Traveling waves in pipe flow.
- H. Faisst, B. Eckhardt
- Physics, EngineeringPhysical Review Letters
- 15 April 2003
A family of three-dimensional traveling waves for flow through a pipe of circular cross section that provide a skeleton for the formation of a chaotic saddle that can explain the intermittent transition to turbulence and the sensitive dependence on initial conditions in this shear flow.
Turbulence transition in pipe flow
- B. Eckhardt, T. Schneider, B. Hof, J. Westerweel
- Physics
- 2007
Pipe flow is a prominent example among the shear flows that undergo transition to turbulence without mediation by a linear instability of the laminar profile. Experiments on pipe flow, as well as…
Torque scaling in turbulent Taylor–Couette flow between independently rotating cylinders
- B. Eckhardt, S. Grossmann, D. Lohse
- PhysicsJournal of Fluid Mechanics
- 22 May 2007
Turbulent Taylor–Couette flow with arbitrary rotation frequencies ω1, ω2 of the two coaxial cylinders with radii r1 < r2 is analysed theoretically. The current Jω of the angular velocity ω(x,t) =…
Edge of chaos in a parallel shear flow.
- J. Skufca, J. Yorke, B. Eckhardt
- PhysicsPhysical Review Letters
- 5 May 2006
It is found that the surface of the edge of chaos coincides with the stable manifold of a periodic orbit, whereas at higher Reynolds numbers it is the stable set of a higher-dimensional chaotic object.
Finite lifetime of turbulence in shear flows
- B. Hof, J. Westerweel, T. Schneider, B. Eckhardt
- Physics, EngineeringNature
- 19 July 2006
Experimental data and numerical calculations covering more than two decades of lifetimes are presented, showing that the lifetime does not in fact diverge but rather increases exponentially with the Reynolds number, implying that turbulence in pipes is only a transient event, and that the turbulent and laminar states remain dynamically connected, suggesting avenues for turbulence control.
A low-dimensional model for turbulent shear flows
- J. Moehlis, H. Faisst, B. Eckhardt
- Physics
- 27 May 2004
We analyse a low-dimensional model for turbulent shear flows. The model is based on Fourier modes and describes sinusoidal shear flow, in which the fluid between two free-slip walls experiences a…
Sensitive dependence on initial conditions in transition to turbulence in pipe flow
- H. Faisst, B. Eckhardt
- PhysicsJournal of Fluid Mechanics
- 11 December 2003
The experiments by Darbyshire & Mullin (1995) on the transition to turbulence in pipe flow show that there is no sharp border between initial conditions that trigger turbulence and those that do not.…
Experimental Observation of Nonlinear Traveling Waves in Turbulent Pipe Flow
- B. Hof, C. van Doorne, F. Waleffe
- Physics, EngineeringScience
- 10 September 2004
Experimental observation of unstable traveling waves in pipe flow is reported, confirming the proposed transition scenario and suggesting that the dynamics associated with these unstable states may indeed capture the nature of fluid turbulence.
Intermittent boundary layers and torque maxima in Taylor-Couette flow
- H. Brauckmann, B. Eckhardt
- Physics, Engineering
- 22 October 2012
Turbulent Taylor-Couette flow between counter-rotating cylinders develops intermittently fluctuating boundary layers for sufficient counter-rotation. We demonstrate the phenomenon in direct numerical…
Laminar-turbulent boundary in plane Couette flow.
- T. Schneider, J. Gibson, M. Lagha, F. De Lillo, B. Eckhardt
- PhysicsPhysical review. E, Statistical, nonlinear, and…
- 7 May 2008
The results reported here show that in cases where a fixed point has only one unstable direction, such as for the lower-branch solution in plane Couette flow, the iterated edge tracking algorithm converges to this state and that the choice of initial state is not critical and that essentially arbitrary initial conditions can be used to find the edge state.
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