Transient growth of perturbations in Stokes oscillatory flows

Abstract

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Oscillatory Stokes flows, with zero mean, are subjected to subcritical transition to turbulence. The maximal energy growth of perturbations is computed in the subcritical regime through an optimisation method. The results show strong amplifications during half a period. The energy transfer from the base flow involves an Orr mechanism with two-dimensional vorticity waves, and the maximum energy scales exponentially with the Reynolds number. Nonlinear simulations show that low-energy perturbations are sufficient to trigger turbulent flow.

Non-modal transient growth of disturbances in pulsatile and oscillatory pipe flows

“…Nebauer (2019) anticipated that in certain regimes of pulsatile pipe flow, the energy growth scales exponentially with the Reynolds number. This was also reported for the oscillatory Stokes layer over a flat plate (Biau 2016) and for the flow following an axisymmetric stenosis (Blackburn, Sherwin & Barkley 2008). Large non-modal transient amplification of disturbances has also been found in pulsatile channel flow (Tsigklifis & Lucey 2017).…”

“…However, approximately of the kinetic energy is shared in equal parts between the azimuthal and stream-wise components, which indicates a strong three-dimensional effect, distinct from the two-dimensional Orr mechanism reported for many flows (see e.g. Boyd 1983; Farrell 1988; Maretzke, Hof & Avila 2014; Biau 2016).…”

Nonlinear Nonmodal Stability Theory

“…This would imply that the finite amplitude instability can be triggered very easily in both experiments by ambient noise and numerical simulations by the supposedly small initial conditions used to initiate runs (Ozdemir et al 2014). The linear nonmodal analysis also indicates that only the Orr mechanism is important and so the optimal starting time found there may be good for the nonlinear nonmodal analysis too: see Table 1 of Biau (2016).…”

Non-modal stability analysis of the boundary layer under solitary waves

“…This exponential growth of the maximum amplification with the Reynolds number has also been observed for other flows displaying an adverse pressure gradient. For example, Biau (2016) observed that the maximum amplification of two-dimensional perturbations for Stokes' second problem grows exponentially with the Reynolds number. In the following, we shall see that the competition of the maximum amplification between the quadratic growth in Re δ of streamwise streaks, equation (3.5), and the exponential growth in Re δ of two-dimensional structures, equation (3.20), composes the essential primary instability mechanism of this flow.…”