For 10 points, name this operator denoted capital D divided by capital Dt with lowercase t that describes the time rate of change of a property of a fluid as it moves.
Although not the time derivative, for Kelvin's theorem around a curve, this operator is applied to circulation and results in zero. When applied to total energy, this operator yields time change of heat and of work. The time rate of a property C within a volume fixed in space plus the net flux of the property C passing through a bounding surface is equal to this operator applied to the property C as seen in the Reynolds transport theorem. When this operator is applied on a field, it results in the time partial derivative of the field plus the velocity of the fluid dotted to the gradient of the field. For 10 points, name this operator denoted capital D divided by capital Dt with lowercase t that describes the time rate of change of a property of a fluid as it moves.
Although not the time derivative, for Kelvin's theorem around a curve, this operator is applied to circulation and results in zero.
{material} derivative [accept {convective derivative}; accept {advective derivative}; accept {substantive derivative}; accept {Lagrangian derivative}; accept {Stokes derivative}; accept {particle derivative}; accept {hydrodynamic derivative}; accept {total derivative}; accept {capital D divided} by {Dt} or equivalents before mention; prompt on {derivative}]