  A static correlation function of concentration fluctuations in a (dilute)
binary liquid mixture subjected to both a concentration gradient and uniform
shear flow is investigated within the framework of fluctuating hydrodynamics.
It is shown that a well-known $|\nabla c|^2/k^4$ long-range correlation at
large wave numbers $k$ crosses over to a weaker divergent one for wave numbers
satisfying $k<(\dot{\gamma}/D)^{1/2}$, while an asymptotic shear-controlled
power-law dependence is confirmed at much smaller wave numbers given by $k\ll
(\dot{\gamma}/\nu)^{1/2}$, where $c$, $\dot{\gamma}$, $D$ and $\nu$ are the
mass concentration, the rate of the shear, the mass diffusivity and the
kinematic viscosity of the mixture, respectively. The result will provide for
the first time the possibility to observe the shear-induced suppression of a
long-range correlation experimentally by using, for example, a low-angle light
scattering technique.
