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The science
Why a jet exists. Hydrostatic air plus the Coriolis force gives thermal wind balance: ∂u/∂ln p = -(R/f) ∂T/∂y. Integrating from 1000 to 250 hPa gives Δu = (R/f) ln(4) |∂T/∂y|. A temperature contrast ΔT across a zone of width W therefore fixes the jet speed. The page assumes calm winds near the ground, so the upper wind equals this shear.
Why it meanders. On a rotating sphere the Coriolis parameter grows towards the pole, beta = 2Ω cosφ / a. For a barotropic wave psi ~ cos k(x - ct) the vorticity equation ζt + U ζx + beta v = 0 gives the Rossby dispersion relation c = U - beta/k². A wave is stationary at k = sqrt(beta/U), wavelength 2π sqrt(U/beta).
The picture. The streaks are tracers moved by Bower's kinematic meandering jet: psi = -U L tanh[(y - A cos θ)/(L sqrt(1 + (kA sin θ)²))], θ = k(x - ct), u = -psiy, v = psix. Large amplitudes pinch off the loops and eddies you see in strong blocking events.
Flight times. Ground speed is airspeed plus the wind component along the route, t = ∫ ds/(V ± u), sampled along a 5,500 km track at the instantaneous wind. Riding the jet east and avoiding it west saves time; the eastbound gain is bigger than the westbound loss (the average over both legs is still longer than in calm air).
Honest simplifications. The flow is a kinematic 2D model on a beta plane at the jet latitude, not a weather forecast; the real jet is driven by eddies, topography and moisture. The steering flow is set to an illustrative 60 % of the jet core speed. The continents and clouds are a stylised procedural planet baked in Blender, not real geography. Aircraft size is exaggerated about 10x so you can see it. Typical real jets reach 40-80 m/s at 9-12 km; check against observations before quoting numbers.