Ocean physics (physical oceanography) — the study of the global ocean's momentum, heat, salt, and tracer budgets on scales from individual eddies (O(10 km)) to the global meridional overturning circulation (O(10⁴ km, 10³ yr)). Four…
ocean-physics
Rossby number: Ro = U/(L·f)
The Rossby number Ro = U/(L·f) is the fundamental dimensionless control parameter of rotating-fluid dynamics, measuring the relative…
Thermohaline buoyancy: b = -g·(ρ-ρ₀)/ρ₀
Buoyancy per unit mass b = -g·(ρ-ρ₀)/ρ₀ is the net body force acting on a fluid parcel of density ρ immersed in a reference density ρ₀,…
Ekman depth: D_E = √(2·ν/f)
The Ekman depth D_E = √(2·ν/f) is the e-folding decay scale of wind-driven surface currents in a rotating viscous fluid, derived by Ekman…
Rossby-number equator: Ro(f→0) = ∞; Ro(U=L=f=1) = 1
Sympy-exact witness of the Rossby-number limiting cases. Setup: Ro = U/(L·f) as a three-symbol rational function. Identity 1 (equatorial…
Buoyancy anchors: b(ρ=ρ₀)=0; b(ρ=2·ρ₀)=-g
Sympy-exact witness of the thermohaline-buoyancy limiting anchors. Setup: b = -g·(ρ-ρ₀)/ρ₀. Identity 1 (neutral): at ρ=ρ₀, b = 0 — parcel…
Ekman-depth ratio: D_E(2f)/D_E(f) = √2/2
Sympy-exact witness of the Ekman-depth Coriolis-scaling identity. Setup: D_E = √(2·ν/f) as a two-symbol function of ν and f. Identity:…