Systems of multiple current sheets arise in various situations in natu
ral plasmas, such as
at the heliospheric current sheet in the solar wind and in the outer he
liosphere in the
heliosheath. Previous three-dimensional simulations have shown th
at such systems can
develop turbulent-like fluctuations resulting from forward and inve
rse cascade in wave
vector space. We present a study of the transition to turbulence
of such multiple current
sheet systems, including the effects of adding a magnetic guide field a
nd velocity shears
across the current sheets. Three-dimensional hybrid simulations
are performed of systems
with eight narrow current sheets in a triply-periodic geometry. We c
arry out a number
of different analyses of the evolution of the fluctuations as the initia
lly highly ordered
state relaxes to one which resembles turbulence. Despite the evide
nce of forward and
inverse cascade in the fluctuation power spectra, we find that non
e of the simulated cases
have evidence of intermittency after the initial period of fast reco
nnection associated
with the ion tearing instability at the current sheets. Cancellation an
alysis confirms that
the simulations have not evolved to a state which can be identified as f
ully developed
turbulence. The addition of velocity shears across the current sh
eets slows the evolution
in the properties of the fluctuations, but by the end of the simulatio
n they are broadly
similar. However, if the simulation is constrained to be two-dimensiona
l, differences are
found, indicating that fully three-dimensional simulations are import
ant when studying
the evolution of an ordered equilibrium towards a turbulent-like stat
e.