The GATE Grind

GATE 2025 AE – Question 20

Aerodynamics · Two-dimensional potential flow: sources, sinks, doublets, point vortex and Bernoulli's equation · 1 mark · Multiple choice

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?

Two clockwise point vortices of strength $\Gamma$ side by side, a distance $a$ apart, with their centroid O midway between them.
  1. The vortices translate downwards together with a velocity $\frac{\Gamma}{2\pi a}$.
  2. The vortices translate upwards together with a velocity $\frac{\Gamma}{2\pi a}$.
  3. The vortices rotate clockwise around each other about their centroid O.
  4. The vortices rotate counter-clockwise around each other about their centroid O.

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Show answer and explanation

Correct answer: (C) The vortices rotate clockwise around each other about their centroid O.

Explanation

Each vortex is carried by the velocity induced by the other, $\frac{\Gamma}{2\pi a}$, perpendicular to the line joining them. For a clockwise vortex the flow on its right is downwards and on its left is upwards, so the right vortex moves down and the left one up. That is a rotation of the pair about its centroid in the clockwise sense, with no net translation.