  We numerically investigate non-local effects on inhomogeneous flows of soft
athermal disks close to but below their jamming transition. We employ molecular
dynamics to simulate Kolmogorov flows, in which a sinusoidal flow profile with
fixed wave number is externally imposed, resulting in a spatially inhomogeneous
shear rate. We find that the resulting rheology is strongly wave
number-dependent, and that particle migration, while present, is not sufficient
to describe the resulting stress profiles within a conventional local model. We
show that, instead, stress profiles can be captured with non-local constitutive
relations that account for gradients to fourth order. Unlike nonlocal flow in
yield stress fluids, we find no evidence of a diverging length scale.
