  We discuss the observability of circular polarisation of the stochastic
gravitational-wave background (SGWB) generated by helical turbulence following
a first-order cosmological phase transition, using a model that incorporates
the effects of both direct and inverse energy cascades. We explore the strength
of the gravitational-wave signal and the dependence of its polarisation on the
helicity fraction, $\zeta_*$, the strength of the transition, $\alpha$, the
bubble size, $R_*$, and the temperature, $T_*$, at which the transition
finishes. We calculate the prospective signal-to-noise ratios of the SGWB
strength and polarisation signals in the LISA experiment, exploring the
parameter space in a way that is minimally sensitive to the underlying particle
physics model. We find that discovery of SGWB polarisation is generally more
challenging than measuring the total SGWB signal, but would be possible for
appropriately strong transitions with large bubble sizes and a substantial
polarisation fraction.
