Ocean Circulation from First Principles CPU

dq/dt + J(ψ, q) = curl(τ)/ρH − r∇²ψ + A∇&sup4;ψ − α_T∂T/∂x
dT/dt + J(ψ, T) = S·cosθ_z(lat,t) − (A + BT) + κ∇²T

β creates western intensification (Stommel 1948)
T_s surface temp with seasonal insolation + ice-albedo feedback
T_d deep ocean (4000m) exchanges heat with surface via mixing
A + BT outgoing longwave radiation (global heat balance)
α_T buoyancy coupling: warm water → anticyclonic
Freshwater forcing can collapse the AMOC (Stommel bifurcation)

Wind-driven gyres + thermohaline circulation from first principles.

Understand the equation →