Helmholtz Principle and Vortex Motion

Explore the fascinating world of fluid dynamics in this 36-minute video lecture where Oxford Mathematician Dr Tom Crawford explains Helmholtz' Principle and its application to calculate vortex motion in 2D potential flow. Begin with an introduction to 2D potential flow, examining incompressibility and irrotationality concepts. Discover how velocity potential and streamfunction combine using Complex Analysis and Cauchy-Riemann Equations to form a complex potential. Analyze a vortex in the positive quadrant bounded by x and y axes, deriving the full complex potential using the Method of Images. Learn to apply Helmholtz' Principle, which states that a vortex moves due to the velocity field of everything except itself, to determine the vortex trajectory in the fluid. Gain insights into advanced mathematical concepts while enjoying the collaborative teaching style between Dr Crawford and @DrTrefor.