Substantive Derivative -- from Eric Weisstein's World of Physics

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Substantive Derivative

A form of derivative Eric Weisstein's World of Math which takes into account the fact that a quantity changes both as it moves to a different region and as the overall field is changing. It most commonly used in fluid mechanics, is also called the advective derivative, and is defined by

where is the velocity of a fluid parcel and is a vector operator obtained by taking the dot product Eric Weisstein's World of Math of u and the gradient Eric Weisstein's World of Math operator.

Navier-Stokes Equations, Newton's Law for Fluids, Viscosity