Subcritical route to turbulence via the Orr mechanism in a quasi-two-dimensional boundary layer

TL;DR

This study investigates a subcritical transition to turbulence in a quasi-two-dimensional boundary layer, revealing the critical role of the Orr mechanism and Tollmien-Schlichting waves, with implications for liquid metal coolant systems in fusion reactors.

Contribution

It demonstrates that purely quasi-two-dimensional mechanisms can induce subcritical turbulence, highlighting the importance of initial perturbation structure and domain length in transition dynamics.

Findings

Transition occurs only at weakly subcritical Reynolds numbers.

Tollmien-Schlichting waves can trigger transition via the Orr mechanism.

Nonlinear energy gains vastly exceed linear gains, enabling turbulence onset.

Abstract

The link to the online abstract of this manuscript, accepted in Phys. Rev. Fluids, is https://journals.aps.org/prfluids/accepted/32074S4aH8b1c608e19768b42571f9001086a3f44. A subcritical route to turbulence via purely quasi-two-dimensional mechanisms, for a quasi-two-dimensional system composed of an isolated exponential boundary layer, is numerically investigated. Exponential boundary layers are highly stable, and are expected to form on the walls of liquid metal coolant ducts within magnetic confinement fusion reactors. Subcritical transitions were detected only at weakly subcritical Reynolds numbers (at most $\approx 70$% below critical). Furthermore, the likelihood of transition was very sensitive to both the perturbation structure and initial energy. Only the quasi-two-dimensional Tollmien-Schlichting wave disturbance, attained by either linear or nonlinear optimisation, was able to initiate the transition process, by means of the Orr mechanism. The lower initial energy bound sufficient to trigger transition was found to be independent of the domain length. However, longer domains were able to increase the upper energy bound, via the merging of repetitions of the Tollmien-Schlichting wave. This broadens the range of initial energies able to exhibit transitional behaviour. Although the eventual relaminarization of all turbulent states was observed, this was also greatly delayed in longer domains. The maximum nonlinear gains achieved were orders of magnitude larger than the maximum linear gains (with the same initial perturbations), regardless if the initial energy was above or below the lower energy bound. Nonlinearity provided a second stage of energy growth by an arching of the conventional Tollmien-Schlichting wave structure. A streamwise independent structure, able to efficiently store perturbation energy, also formed.