Uniform flow past a circular cylinder with circulation

Consider the stream function defined as

where is arbitrary, and represents the circulation about the cylinder. The resulting flow is shown in the following simulation, with a cylinder of radius , circulation , and speed . In this case, for convenience, we define the parameter

Observe what happens when you change the values of the parameter .

Question 1:

Describe the flow when .

Question 2:

Describe the flow when .

Question 3:

Describe the flow when .

Question 4:

Describe the flow when .