Tropical Cyclone Lab - 2D Wind Profile and Intensity Map

Presets

Live readouts

Graphs

Wind profile V(r): Holland vs Rankine

Pressure profile p(r)

Intensity history: Vmax, potential and target (m/s)

Potential intensity vs SST (red dot = storm now)

SST under the eye (blue = 26.5 C)

Numerical checks

running...

How to use

Pick a preset or move the sliders, then watch the storm move across a map of sea-surface temperature. The colour of the sea is the SST including the cold wake the storm leaves behind; white dashed rings are the 34, 50 and 64 knot wind radii, purple circles are isobars, arrows are the surface wind. Try: (1) Cool water, then raise SST with the slider and see where Vmax stops following; (2) Wind shear at 18 m/s versus 3 m/s; (3) Slow mover, and look at the cold wake behind the eye and the SST-under-eye graph; (4) Island pass for abrupt decay and recovery; (5) Compact core (B = 2.2) versus Large and weak (B = 1.0) in the wind profile graph. Click on the sea to restart the storm there. Space pauses, R resets.

The science

1. Wind profile (Holland 1980). In a mature vortex the wind is close to gradient-wind balance: pressure force, centrifugal force and Coriolis force cancel along the radius.

V²/r + f V = (1/ρ) dp/dr, f = 2Ω sin(φ), ρ = 1.15 kg/m³

Holland's pressure profile has three numbers: the central deficit Δp = p_n - p_c, the radius of maximum wind R_max and a shape parameter B (1 to 2.5; large B means a narrow, peaked wind maximum).

p(r) = p_c + Δp exp[-(R_max/r)^B] V(r) = √{ (B Δp/ρ) (R_max/r)^B exp[-(R_max/r)^B] + (r f/2)² } - r f/2

Without rotation the peak is V_max = √(B Δp / (ρ e)), so a 60 hPa deficit with B = 1.5 gives about 55 m/s. The panel inverts this numerically (with Coriolis) to find the pressure deficit that belongs to the current V_max. The dashed grey curve in the profile graph is a Rankine vortex with the same V_max and R_max for comparison; the real profile decays more slowly than 1/r and has no sharp corner.

2. Potential intensity from the sea. A hurricane is a heat engine: it takes enthalpy from the warm sea surface and rejects heat at the cold outflow level. Emanuel's steady-state energy balance gives an upper bound on the wind:

V_p² = (C_k/C_d) · (T_s - T_o)/T_o · (k₀* - k) k₀* - k = L_v [q*(SST) - RH q*(T_air)] + c_p (SST - T_air), C_k/C_d = 0.9

The saturation humidity q* comes from the Bolton (1980) form of Clausius-Clapeyron, e_s = 611.2 exp[17.67 T/(T+243.5)] Pa. Warmer sea raises both the Carnot factor and the air-sea moisture disequilibrium, so V_p grows steeply with SST and collapses to zero when the sea is no warmer than the air it heats. Real storms reach only a fraction of V_p; that fraction is the "realised fraction" slider.

3. Intensity change. Each hour the storm relaxes toward a target wind V_t with a time scale τ:

dV/dt = (V_t - V)/τ, V_t = ε V_p · 1/(1 + (S/12)²) · min(1, |φ|/6)

The shear factor (S in m/s) and the low-latitude factor (no Coriolis force, no organised vortex) are simple illustrative shapes, not fitted laws. Over land V_t = 0 and τ = 10.5 h, which is the exponential decay constant 0.095 per hour reported by Kaplan and DeMaria (1995) for storms after landfall (their formula keeps a small background wind that is left out here).

4. Cold wake. The storm's wind stirs the ocean mixed layer and brings cold water up. The wake is parameterised, not simulated: the peak cooling is 3 K × (V/50)² × (50 m / mixed-layer depth) × min(2.2, 6/c), with c the translation speed, and it relaxes back with a 6-day time scale. Slow storms over a shallow mixed layer cool their own fuel supply and weaken; fast storms leave a weaker wake. The SST under the eye (sea field plus wake) feeds V_p every step.

5. Wind map. The surface wind at any point is the Holland tangential wind rotated 20 degrees inward near the eye, plus 55% of the translation vector fading with distance, so the right-hand side of the track (Northern Hemisphere) is stronger. R34, R50 and R64 are the radii where V falls to 17.5, 25.7 and 32.9 m/s (34, 50 and 64 knots). Categories use the Saffir-Simpson thresholds converted to m/s. ACE is 10^-4 Σ v_kt² summed every 6 h while V ≥ 34 kt. The sea-level rise shown is only the inverse-barometer part, Δp/(ρ_w g) = 1 cm per hPa; real surge is dominated by wind stress and coastal shape and is not modelled.

Simplifications. The geography is invented (a continent coast, a central island and a small island, 2400 km by 1600 km). There is no steering flow, beta drift, eyewall-replacement cycle, dry-air intrusion or real SST data; track and heading are inputs. Holland's gradient wind is used directly as the surface wind. This is a teaching model and must not be used for forecasts or safety decisions: follow your national weather service.