Convective Derivative

A Derivative taken with respect to a moving coordinate system, also called a Lagrangian Derivative. It is given by

$${D\over Dt} = {\partial\over\partial t}+{\bf v}\cdot\nabla,$$

where $\nabla$ is the Gradient operator and ${\bf v}$ is the Velocity of the fluid. This type of derivative is especially useful in the study of fluid mechanics. When applied to ${\bf v}$,

$${D{\bf v}\over Dt}= {\partial {\bf v}\over\partial t}+(\nabl... ...\bf v})\times {\bf v}+\nabla({\textstyle{1\over 2}}{\bf v}^2).$$

See also Convective Operator, Derivative, Velocity

References

Batchelor, G K. An Introduction to Fluid Dynamics. Cambridge, England: Cambridge University Press, p. 73, 1977.