Optimizing the control of transition to turbulence using a Bayesian method

Abstract

The nonlinear robustness of laminar plane Couette flow is considered under the action of in-phase spanwise wall oscillations by computing properties of the edge of chaos, i.e. the boundary of its basins of attraction. Three measures are used to quantify the chosen control strategy on laminar-to-turbulent transition: the kinetic energy of edge states (local attractors on the edge of chaos), the form of the minimal seed (least energetic perturbation on the edge of chaos), and the laminarization probability (the probability that a random perturbation from the laminar flow of given kinetic energy will laminarize). A novel Bayesian approach is introduced to enable the accurate computation of the laminarization probability at a fraction of the cost of previous methods. While the edge state and the minimal seed provide useful information about the dynamics of transition to turbulence, neither measure is particularly useful to judge the effectiveness of the control strategy since they are not representative of the global geometry of the edge. In contrast, the laminarization probability provides global information about the edge and can be used to evaluate the control effectiveness by computing a laminarization score (the expected laminarization probability) and the associated expected dissipation rate of the controlled flow. These two quantities allow for the determination of optimal control parameter values subject to desired constraints. The results discussed in the paper are expected to be applied to a wide range of transitional flows and control strategies aimed at suppressing or triggering transition to turbulence.

Transition to turbulence in viscoelastic channel flow of dilute polymer solutions

“…2015; Pershin et al. 2022). However, it should be emphasized that the particular form of does not matter as long as it leads to an instability that triggers a transition to turbulence (Faisst & Eckhardt 2004).…”

“…The perturbation field also satisfies no-slip and divergence-free conditions (see Appendix C in Pershin et al (2022) for details of the subroutine randomfield). This perturbation field is similar to that commonly used for the optimal disturbance to control a transition to turbulence (Farano et al 2015;Pershin et al 2022). However, it should be emphasized that the particular form of u p does not matter as long as it leads to an instability that triggers a transition to turbulence (Faisst & Eckhardt 2004).…”

“…The perturbation field also satisfies no-slip and divergence-free conditions (see Appendix C in Pershin et al. (2022) for details of the subroutine randomfield). This perturbation field is similar to that commonly used for the optimal disturbance to control a transition to turbulence (Farano et al.…”

“…The perturbation field u p is generated using the subroutine randomfield through Channelflow (Gibson 2012), where its spectral coefficients of the three velocity components are set to decay exponentially with respect to the wavenumber to ensure the smoothness of the flow, similar to turbulent fields. The perturbation field also satisfies no-slip and divergence-free conditions (see Appendix C in Pershin et al (2022) for details of the subroutine randomfield). This perturbation field is similar to that commonly used for the optimal disturbance to control a transition to turbulence (Farano et al 2015;Pershin et al 2022).…”