Material derivative

Summary

The material derivative of a field is its rate of change seen by a fluid parcel that moves with the flow. For a field $f$ and a velocity field $\mathbf{u}$ it equals $\partial f / \partial t + \mathbf{u} \cdot \nabla f$. It links the Lagrangian and Eulerian descriptions of a flow. It appears in every law of motion of a continuum, such as the acceleration term of the Navier–Stokes equations.