Analysis and modeling of localized invariant solutions in pipe flow

Abstract

Turbulent spots surrounded by laminar flow are a landmark of transitional shear flows, but the dependence of their kinematic properties on spatial structure is poorly understood. We here investigate this dependence in pipe flow for Reynolds numbers between 1500 and 5000. We compute spatially localized relative periodic orbits in long pipes and show that their upstream and downstream fronts decay exponentially towards the laminar profile. This allows to model the fronts by employing the linearized Navier-Stokes equations, and the resulting model yields the spatial decay rate and the front velocity profiles of the periodic orbits as a function of Reynolds number, azimuthal wave number and propagation speed. In addition, when applied to a localized turbulent puff, the model is shown to accurately approximate the spatial decay rate of its upstream and downstream tails. Our study provides insight into the relationship between the kinematics and spatial structure of localized turbulence and more generally into the physics of localization.

References in corpus (7)

• Relative periodic orbits in transitional pipe flow
• Statistical analysis of coherent structures in transitional pipe flow
• Streamwise and doubly-localised periodic orbits in plane Poiseuille flow
• A doubly-localized equilibrium solution of plane Couette flow
• Crisis bifurcations in plane Poiseuille flow
• Heteroclinic path to spatially localized chaos in pipe flow
• Streamwise decay of localized states in channel flow

Cited by in corpus (5)

• Statistical transition to turbulence in plane channel flow
• Transition to turbulence in shear flows
• Self-sustainment of coherent structures in counter-rotating Taylor-Couette flow
• Propagation speed of turbulent fronts in pipe flow at high Reynolds numbers
• The origin of localized snakes-and-ladders solutions of plane Couette flow