Long-ranged correlations in sheared fluids

The presence of long-ranged correlations in a fluid undergoing uniform shear flow is investigated. An exact relation between the density autocorrelation function and the density-mometum correlation function implies that the former must decay more rapidly than $1/r,$ in contrast to predictions of simple mode-coupling theory. Analytic and numerical evaluation of a nonperturbative mode-coupling model confirms a crossover from $1/r$ behavior at “small” r to a stronger asymptotic power-law decay. The characteristic length scale is $\mathcal{l}\approx \sqrt{{\lambda }_0/a},$ where ${\lambda }_0$ is the sound damping constant and a is the shear rate.