Day 0Wind 0 m/sτ 0 N/m²Upwelling w 0 m/dayThermocline 0 mPhyto 0—FPS 0

Cut-away of a coastal ocean (coast on the right, vertical scale exaggerated). White arrows: wind along the coast. Light-blue arrows: Ekman transport pushing surface water offshore. Cyan arrows: water rising to replace it; blue arrows: onshore return flow below. Colours show temperature (red warm to deep blue cold); green is the plankton bloom. Gold arrows: the Ekman spiral.

Ekman Spiral and Coastal Upwelling: Wind Stress, Thermocline Front and Plankton Bloom

Blow the wind along a coast and follow the chain: stress, Ekman transport, rising cold water, nutrients, bloom, tuna.

Wind

Ocean and plankton

Time

Live readouts

Ekman spiral (current hodograph)

Thermocline and upwelling

Nutrient, phytoplankton, zooplankton

Experiments

Each button runs 80 model days headless from the current settings and lists transport, upwelling, thermocline depth and phytoplankton at day 80 and at the peak.

Independent numerical checks

Controls

Drag or one finger: orbit; wheel or pinch: zoom. Camera buttons jump to the whole section, the coastal front, the spiral or a top-down view.
Wind is positive when it blows toward the equator along the coast (north-hemisphere eastern-ocean coast, like California or Peru-type systems); negative wind drives downwelling.
The time scale is model days per real second. Sliders act immediately; Reset restarts the plankton and thermocline.

The science

Wind stress. τ = ρ_a C_D U² with ρ_a = 1.22 kg/m³ and a constant C_D = 1.3×10⁻³ (real drag grows slightly with wind speed).

Ekman layer. Balancing Coriolis force and vertical friction (eddy viscosity A_z) gives a spiral: u = V₀ e^z/D cos(π/4 + z/D), v = V₀ e^z/D sin(π/4 + z/D), depth scale D = √(2A_z/f), V₀ = √2 τ/(ρ f D), f = 2Ω sin φ. In the northern hemisphere the surface current is 45° to the right of the wind and turns further right with depth. The depth-integrated transport is exactly M = τ/(ρ f), 90° to the right of the wind, and does not depend on A_z.

Coastal upwelling. Equatorward wind along an eastern-ocean coast pushes surface water offshore; mass must be replaced from below inside about one internal Rossby radius L_R = √(g′H₀)/f (g′ = 0.02 m/s²). Upwelling speed w = M/L_R. The thermocline depth at the coast obeys dH/dt = −w + (H₀ − H)/τ_r, so the steady value is H₀ − w τ_r; when H reaches 0 cold water outcrops. Away from the coast the thermocline relaxes back as H₀ − (H₀ − H) e^−d/L_R (the drawn isotherms).

Plankton box. A mixed-layer box of depth 20 m: dN/dt = λ(N_in − N) − μ P N/(K+N) + (1 − β)G + m_Z Z + m_P P, dP/dt = μ P N/(K+N) − G − m_PP − λP, dZ/dt = βG − m_ZZ − λZ, with grazing G = g_max Z P/(P + k_g), flushing rate λ = w/H_m (water leaves offshore as fast as it upwells) and supply N_in rising to 22 mmol/m³ once the thermocline is shallower than about 30 m. μ = 1.6/day × light. N + P + Z is conserved without flushing.

Simplifications: steady 2D cross-section, a single wind-driven thermocline layer, constant eddy viscosity, no alongshore variation, no wind-curl upwelling, no light limitation by depth or self-shading, nutrient and plankton constants typical rather than fitted, and the vertical scale of the picture exaggerated. Fish positions are decorative. Assets built with Blender; scene by Three.js.