  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.

Fluid Dynamics