Rectilinear flow

A rectilinear flow has velocity everywhere parallel to a fixed direction and independent of the coordinate in that direction, for example $U(y,z)\hat{x}$. Its convective acceleration vanishes. A steady incompressible viscous rectilinear flow obeys the linear transverse Poisson equation $\nu \Delta U={\rho }^{-1}dp/dx$, rather than an inertia-viscosity balance. This explains Reynolds-number independence of the spatial equation with fixed scaled forcing and boundary data.