We study the passive transport of a scalar field by a spatially smooth but white-in-time incompressible Gaussian random velocity field on R d . If the velocity field u is homogeneous, isotropic, and statistically self-similar, we derive an exact formula which captures non-diffusive mixing. For zero diffusivity, the formula takes the shape of E ‖ θ t ‖ H ˙ - s 2 = e - λ d , s t ‖ θ 0 ‖ H ˙ - s 2 with any s ∈ (0 , d / 2) and λ d , s D 1 : = s (λ 1 D 1 - 2 s) where λ 1 / D 1 = d is the top Lyapunov exponent associated to the random Lagrangian flow generated by u and D 1 is small-scale shear rate of the velocity. Moreover, the mixing is shown to hold uniformly in diffusivity. [ABSTRACT FROM AUTHOR]