The notation "D/Dt" is used in problems dealing with fluid flow and is "rate of change with the flow".

For example, if T(x, y, z, t) is the temperature at each point (x, y, z) and time t of water in some channel and you lean over and stick a thermometer into the water to record the temperature at a specific point, you would be measuring the temperature of different "bits" of water as they flow by the thermometer. The rate of change of your readings would be dT/dt (or, more correctly, ). If, instead, you attach a thermometer to a small block of wood and let it move with the flow, so that your thermometer records the temperature of a single "bit" of water as it flows, the rate of change of your readings would be DT/Dt.

If I remember corrrectly (it's been a while), If the velocity vector is , again at each point (x, y, z) and time t, then where