Bruno Eckhardt

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Plane Couette flow and pressure-driven pipe flow are two examples of flows where turbulence sets in while the laminar profile is still linearly stable. Experiments and numerical studies have shown that the transition has features compatible with the formation of a strange saddle rather than an attractor. In particular, the transition depends sensitively on(More)
We apply the iterated edge-state tracking algorithm to study the boundary between laminar and turbulent dynamics in plane Couette flow at Re=400. Perturbations that are not strong enough to become fully turbulent or weak enough to relaminarize tend toward a hyperbolic coherent structure in state space, termed the edge state, which seems to be unique up to(More)
The linear stability of pipe flow implies that only perturbations of sufficient strength will trigger the transition to turbulence. In order to determine this threshold in perturbation amplitude we study the edge of chaos which separates perturbations that decay towards the laminar profile and perturbations that trigger turbulence. Using the lifetime as an(More)
A family of three-dimensional traveling waves for flow through a pipe of circular cross section is identified. The traveling waves are dominated by pairs of downstream vortices and streaks. They originate in saddle-node bifurcations at Reynolds numbers as low as 1250. All states are immediately unstable. Their dynamical significance is that they provide a(More)
Transition to turbulence in pipe flow is one of the most fundamental and longest-standing problems in fluid dynamics. Stability theory suggests that the flow remains laminar for all flow rates, but in practice pipe flow becomes turbulent even at moderate speeds. This transition drastically affects the transport efficiency of mass, momentum, and heat. On the(More)
Abstract. We consider the dynamics of a low-dimensional model for turbulent shear flows. The model is based on Fourier modes and describes sinusoidal shear flow, in which fluid between two free-slip walls experiences a sinusoidal body force. The model contains nine modes, most of which have a direct hydrodynamical interpretation. We analyze the stationary(More)
Numerical and experimental studies of transitional pipe flow have shown the prevalence of coherent flow structures that are dominated by downstream vortices. They attract special attention because they contribute predominantly to the increase of the Reynolds stresses in turbulent flow. In the present study we introduce a convenient detector for these(More)
The 125th anniversary of Osborne Reynolds’ seminal publication on the transition to turbulence in pipe flow offers an opportunity to survey our understanding of the nature of the transition. Dynamical systems concepts, computational methods and dedicated experiments have helped to elucidate some of Reynolds’ observations and to extract new quantitative(More)
We study the transition between laminar and turbulent states in a Galerkin representation of a parallel shear flow, where a stable laminar flow and a transient turbulent flow state coexist. The regions of initial conditions where the lifetimes show strong fluctuations and a sensitive dependence on initial conditions are separated from the ones with a smooth(More)