Damping in a fluid

Question

I am trying to understand damping in a fluid.Take, for instance, water flowing down a surface. I know a damping term $-\alpha\mathbf{u}$, where $\mathbf{u}$ is the velocity field, is added to the sum of forces in the momentum equation. Can I think of this damping term as being analogous to the damping term of a mass-spring oscillator, i.e., that the faster the water flows down the surface, the greater the friction between the water and the surface is, and that's why the damping term is proportional to the velocity?