text: It may be shown that, in orthogonal coordinates, the -th component of the convection term of the material derivative of a vector field  is given by
  where the  are related to the metric tensors by 
  In the special case of a three-dimensional Cartesian coordinate system (x, y, z), and  being a 1-tensor (a vector with three components), this is just:
  where  is a Jacobian matrix.