Contour plot of the velocity field

At this point it is interesting to look at the velocity field.  A way to do it is to look at the mean velocity as a function of the distance from the sphere and the angular location.  This is done by computing a total velocity, [Graphics:../Images/creeping_sphere_gr_138.gif] + [Graphics:../Images/creeping_sphere_gr_139.gif].  

[Graphics:../Images/creeping_sphere_gr_140.gif]
[Graphics:../Images/creeping_sphere_gr_141.gif]

Use the polar to Cartesian transformation:

[Graphics:../Images/creeping_sphere_gr_142.gif]
[Graphics:../Images/creeping_sphere_gr_143.gif]
[Graphics:../Images/creeping_sphere_gr_144.gif]

[Graphics:../Images/creeping_sphere_gr_145.gif]

[Graphics:../Images/creeping_sphere_gr_146.gif]

The result is shown here with the sphere blacked out (and unfortunately some frame).  Note that the contours smoothly change as we approach the sphere.  The darker, the shading, the lower the velocity.  The point that could be surprising is that the fluid close to the sphere is always slower than far away.  There is no region where the fluid "speeds up" to get around the sphere which might happen for your "intuitively flowing" fluid.   

back to objectives(physical)

back to conclusions

[Graphics:../Images/creeping_sphere_gr_147.gif]

[Graphics:../Images/creeping_sphere_gr_148.gif]


Converted by Mathematica      August 7, 2000