  We carry our numerical simulations of athermally sheared, bidisperse,
frictionless disks in two dimensions. From an appropriately defined velocity
correlation function, we determine that there are two diverging length scales,
$\xi$ and $\ell$, as the jamming transition is approached. We analyze our
results using a critical scaling ansatz for the correlation function, and argue
that the more divergent length $\ell$ is a consequence of a dangerous
irrelevant scaling variable, and that it is $\xi$ which is the correlation
length that determines the divergence of the system viscosity as jamming is
approached from below in the liquid phase. We find that $\xi\sim
(\phi_J-\phi)^{-\nu}$ diverges with the critical exponent $\nu=1$. We provide
evidence that $\xi$ measures the length scale of fluctuations in the rotation
of the particle velocity field, while $\ell$ measures the length scale of
fluctuations in the divergence of the velocity field.

Soft Condensed Matter