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: