Sub critical transition to turbulence in three-dimensional Kolmogorov flow

Abstract

We study Kolmogorov flow on a three dimensional, periodic domain with aspect ratios fixed to unity. Using an energy method, we give a concise proof of the linear stability of the laminar flow profile. Since turbulent motion is observed for high enough Reynolds numbers, we expect the domain of attraction of the laminar flow to be bounded by the stable manifolds of simple invariant solutions. We show one such edge state to be an equilibrium with a spatial structure reminiscent of that found in plane Couette flow, with stream wise rolls on the largest spatial scales. When tracking the edge state, we find an upper and a lower branch solution that join in a saddle node bifurcation at finite Reynolds number.

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Cited by in corpus (8)

• Layer formation in horizontally forced stratified turbulence: connecting exact coherent structures to linear instabilities
• Coarse graining the state space of a turbulent flow using periodic orbits
• Sustaining processes from recurrent flows in body-forced turbulence
• Transitions of turbulent superstructures in generalized Kolmogorov flow
• Minimal model of quasi-cyclic behaviour in turbulence driven by Taylor--Green forcing
• Pseudospectral bound and transition threshold for the 3D Kolmogorov flow
• Preferential concentration by mechanically-driven turbulence in the two-fluid formalism
• Stability Theory of the 3-Dimensional Euler Equations