text: Contour advection is another useful method for characterizing chaotic mixing.
  In chaotic flows, advected contours will grow exponentially over time.
  The figure above shows the frame-by-frame evolution of a contour advected over
  several days.  The figure to the right shows the length of this contour
  as a function of time.
  The link between exponential contour growth and positive Lyapunov exponents is
  easy to see.  The rate of contour growth is given as:
  where  is the path 
  and the integral is performed over the length of the contour.  
  Contour growth rates will approximate the average of the large Lyapunov exponents: