Flow Around a Cylinder

The vector field

defined for

with parameters

- radius of the obstacle, and

- velocity of the fluid far from the obstacle

describes two-dimensional flow around a circular obstacle.

We can see the vector field
with the Mathematica
commands:

Changing the parameters
or
simply changes the scales of the resulting graphs. Indeed, if we make
the definition

if ,

if ,

then we see that

.

Changing , on the other hand, simply
dilates the size of the resulting vectors. We can see both of these
effects graphically in the following animations. First we adjust .

While here we adjust .