Shear flow

A shear flow has a velocity field varying across adjacent fluid layers, giving a nonzero shear rate. A parallel example is $\mathbf{u}=U(z){\mathbf{e}}_x$, with vertical shear $U^{\prime }$. Linear shear flow has constant shear, while a shear layer concentrates the velocity change in a narrow region.

A linear shear flow has velocity that varies linearly in a transverse coordinate, such as $\mathbf{u}=-Sx{\mathbf{e}}_y$. Its velocity gradient and shear rate are spatially constant.