  This manuscript has been accepted for publication in Physical Review Fluids,
see
https://journals.aps.org/prfluids/accepted/d5074S28J6b11905012b7cb06505e8f2149dd5f20.
  This work investigates the mechanisms that underlie transitions to turbulence
in a three-dimensional domain in which the variation of flow quantities in the
out-of-plane direction is much weaker than any in-plane variation. This is
achieved using a model for the quasi-two-dimensional magnetohydrodynamic flow
in a duct with moving lateral walls and an orthogonal magnetic field. In this
environment, conventional subcritical routes to turbulence, which are highly
three-dimensional, are prohibited. To elucidate the remaining mechanisms
involved in quasi-two-dimensional turbulent transitions, the magnetic field
strength and degree of antisymmetry in the base flow are varied, the latter via
the relative motion of the lateral duct walls. Introduction of any amount of
antisymmetry to the base flow drives the critical Reynolds number infinite, as
the TS instabilities take on opposite signs of rotation, and destructively
interfere. However, an increasing magnetic field strength limits interaction
between the instabilities, permitting finite critical Reynolds numbers. The
transient growth only mildly depends on the base flow, with negligible
differences for friction parameters $H \gtrsim 30$. Direct numerical
simulations, initiated with random noise, indicate that for $H \leq 1$,
supercritical exponential growth leads to saturation, but not turbulence. For
higher $3 \leq H \leq 10$, a turbulent transition occurs, and is maintained at
$H=10$. For $H \geq 30$, the turbulent transition still occurs, but is short
lived, as the turbulent state quickly collapses. In addition, for $H \geq 3$,
an inertial subrange is identified, with the perturbation energy exhibiting a
$-5/3$ power law dependence on wave number.
