title: Rivlin–Ericksen tensor
text: # Rivlin–Ericksen tensor
  
  A Rivlin–Ericksen temporal evolution of the strain rate tensor such that the derivative translates and rotates with the flow field. The first-order Rivlin–Ericksen is given by
  
      $\mathbf {A} _{ij(1)}={\frac {\partial v_{i}}{\partial x_{j}}}+{\frac {\partial v_{j}}{\partial x_{i}}}$
  
  where
  
      $v_{i}$ is the fluid's velocity and
      $A_{ij(n)}$ is $n$-th order Rivlin–Ericksen tensor.
  
  Higher-order tensor may be found iteratively by the expression
  
      $A_{ij(n+1)}={\frac {\mathcal {D}}{{\mathcal {D}}t}}A_{ij(n)}.$
  
  The derivative chosen for this expression depends on convention. The upper-convected time derivative, lower-convected time derivative, and Jaumann derivative are often used.
  
  