a stochastic version of an inviscid shell model of turbulence with multiplicative noise. The deterministic counterpart of this model is quite general and includes inviscid GOY and Sabra shell models of turbulence. We…
We explore the utility of the recently proposed alpha equations in providing a subgrid model for fluid turbulence. Our principal results are comparisons of direct numerical simulations of fluid turbulence using several values of the…
The theory of controlled mechanical systems of [6, 3, 4] is extended to the case of ideal incompressible fluids consisting of charged particles in the presence of an external magnetic field. The resulting control is of feedback type and…
We consider shell models that display an inverse energy cascade similar to 2-dimensional turbulence (together with a direct cascade of an enstrophy-like invariant). Previous attempts to construct such models ended negatively, stating that…
A number of simplified dynamical problems is studied in an attempt to clarify some of the mechanisms leading to turbulence and the existing proposals to control this transition. A simplified set of boundary layer equations displays a…
This paper describes a robust linear time-invariant output-feedback control strategy to reduce turbulent fluctuations, and therefore skin-friction drag, in wall-bounded turbulent fluid flows, that nonetheless gives performance guarantees in…
The transition to turbulence in conduits is among the longest-standing problems in fluid mechanics. Challenges in producing or saving energy hinge on understanding promotion or suppression of turbulence. While a global picture based on an…
We consider linear feedback flow control of the largest scales in an incompressible turbulent channel flow at a friction Reynolds number of Re$_{\tau}$ = 2000. A linear model is formed by linearizing the Navier-Stokes equations about the…
This work studies an a posteriori data-driven approach (known as solver-in-the-loop) for sub-grid modeling of a shell model for turbulence. This approach takes advantage of the differentiable physics paradigm of deep learning, allowing a…
Numerical simulations of turbulence provide non-intrusive access to all the resolved scales, although they often invoke idealizations that can compromise realism. In contrast, experimental measurements probe the true flow with lesser…
When time and velocities are dynamically rescaled relative to the instantaneous turnover time, the Sabra shell model acquires another (hidden) form of scaling symmetry. It has been previously shown that this symmetry is statistically…
This paper deals with the stabilization problem for nonlinear control-affine systems with the use of oscillating feedback controls. We assume that the local controllability around the origin is guaranteed by the rank condition with Lie…
In this paper, we address the problem of closed-loop control of nonlinear dynamical systems subjected to probabilistic uncertainties. More precisely, we design time-varying polynomial feedback controllers to follow the given nominal…
In a recent paper it was proposed that for some nonlinear shell models of turbulence one can construct a linear advection model for an auxiliary field such that the scaling exponents of all the structure functions of the linear and…
Engineering design and scientific analysis rely upon computer simulations of turbulent fluid flows using turbulence models. These turbulence models are empirical and approximate, leading to large uncertainties in their predictions that…
Sedimentation is a crucial phenomenon in recovering water from slurries by separating solid-liquid. Thickeners and sedimentation columns are equipments widely used in the process industry to reclaim water from process slurries. This…
A linear non-modal mechanism for transient amplification of perturbation energy is known to trigger sub-critical transition to turbulence in many shear flows. Feedback control strategies for minimizing this transient energy growth can be…