About: Upper-convected time derivative

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In continuum mechanics, including fluid dynamics, an upper-convected time derivative or Oldroyd derivative, named after James G. Oldroyd, 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: where: * is the upper-convected time derivative of a tensor field * is the substantive derivative * is the tensor of velocity derivatives for the fluid. The formula can be rewritten as:

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  • In continuum mechanics, including fluid dynamics, an upper-convected time derivative or Oldroyd derivative, named after James G. Oldroyd, 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: where: * is the upper-convected time derivative of a tensor field * is the substantive derivative * is the tensor of velocity derivatives for the fluid. The formula can be rewritten as: By definition, the upper-convected time derivative of the Finger tensor is always zero. It can be shown that the upper-convected time derivative of a spacelike vector field is just its Lie derivative by the velocity field of the continuum. The upper-convected derivative is widely used in polymer rheology for the description of the behavior of a viscoelastic fluid under large deformations. (en)
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  • In continuum mechanics, including fluid dynamics, an upper-convected time derivative or Oldroyd derivative, named after James G. Oldroyd, 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: where: * is the upper-convected time derivative of a tensor field * is the substantive derivative * is the tensor of velocity derivatives for the fluid. The formula can be rewritten as: (en)
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  • Upper-convected time derivative (en)
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