Media Summary: Same as the colour version but in black and white so the tracer particles don't fade away as the induced velocity magnitude ... Vortex leapfrogging: numerical solution of vortex dynamical equations Re = 1e5 180 particles on each ring. Dimensionless inputs: Radius of each ring = 1.0 Circulation ( Γ) = 1.0 dt = 0.1.

4 Vortex Leapfrogging - Detailed Analysis & Overview

Same as the colour version but in black and white so the tracer particles don't fade away as the induced velocity magnitude ... Vortex leapfrogging: numerical solution of vortex dynamical equations Re = 1e5 180 particles on each ring. Dimensionless inputs: Radius of each ring = 1.0 Circulation ( Γ) = 1.0 dt = 0.1. Additional results from Narain et al., "A Second-Order Advection-Reflection Solver", 2019 Joukowsky (1912) deduced that any number of equal helical

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4 Vortex Leapfrogging
4 Vortex Bifurcated Asymmetric Leapfrogging
Leapfrogging vortices (B&W)
Leapfrogging vortices simulation
LeapFroggingVortexRings.mp4
Leapfrogging Helical Vortices
vortex leapfrogging: numerical solution
Leapfrogging Vortex Rings
Vortex leapfrogging: numerical solution of vortex dynamical equations
Leapfrogging of vortex rings simulated using the vortex particle method
Leapfrogging vortex rings
Trio of leapfrogging Vortex Rings
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4 Vortex Leapfrogging

4 Vortex Leapfrogging

Leapfrogging

4 Vortex Bifurcated Asymmetric Leapfrogging

4 Vortex Bifurcated Asymmetric Leapfrogging

Bifurcated asymmetric

Leapfrogging vortices (B&W)

Leapfrogging vortices (B&W)

Same as the colour version but in black and white so the tracer particles don't fade away as the induced velocity magnitude ...

Leapfrogging vortices simulation

Leapfrogging vortices simulation

Four leapfrogging vortices

LeapFroggingVortexRings.mp4

LeapFroggingVortexRings.mp4

Leapfrogging

Leapfrogging Helical Vortices

Leapfrogging Helical Vortices

Leapfrogging

vortex leapfrogging: numerical solution

vortex leapfrogging: numerical solution

vortex leapfrogging: numerical solution

Leapfrogging Vortex Rings

Leapfrogging Vortex Rings

In this video, I model the

Vortex leapfrogging: numerical solution of vortex dynamical equations

Vortex leapfrogging: numerical solution of vortex dynamical equations

Vortex leapfrogging: numerical solution of vortex dynamical equations

Leapfrogging of vortex rings simulated using the vortex particle method

Leapfrogging of vortex rings simulated using the vortex particle method

Re = 1e5 180 particles on each ring. Dimensionless inputs: Radius of each ring = 1.0 Circulation ( Γ) = 1.0 dt = 0.1.

Leapfrogging vortex rings

Leapfrogging vortex rings

Additional results from Narain et al., "A Second-Order Advection-Reflection Solver", 2019 http://rahul.narain.name/ar2/

Trio of leapfrogging Vortex Rings

Trio of leapfrogging Vortex Rings

The time evolution of a trio of

Leap-frogging helical vortices

Leap-frogging helical vortices

Joukowsky (1912) deduced that any number of equal helical