  The generation of large scale flows by the anisotropic kinetic alpha (AKA)
effect is investigated in simulations with a suitable time-dependent space- and
time-periodic anisotropic forcing lacking parity invariance. The forcing
pattern moves relative to the fluid, which leads to a breaking of the Galilean
invariance as required for the AKA effect to exist. The AKA effect is found to
produce a clear large scale flow pattern when the Reynolds number, R, is small
as only a few modes are excited in linear theory. In this case the
non-vanishing components of the AKA tensor are dynamically independent of the
Reynolds number. For larger values of R, many more modes are excited and the
components of the AKA tensor are found to decrease rapidly with increasing
value of R. However, once there is a magnetic field (imposed and of sufficient
strength, or dynamo-generated and saturated) the field begins to suppress the
AKA effect, regardless of the value of R. It is argued that the AKA effect is
unlikely to be astrophysically significant unless the magnetic field is weak
and R is small.
