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Upper convected time derivative
In continuum mechanics, including fluid dynamics upper convected time derivative or Oldroyd derivative is the rate of change of some tensor property of a small parcel of fluid that is written in the coordinate system rotating and stretching with the fluid.
The operator is specified by the following formula:
The formula can be rewritten as:
By definition the upper convected time derivative of the Finger tensor is always zero.
Additional recommended knowledge
Examples for the symmetric tensor A
For the case of simple shear:
Uniaxial extension of uncompressible fluid
In this case a material is stretched in the direction X and compresses in the direction s Y and Z, so to keep volume constant. The gradients of velocity are:
|This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Upper_convected_time_derivative". A list of authors is available in Wikipedia.|