Vmax 0 m/sMin pressure 0 hPaRmax 0 kmSST 0 °CTime 0 h—FPS 0

Drag to orbit, wheel or pinch to zoom. Cyan arrows: air spiralling in through the boundary layer, each carrying its own angular momentum. Gold arrows: the updraft in the eyewall. Ocean colour shows warm (gold/orange) and cool (blue) water. Vertical scale exaggerated x3.

Cyclone Heat Engine

Warm ocean in, spin-up by angular momentum, limits from Coriolis, shear and friction. Virtual physics model, not a forecast.

Ocean and air

Storm structure

Time

Live readouts

Wind profile: Holland vs angular momentum

Intensity history

Missions

Mission 5: predicted ideal speed at Rmax for the white tagged parcel (m/s)

The ideal value assumes angular momentum is conserved with no friction; the readout above shows it once the tagged parcel has been released.

Experiments

Each button runs the storm headless for 120 hours at several values and reports the final intensity.

Independent numerical checks

Controls

Drag / one finger: orbit; wheel / pinch: zoom; three camera presets (hero, cross-section through the eyewall, top-down).
Sliders change the ocean, air and storm geometry while it runs; the potential intensity responds at once and the storm relaxes towards it over about 18 hours.
Time scale is simulated hours per real second. Reset storm restarts at Vmax = 18 m/s.

The science

Heat engine. The storm takes heat from the warm sea at temperature T_s and rejects it near the cold outflow at T_o. The Carnot efficiency is ε = (T_s − T_o)/T_s (kelvin), about 0.33 for 30 °C and −70 °C. Emanuel-type potential intensity (simplified): V_pi² = (C_k/C_d) · (T_s − T_o)/T_o · (k*_s − k_a), with moist enthalpy k = c_pT + L_vq, saturation humidity from the Magnus formula, air 1 K cooler than the sea at relative humidity RH, and C_k/C_d = 0.9 (model value). The dissipative-heating correction is left out.

Holland (1980) profile. With pressure p(r) = p_c + Δp exp(−(R_max/r)^B) the gradient-wind balance V²/r + fV = (1/ρ) dp/dr gives V(r) = √( B Δp x e^−x / ρ + (rf/2)² ) − rf/2, x = (R_max/r)^B. Without rotation the maximum is V_max² = B Δp/(ρ e), which sets the pressure deficit shown.

Angular momentum. Absolute angular momentum per unit mass is M = r v + f r²/2. Air that flows inward without friction keeps M, so v = (M − f r²/2)/r rises steeply towards the axis; surface drag dM/dt = −(C_D/h) r |v| v (h = 1 km boundary layer) removes much of it, which is why real winds are far below the frictionless value. Parcels move inward at 0.3 times the local gradient wind (illustrative).

Intensity. dV/dt = (V_eq − V)/τ with τ = 18 h (decay 11 h), V_eq = V_pi (1 − S/22 m/s) when latitude ≥ 5° (Coriolis threshold) and SST ≥ 26.5 °C. The cold wake lowers the sea temperature by 0.6 K (V/50 m/s)(40 m/h_ml). Thresholds, τ, shear scale and wake size are model values [перевірити за джерелом].

Simplifications. Axisymmetric parametrisation: no 3D dynamics, no eyewall replacement cycles, no land, no real forecast. Cloud look and the x3 height exaggeration are illustrative. Categories use the Saffir-Simpson wind thresholds (33, 43, 50, 58, 70 m/s) [перевірити за джерелом]. Assets built with Blender; scene by Three.js.