Uniform flow ($\mathbf{u}(\mathbf{x})=\mathbf{U}$)

A uniform flow has the same velocity at every position. A constant velocity field has zero divergence and zero vorticity; a velocity potential is $\varphi (\mathbf{x})=\mathbf{U}\cdot \mathbf{x}$. It describes the remote ambient flow in idealized obstacle and line vortex problems.