Question

Consider a pair of point vortices with clockwise circulation \( \Gamma \) each. The distance between their centers is \( a \), as shown in the figure. Assume two-dimensional, incompressible, inviscid flow. Which one of the following options is correct?
\includegraphics[width=0.5\linewidth]{20.png}

• A. The vortices translate downwards together with a velocity \( \frac{\Gamma}{2\pi a} \).
• B. The vortices translate upwards together with a velocity \( \frac{\Gamma}{2\pi a} \).
• C. The vortices rotate clockwise around each other about their centroid O.
• D. The vortices rotate counter-clockwise around each other about their centroid O.

Hint:

In a system of two point vortices, they will rotate around their common centroid, with the direction of rotation depending on the sign of their circulation. In this case, with clockwise circulation, the vortices rotate clockwise around each other.

Answer 1

The Correct Option is C

When two vortices of equal and opposite circulation are placed in a two-dimensional, incompressible, inviscid flow, they will rotate around each other with respect to their centroid. In this scenario, the vortices have clockwise circulation, and they rotate in a clockwise direction around their common centroid. Therefore, option (C) is correct.