Subcritical transition scenarios via linear and nonlinear localized optimal perturbations in plane Poiseuille flow

Abstract

transition path similar to the oblique transition scenario, with slightly oscillating streaks which saturate and eventually experience secondary instability. On the other hand, the nonlinear OP rapidly forms large-amplitude bent streaks and skips the phases of streak saturation, providing a contemporary growth of all of the velocity components due to strong nonlinear coupling.

Nonlinear Nonmodal Stability Theory

“…In fact, the latter study was able to reduce T down to ≈ 16 D/U before finding any significant structural change in the NLOP. There is also further indirect evidence for this robustness to the choice T in that similar optimals are reported across a variety of flows: in plane Couette flow (Cherubini & De Palma 2013, 2014a; the Blasius boundary layer (Cherubini et al 2010(Cherubini et al , 2011(Cherubini et al , 2012; the asymptotic suction boundary layer (Cherubini et al 2015) and plane Poiseuille flow (Farano et al 2015(Farano et al , 2016). If T is too small, transients can obscure the situation (Rabin et al 2012) or new optimals become preferred (Pringle et al 2015, Farano 2015.…”

“…) Other strategies have been adopted -e.g. a relaxation approach (Monokrousos et al 2011, Duguet et al 2013), a conjugate gradient method (Cherubini et al 2010, Cherubini & De Palma 2013, Juniper 2011a) and a gradient rotation method (Farano et al 2016(Farano et al , 2017. Evidence for which approach is best is anecdotal and probably varies with the situation.…”

Experiments on transient growth of turbulent spots

“…We also note that the full comparison of the energy gain between the theory and experiment would require to measure also the wall-normal component. Nonlinear transient growth concepts described in (Kerswell et al 2014;Duguet et al 2013;Farano et al 2016) can give further insight on the dynamics of transient states. These theories are based on fully nonlinear Navier-Stokes equations and provide the nonlinear optimal perturbation (NLOP) (typically in the sense of the minimal energy difference from the laminar flow) that can lead to turbulence.…”

Time-Stepping and Krylov Methods for Large-Scale Instability Problems

“…Nonetheless, the optimization formulation offers much more flexibility than simply computing the optimal perturbation in the 2 sense. Indeed, one can choose the objective function J (x) and the associated constraints according to the specific problem he/she aims to solve, see for instance [28,29,23] for optimization based on the 1 norm of the perturabtion.…”