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We demonstrate the existence of a large number of exact solutions of plane Couette flow, which share the topology of known periodic solutions but are localized in one spatial dimension. Solutions of different size are organized in a snakes-and-ladders structure strikingly similar to that observed for simpler pattern-forming partial differential equations.… (More)

Generally, the motion of fluids is smooth and laminar at low speeds but becomes highly disordered and turbulent as the velocity increases. The transition from laminar to turbulent flow can involve a sequence of instabilities in which the system realizes progressively more complicated states, or it can occur suddenly. Once the transition has taken place, it… (More)

In shear flows like pipe flow and plane Couette flow there is an extended range of parameters where linearly stable laminar flow coexists with a transient turbulent dynamics. When increasing the amplitude of a perturbation on top of the laminar flow, one notes a a qualitative change in its lifetime, from smoothly varying and short one on the laminar side to… (More)

- Tobias M Schneider, Daniel Marinc, Bruno Eckhardt
- 2009

We study the turbulence transition of plane Couette flow in large domains where localised perturbations are observed to generate growing turbulent spots. Extending previous studies on the boundary between laminar and turbulent dynamics we determine invariant structures intermediate between laminar and turbulent flow. In wide but short domains we find states… (More)

- P K Bhattacharjee, T M Schneider, M P Brenner, G H Mckinley, G C Rutledge
- 2009

The origin and scaling of the current measured during steady electrospinning of polymer solutions in organic solvents is considered. It is demonstrated that, for a specified electric field strength, E, flow rate, Q, and conductivity, K, the total measured current scales as I TOTAL ~EQ 0.5 K 0.4 , for a wide variety of polymer solutions with different… (More)

Microfluidic technology has revolutionized the control of flows at small scales giving rise to new possibilities for assembling complex structures on the microscale. We analyze different possible algorithms for assembling arbitrary structures, and demonstrate that a sequential assembly algorithm can manufacture arbitrary 3D structures from identical… (More)

Flows through pipes and channels are the most common means to transport fluids in practical applications and equally occur in numerous natural systems. In general, the transfer of fluids is energetically far more efficient if the motion is smooth and laminar because the friction losses are lower. However, even at moderate velocities pipe and channel flows… (More)

- Tobias M Schneider, Marburg Lahn, Marburg Bruno Eckhardt, Zweitgutachter, Göttingen Eberhard Bodenschatz, Zusammenfassung Einführung +1 other

Transitional Pipe Flow " Although in most ways the exact manner in which water moves is difficult to perceive and still more difficult to define, as are also the forces attending such motion, certain general features both of the forces and motions stand prominently forth, as if to invite or to defy theoretical treatment. " O. Reynolds [93] Praise be to the… (More)

- Tobias Kreilos, Gregor Veble, Tobias M Schneider, Bruno Eckhardt, J M Burgerscentrum
- 2013

We demonstrate the existence of an exact invariant solution to the Navier-Stokes equations for the asymptotic suction boundary layer. The identified periodic orbit with a very long period of several thousand advective time units is found as a local dynamical attractor embedded in the stability boundary between laminar and turbulent dynamics. Its dynamics… (More)

The transition to turbulence in pipe flow does not follow the scenario familiar from Rayleigh-Benard or Taylor-Couette flow since the laminar profile is stable against infinitesimal perturbations for all Reynolds numbers. Moreover, even when the flow speed is high enough and the perturbation sufficiently strong such that turbulent flow is established, it… (More)