Max wind0 kt

Category-

Central p1010 hPa

Rmax- km

Time0 h

Drag: orbit · wheel/pinch: zoom · green: inflow, orange: eyewall updraft, violet: outflow

Loading the storm...

Hurricane Eyewall Cutaway: Heat-Engine Potential Intensity, Ocean Cooling and Shear

Cut open a tropical cyclone. Set the sea temperature, outflow temperature, shear and landfall and watch the storm climb toward (or fall short of) its potential intensity.

Live measurements

■ maximum wind ■ current target intensity (potential, after shear and ocean cooling)

Maximum sustained wind- Potential intensity V_p (with ocean feedback)- Target after shear- Ocean cooling under the storm- Carnot-like factor (T_s−T_o)/T_o- Enthalpy disequilibrium k*−k- Central pressure- Radius of 34-kt winds- Elapsed-

Wind profile (Holland gradient wind):

Ocean, air and storm

Sea temperature

Outflow temp. T_o

Boundary-layer RH

Wind shear

Mixed-layer depth

Translation speed

Latitude

Response time τ

Holland B

Landfall at hour

Time scale

Ocean cooling

Lower sea temperature, deeper mixed layer and faster motion all change the engine. Moving a slider changes the target intensity at once; the storm follows with its response time τ.

Experiment: how hot must the ocean be?

Computes the steady intensity for SST 22-32 C (shear 0, your other settings) three ways: the bare potential-intensity formula, the equilibrium with ocean cooling, and a real time-marched run of 400 h.

Independent numerical checks

Check	Theory	Measured

The science

A tropical cyclone is a heat engine (Emanuel 1986): it takes heat from a warm ocean at temperature T_s (isothermal evaporation and sensible heat, spiralling inward in the boundary layer), carries it up the eyewall and dumps it at the cold outflow temperature T_o near the tropopause. The mechanical work is dissipated by surface friction.

Balancing that work against frictional dissipation gives the potential intensity: V_p² = (C_k/C_d) · (T_s−T_o)/T_o · (k*₀−k). Here C_k/C_d is the ratio of enthalpy to drag exchange coefficients (about 0.5-1; 0.55 used) and k*₀−k ≈ L_v(q*₀ − RH q*) + c_p(T_s − T_air) is the air-sea enthalpy disequilibrium (L_v = 2.5e6 J/kg, boundary-layer air 1 K cooler than the sea, q* from the Bolton saturation vapour pressure).

Intensification: dV/dt = (V_target − V)/τ. The target is V_p reduced by shear and by the ocean cooling the storm causes: ΔT = 2.2 (V/50)² (40/h) (5/(c+3)) °C (h = mixed-layer depth m, c = translation speed m/s). Over land dV/dt = −V/10.5 h.

Wind field: the Holland (1980) gradient-wind profile V(r) = √[(B Δp/ρ) (R_m/r)^B e^{−(R_m/r)^B + (rf/2)²] − rf/2} with Δp chosen so that V(R_m) = V_max. R_m uses a typical empirical regression 46.4 exp(−0.0155 V + 0.0169 φ) km (quoted from memory: spot-check). Categories are the Saffir-Simpson thresholds in knots (1-min sustained wind).

Honest limits: this is a toy relaxation model on top of the potential-intensity formula, not a forecast model. Not modelled: eyewall replacement cycles, mid-level dry air, storm size changes, structure asymmetries, moving ocean eddies. Lower boundary-layer humidity raises V_p in the formula (more disequilibrium) although dry mid-level air hurts real storms, so RH is limited to 0.7-0.95. The shear factor 1 − 0.55 (S/22)^1.3, the cooling coefficient, the 10.5 h land decay and the 22.5-26.5 °C ramp (which makes the engine fade near the observed ~26.5 °C threshold) are illustrative numbers, not fitted constants. The 3D scene exaggerates height by about 2.5 and flow tracers are a kinematic sketch (inflow, eyewall updraft, outflow), not a fluid simulation.

Models and textures: Blender 5.2, procedurally baked with Cycles; rendering Three.js r160.