  We present scale-dependent measurements of the normalised growth rate of
structure $f\sigma_{8}(k, z=0)$ using only the peculiar motions of galaxies. We
use data from the 6-degree Field Galaxy Survey velocity sample (6dFGSv)
together with a newly-compiled sample of low-redshift $(z < 0.07)$ type Ia
supernovae. We constrain the growth rate in a series of $\Delta k \sim 0.03
h{\rm Mpc^{-1}}$ bins to $\sim35\%$ precision, including a measurement on
scales $>300 h^{-1}{\rm Mpc}$, which represents one of the largest-scale growth
rate measurement to date. We find no evidence for a scale dependence in the
growth rate, or any statistically significant variation from the growth rate as
predicted by the {\it Planck} cosmology. Bringing all the scales together, we
determine the normalised growth rate at $z=0$ to $\sim15\%$ in a manner {\it
independent} of galaxy bias and in excellent agreement with the constraint from
the measurements of redshift-space distortions from 6dFGS. We pay particular
attention to systematic errors. We point out that the intrinsic scatter present
in Fundamental-Plane and Tully-Fisher relations is only Gaussian in logarithmic
distance units; wrongly assuming it is Gaussian in linear (velocity) units can
bias cosmological constraints. We also analytically marginalise over zero-point
errors in distance indicators, validate the accuracy of all our constraints
using numerical simulations, and demonstrate how to combine different
(correlated) velocity surveys using a matrix `hyper-parameter' analysis.
Current and forthcoming peculiar velocity surveys will allow us to understand
in detail the growth of structure in the low-redshift universe, providing
strong constraints on the nature of dark energy.
