Material derivative

The rate of change felt by a moving fluid parcel, $D/Dt = \partial/\partial t + \mathbf{v}\cdot\nabla$ -- not the rate of change at a fixed point.

The material derivative $D/Dt=\partial/\partial t+\mathbf{v}\cdot\nabla$ gives the rate of change experienced by a fluid parcel as it moves, combining the field's own time-dependence with the change it experiences just from moving to a new location.

Examples

A weather balloon's temperature reading changes via the material derivative; a fixed thermometer's reading changes via the ordinary partial time derivative alone.