Since the velocity at an arbitrary point u( x,y,t ) can be obtained by (2.11), contours put on anywhere can be advected by same numerical method without affecting on the velocity field.

Initial conditions are given as follows:

Vortex patch: same as in section 4.1 ( bold line ).
Passive contours (inside): Ellipses similar to the vortex patch with their major axis shrinking at an interval of 0.1 ( blue to light purple ).
Passive contours (outside): Ellipses similar to the vortex patch with their major axis extending at an interval of 0.1 ( blue to green, yellow, and red ).

Animation 2: Advection of passive contours (GIF animation; 1990kB).
The contour positions are displayed from t = 0.0 to t = 10.0 at an interval of 0.1 . Fluid in y < 0 at initial time is colored light blue.

- Passive contours clearly show the flow in other regions than the patch contour where little interest was put on in the previous analyses.

- The fluid are deformed even while the elliptical vortex keeps its shape. Especially at the edge of the ellipse, the fluid outside the vortex is dragged and stretched out.

- Fluid particles are stretched near the sreamlines containing the stagnation points in the co-rotating frame analyzed in section 4.2 .

- A complex flow pattern is produced after the streamer formation. There are many indications of stretching and folding.

- This stretching is also recognized as the time evolution of the length of each passive contour. ( Note that the area between two contours is preserved due to the nondivergent fluid. )

Figure 3: Time evolution of the passive contour length (click for the expanded figure).

- The contours inside the vortex are hardly stretched out.

- The contours a little outside are stretched at an almost constant rate in the early phase.

- After t = 6.0 , at which the streamer turns up to make the flow complex, the contours are stretched at a higher rate than before.

- This stretching is seen only inside the circle with its radius a little longer than the major axis of the elliptical vortex, and the contour lengths in the outside the circle changes much more slowly.