Time rate of change of some physical quantity of a material element in a velocity field
In continuum mechanics, the material derivative[1][2] describes the time rate of change of some physical quantity (like heat or momentum) of a material element that is subjected to a space-and-time-dependent macroscopic velocity field. The material derivative can serve as a link between Eulerian and Lagrangian descriptions of continuum deformation.[3]
For example, in fluid dynamics, the velocity field is the flow velocity, and the quantity of interest might be the temperature of the fluid. In which case, the material derivative then describes the temperature change of a certain fluid parcel with time, as it flows along its pathline (trajectory).
^Cite error: The named reference BSLr2 was invoked but never defined (see the help page).
^Batchelor, G. K. (1967). An Introduction to Fluid Dynamics. Cambridge University Press. pp. 72–73. ISBN 0-521-66396-2.
^Trenberth, K. E. (1993). Climate System Modeling. Cambridge University Press. p. 99. ISBN 0-521-43231-6.
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