Berkeley Fluids Seminar
University of California, Berkeley
Bring your lunch and enjoy learning about fluids!
May 12, 2015
3110 Etcheverry Hall, 12:00-13:00
Dr. Cédric Beaume (Imperial Collge London)
Transitional shear flows: computing exact coherent states in two dimensions
Abstract: In parallel shear flows, the lower branch acts as a separatrix between laminar and turbulent flows while the corresponding upper branch is embedded within the turbulent attractor. In plane Couette flow, the lower branch states are comprised of O(1) streamwise streaks, O(1/Re) streamwise rolls and streamwise-varying fluctuations, and negligibly smaller remaining modes. We use this scaling to derive a closed set of two-dimensional equations that we regularize using subdominant dissipation. This choice for the regularization allows to depart from the inifnite Reynolds critical layer theory and compute relevant transitional states. In this talk, I will introduce the reduced model and explain the numerical strategy to solve efficiently the resulting equations. I will then apply it to a close cousin of plane Couette flow and show the lower branch as well as its saddle-node and the associated upper branch. The reduced model also proves useful in capturing bifurcations to new patterns in extended domains, and is directly applicable to other shear flows.