Data-driven modeling of subharmonic forced response due to nonlinear resonance.

Complex behavior in nonlinear dynamical systems often arises from resonances, which enable intricate energy transfer mechanisms among modes that otherwise would not interact. Theoretical, numerical and experimental methods are available to study such behavior when the resonance arises among modes of the linearized system. Much less understood are, however, resonances arising from nonlinear modal interactions, which cannot be detected from a classical linear analysis.

Routes to turbulence in Taylor-Couette flow.

Fluid flows between rotating concentric cylinders exhibit two distinct routes to turbulence. In flows dominated by inner-cylinder rotation, a sequence of linear instabilities leads to temporally chaotic dynamics as the rotation speed is increased. The resulting flow patterns occupy the whole system and sequentially lose spatial symmetry and coherence in the transition process.

Data-driven modeling and prediction of non-linearizable dynamics via spectral submanifolds.

We develop a methodology to construct low-dimensional predictive models from data sets representing essentially nonlinear (or non-linearizable) dynamical systems with a hyperbolic linear part that are subject to external forcing with finitely many frequencies. Our data-driven, sparse, nonlinear models are obtained as extended normal forms of the reduced dynamics on low-dimensional, attracting spectral submanifolds (SSMs) of the dynamical system. We illustrate the power of data-driven SSM reduction on high-dimensional numerical data sets and experimental measurements involving beam oscillations, vortex shedding and sloshing in a water tank.

Phase Transition to Turbulence in Spatially Extended Shear Flows.

Directed percolation (DP) has recently emerged as a possible solution to the century old puzzle surrounding the transition to turbulence. Multiple model studies reported DP exponents, however, experimental evidence is limited since the largest possible observation times are orders of magnitude shorter than the flows' characteristic timescales. An exception is cylindrical Couette flow where the limit is not temporal, but rather the realizable system size.

Second-Order Phase Transition in Counter-Rotating Taylor-Couette Flow Experiment.

In many basic shear flows, such as pipe, Couette, and channel flow, turbulence does not arise from an instability of the laminar state, and both dynamical states co-exist. With decreasing flow speed (i.e.

Liquidlike sloshing dynamics of monodisperse granulate.

Analogies between fluid flows and granular flows are useful because they pave the way for continuum treatments of granular media. However, in practice it is impossible to predict under what experimental conditions the dynamics of fluids and granulates are qualitatively similar. In the case of unsteadily driven systems no such analogy is known.

High-precision Taylor-Couette experiment to study subcritical transitions and the role of boundary conditions and size effects.

A novel Taylor-Couette system has been constructed for investigations of transitional as well as high Reynolds number turbulent flows in very large aspect ratios. The flexibility of the setup enables studies of a variety of problems regarding hydrodynamic instabilities and turbulence in rotating flows. The inner and outer cylinders and the top and bottom endplates can be rotated independently with rotation rates of up to 30 Hz, thereby covering five orders of magnitude in Reynolds numbers (Re = 10(1)-10(6)).

The onset of turbulence in pipe flow.

Shear flows undergo a sudden transition from laminar to turbulent motion as the velocity increases, and the onset of turbulence radically changes transport efficiency and mixing properties. Even for the well-studied case of pipe flow, it has not been possible to determine at what Reynolds number the motion will be either persistently turbulent or ultimately laminar. We show that in pipes, turbulence that is transient at low Reynolds numbers becomes sustained at a distinct critical point.