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− | + | Define the ''convective'', ''total'' or ''material'' [http://en.wikipedia.org/wiki/Convective_derivative ''material'' derivative] operator as | |
− | < | + | |
− | + | <center> | |
− | < | + | <math> |
+ | \frac{D}{Dt} = \frac{\partial}{\partial t} + \mathbf{U} \cdot \nabla | ||
+ | </math> | ||
+ | </center> | ||
+ | |||
+ | This relates the rate of change of a quantity within an infinitesimal control fluid volume that we would witness if we were riding with it along a streamline (Lagrangian viewpoint), to the rate of change of the quantity that a stationary observer would witness from their vantage point on the streamline (Eulerian viewpoint). |
Latest revision as of 00:00, 21 September 2009
Define the convective, total or material material derivative operator as
This relates the rate of change of a quantity within an infinitesimal control fluid volume that we would witness if we were riding with it along a streamline (Lagrangian viewpoint), to the rate of change of the quantity that a stationary observer would witness from their vantage point on the streamline (Eulerian viewpoint).