Presets
Playback
Aircraft and wake
Lift balances weight, so the circulation is Gamma0 = W / (rho V b0) with b0 = pi b / 4. The pair descends at Gamma0 / (2 pi b0) while the core spreads by diffusion.
Model checks
The science
What is modelled
An elliptically loaded wing sheds two counter-rotating vortices whose circulation carries the aircraft weight. Each vortex follows a Lamb-Oseen swirl profile whose core grows with time, and the pair sinks under its own induced velocity.
Equations
- Circulation
Gamma0 = W / (rho V b0), spacingb0 = pi b / 4. - Swirl
v(r) = Gamma / (2 pi r) (1 - exp(-r2/rc2)), corerc2 = rc02 + 4 nu_e t. - Descent speed
w = Gamma0 / (2 pi b0).
Checks run in the page
- Lift from integrating the elliptical circulation.
- The peak swirl at 1.1209 core radii.
- Gaussian vorticity integrating to Gamma.
- Descent of an RK4-integrated vortex pair.
Honest simplifications
Two straight, parallel vortices with a prescribed eddy-viscosity law: no ground effect, atmospheric turbulence, stratification, Crow instability or engine jets, and the follower hazard is shown only as a swirl speed. Not for separation decisions.
What to try
- Press Heavy jet, slow and compare the circulation and descent with the regional jet.
- Raise the wake age and watch the core grow and the peak swirl fall.
- Press Cruise altitude: thin air needs more circulation.