Bypass transition in plane Poiseuille flow and boundary layers

Bruno Eckhardt
Philipps-Universität Marburg

Both plane Poiseuille flow and boundary layers show a linear instability to the formation of Tollmien-
Schlichting waves and a transition at lower Reynolds numbers that is not connected with a linear instability of the
laminar profile but triggered by finite amplitude perturbations, the bypass transition. In the case of plane
Poiseuille flow we show how the two processes are arranged in the state space of the system and explain under
which conditions the bypass process is the more dominant one, with the linear instability confined to a small set
of initial conditions. For the case of the boundary layer, we appeal to the successful modelling of shear flows
with probabilistic cellular automata and concepts from directed percolation. We fit a automaton model to data
from large eddy simulations of boundary layers with different levels of free stream turbulence (Figure 1). The
cellular automaton reproduces the statistics of the simulation data extremely well (Figure 2).

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