Disentangling chaotic laminar and turbulent flow components

Damien Biau (1) , Leonardo Rigo (1)

1 DynFluid - Laboratoire de Dynamique des Fluides

Transition to turbulence generally involves successive bifurcations from steady laminar solution to spatio-temporal chaos. For the case of slightly curved duct flows, the scale separation allows to separate the Navier-Stokes equations into two sets, namely the laminar solution and turbulent fluctuations. The laminar flow is sensitive to the weak curvature and is governed by the Dean number, while the small scale turbulent disturbances are insensitive to the curvature and are governed by the Reynolds number. The laminar solution is subject to super critical bifurcation leading to temporal chaos for increasing Dean number. On the other hand, the turbulent fluctuations show a sub-critical bifurcation depending on the Reynolds number. The separation between laminar, temporally chaotic solution and turbulent disturbances allows to separate the secondary flow in accordance to Prandtl's classification. The frequency analysis of the respective head losses illustrates the nonreciprocal influence of the temporal-chaos onto the spatio-temporal turbulence.

Mots clés: Dean vortices; prandtl vortices; curved duct; Dean number

Domaines: Mécanique des fluides [physics.class-ph]

Damien Biau, Leonardo Rigo. Disentangling chaotic laminar and turbulent flow components. 2022. ⟨hal-03675033v1⟩