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 ≈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 optimization, 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 behavior. 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.
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© 2020 American Physical Society.
The authors are grateful for discussions with Ashley Willis regarding the iterative approach applied to the nonlinear transient growth scheme. C.J.C. receives an Australian Government Research Training Program (RTP) Scholarship. A.P. is supported by Wolfson Research Merit Award Scheme Grant No. WM140032 from the Royal Society. This research was supported by the Australian Government via the Australian Research Council (Discovery Grants No. DP150102920 and No. DP180102647), the National Computational Infrastructure (NCI) and Pawsey Supercomputing Centre (PSC), and Monash University via the MonARCH cluster.
ASJC Scopus subject areas
- Computational Mechanics
- Modelling and Simulation
- Fluid Flow and Transfer Processes