A traveling wave bifurcation analysis of turbulent pipe flow

CDSNS Colloquium
Friday, December 3, 2021 - 1:00pm for 1 hour (actually 50 minutes)
Online via Zoom
Maximilian Engel – FU Berlin – maximilian.engel@fu-berlin.dehttps://sites.google.com/view/maximilian-engel/home
Alex Blumenthal

Please Note: Zoom link-- https://us06web.zoom.us/j/83392531099?pwd=UHh2MDFMcGErbzFtMHBZTmNZQXM0dz09

Using techniques from dynamical systems theory, we rigorously study an experimentally validated model by [Barkley et al., Nature, 526:550-553, 2015], which describes the rise of turbulent pipe flow via a PDE system of reduced complexity. The fast evolution of turbulence is governed by reaction-diffusion dynamics coupled to the centerline velocity, which evolves with advection of Burgers' type and a slow relaminarization term. Applying to this model a spatial dynamics ansatz, we prove the existence of a heteroclinic loop between a turbulent and a laminar steady state and establish a cascade of bifurcations of traveling waves mediating the transition to turbulence, with a focus on an intermediate Reynolds number regime.

This is joint work with Björn de Rijk and Christian Kuehn.