Ocean Circulation from First Principles

Ocean Circulation from First Principles CPU

Wind-driven gyres & thermohaline circulation across the global ocean — computed live from the barotropic vorticity equation

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Select

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Land

☰

Ocean

☀

Heat

❄

Cold

☃

Ice

↻

↺

CCW

Simulation

Max Velocity

Kinetic Energy

Step

Season

Jan

AMOC

Wind Strength — 1.00 i

Bottom Friction (r) — 0.040 i

Lateral Viscosity (A) — 2.0e-4 i

Sim Speed — 50 steps/frame i

Year Speed — 1.00 i

Freshwater Forcing — 0.00 i

Radiative Forcing — 0.0°C i

Deep Water Formation — 0.50 i

Solar Constant — 100 i

The Physics

Two-layer ocean model

Surface: dq/dt + J(ψ, q) = curl(τ) − rζ + A∇²ζ − α_T∂T/∂x + F₁(ψ_d−ψ)
Deep: dq_d/dt + J(ψ_d, q_d) = −r_dζ_d + A∇²ζ_d + F₂(ψ−ψ_d)
T_s: dT/dt = S·cosθ_z·α_ice − (A+BT) + κ∇²T − γ(T_s−T_d)/H(x,y) + Q_land
T_d: dT_d/dt = γ(T_s−T_d)/H_d(x,y) + κ_d∇²T_d

β western intensification · α_ice ice-albedo feedback · H(x,y) bathymetry
F_1,2 interfacial coupling · Q_land land-ocean heat exchange

Understand the equation →

Velocity Profile

Radiative Balance

Paleoclimate Scenarios

Temp

Deep

Speed

Stream

Salt

Density

Bathy

Vorticity

Particles

AMOC

Season

Jan

Paint Tools

Brush: 3

Climate

Freshwater Forcing 0.00

Radiative Forcing 0.0°C

Solar Constant 100

Ocean Physics

Wind Strength 1.00

Bottom Friction 0.040

Viscosity 2.0e-4

Deep Water Formation 0.50

Speed

Sim Speed 50

Year Speed 1.00

Paleoclimate Scenarios

SimAMOC

Ocean Circulation Simulator
Watch Earth's ocean currents emerge from first-principles physics. Wind-driven gyres, thermohaline circulation, and the AMOC — all computed live.

Paint coastlines to reshape the world. Add land, carve ocean, apply heat or cold, freeze ice.

Controls let you adjust CO₂ forcing, melt Greenland's ice, change wind strength, and tune deep physics.

Scenarios replay major events in Earth's ocean history.

Equation guide · GitHub