Convective Derivative

The convective derivative is a derivative taken with respect to a moving coordinate system. It is also called the advective derivative, derivative following the motion, hydrodynamic derivative, Lagrangian derivative, material derivative, particle derivative, substantial derivative, substantive derivative (Tritton 1989), Stokes derivative (Kaplan 1991, pp. 189-191), or total derivative. It is given by

 D/(Dt)=partial/(partialt)+v·del ,

where del is the gradient operator and v is the velocity of the fluid. This type of derivative is especially useful in the study of fluid mechanics. When applied to v,

 (Dv)/(Dt)=(partialv)/(partialt)+(del xv)xv+del (1/2v^2).

See also

Convective Operator, Derivative, Euler's Equations of Inviscid Motion, Navier-Stokes Equations, Vector Derivative, Velocity

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Batchelor, G. K. An Introduction to Fluid Dynamics. Cambridge, England: Cambridge University Press, p. 73, 1977.Kaplan, W. Advanced Calculus, 4th ed. Reading, MA: Addison-Wesley, 1991.Tritton, D. J. "The Substantive Derivative." §5.5 in Physical Fluid Dynamics, 2nd ed. Oxford, England: Clarendon Press, pp. 53-55, 1989.

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Convective Derivative

Cite this as:

Weisstein, Eric W. "Convective Derivative." From MathWorld--A Wolfram Web Resource.

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