Universal dynamics in the onset of a Hagen-Poiseuille flow

Details Universal dynamics in the onset of a Hagen-Poiseuille flow Universal dynamics in the onset of a Hagen-Poiseuille flow

2005-11-07

arxiv.org/abs/physics/0511056v2

Phys. Rev. E 74, 017301 (2006)

Physics

Fluid Dynamics

4 pages including 1 figure

Scientific paper

10.1103/PhysRevE.74.017301

The dynamics in the onset of a Hagen-Poiseuille flow of an incompressible liquid in a channel of circular cross section is well-studied theoretically. We use an eigenfunction expansion in a Hilbert space formalism to generalize the results to channels of arbitrary cross section. We find that the steady state is reached after a characteristic time scale tau = (A/P)^2 (1/nu) where A and P are the cross-sectional area and perimeter, respectively, and $\nu$ is the kinematic viscosity of the liquid. For the initial dynamics of the flow rate Q for t<

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