2017/12/14 by Enrico Rinaldi, Philipp Schlatter, Shervin Bagheri
Engineering · Physics and Astronomy · #Attractor #Biomimetic flight and propulsion mechanisms #Enhanced Data Rates for GSM Evolution #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #Kinetic energy #Laminar flow #Micro and Nano Robotics #Modulation (music) #Reynolds number #Turbulence #Viscosity #physics.flu-dyn
paper · pdf · doi:10.1017/jfm.2017.921
25 pages, 21 figures. Accepted for publication on the Journal of Fluid Mechanics
arxiv created 2017/12/14 · openalex created_date 2017/12/22 · openalex publication_date 2018/01/16 · arxiv updated 2018/02/14 · openalex updated_date 2026/08/05
Motivated by the relevance of edge state solutions as mediators of transition, we use direct numerical simulations to study the effect of spatially non-uniform viscosity on their energy and stability in minimal channel flows. What we seek is a theoretical support rooted in a fully nonlinear framework that explains the modified threshold for transition to turbulence in flows with temperature-dependent viscosity. Consistently over a range of subcritical Reynolds numbers, we find that decreasing viscosity away from the walls weakens the streamwise streaks and the vortical structures responsible for their regeneration. The entire self-sustained cycle of the edge state is maintained on a lower kinetic energy level with a smaller driving force, compared to a flow with constant viscosity. Increasing viscosity away from the walls has the opposite effect. In both cases, the effect is proportional to the strength of the viscosity gradient. The results presented highlight a local shift in the state space of the position of the edge state relative to the laminar attractor with the consequent modulation of its basin of attraction in the proximity of the edge state and of the surrounding manifold. The implication is that the threshold for transition is reduced for perturbations evolving in the neighbourhood of the edge state in the case that viscosity decreases away from the walls, and vice versa .