Editing Material derivative (section)

{{Short description|Time rate of change of some physical quantity of a material element in a velocity field}}
In [[continuum mechanics]], the '''material derivative'''<ref name="BSLr2"/><ref name=Batchelor>{{cite book | first=G. K. | last=Batchelor | author-link=George Batchelor | title=An Introduction to Fluid Dynamics | year=1967 | publisher=Cambridge University Press | isbn=0-521-66396-2 | pages=72–73}}</ref> describes the time [[derivative|rate of change]] of some physical quantity (like [[heat]] or [[momentum]]) of a [[material element]] that is subjected to a space-and-time-dependent [[flow velocity|macroscopic velocity field]]. The material derivative can serve as a link between [[Continuum mechanics#Eulerian description|Eulerian]] and [[Continuum mechanics#Lagrangian description|Lagrangian]] descriptions of continuum [[Deformation (mechanics)|deformation]].<ref name=Trenberth>{{cite book | first=K. E. | last=Trenberth | author-link = Kevin Trenberth | title=Climate System Modeling | year=1993 | publisher=Cambridge University Press | isbn=0-521-43231-6 | page=99 }}</ref>

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 this case, the material derivative then describes the temperature change of a certain [[fluid parcel]] with time, as it flows along its [[Streamlines, streaklines, and pathlines|pathline]] (trajectory).
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