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:…
Stommel western-intensification boundary-layer psi(x) = psi_0 e^{-x/delta_W}
Stommel western-intensification framework (Stommel 1948 Trans Am Geophys Union 29, 202). Setup: in a homogeneous wind-driven ocean basin…
Sverdrup transport beta V H rho - curl tau = 0; volumetric balance
Sverdrup transport framework (Sverdrup 1947 PNAS 33, 318). Setup: depth-integrated meridional volume transport V = int v dz across an…
Internal-wave dispersion omega = N sin(theta); so(2) rotation in (k_h, k_z)
Internal-gravity-wave dispersion framework (Mowbray-Rarity 1967 J Fluid Mech 28, 1). Setup: in a stably-stratified fluid (Brunt-Vaisala N >…
Theorem: psi'(x) + psi(x)/delta_W = 0 (Stommel boundary-layer exponential decay)
Theorem (Stommel-boundary-ODE canonical): for psi(x) = psi_0 exp(-x/delta_W), differentiating gives psi'(x) = -psi_0/delta_W…
Theorem: V beta H rho - curl tau = 0 (Sverdrup interior balance)
Theorem (Sverdrup-residual canonical): beta V = curl tau/(rho H) cleared gives V beta H rho = curl tau, residual V beta H rho - curl tau =…
Theorem: omega^2 - N^2 sin^2(theta) at theta = pi/2 equals 0 (internal-wave isentropic limit)
Theorem (internal-wave-pi/2 canonical): at theta = pi/2 (horizontal wavenumber, vertical particle motion), sin(pi/2) = 1, so omega² = N²·1…
Ekman pumping (1905)
V W Ekman 1905 wind-stress curl drives vertical-pumping w_E = (1/rho_0) curl(tau)/f; basis of subtropical-gyre + upwelling oceanography.
Sverdrup balance (1947)
H U Sverdrup 1947 wind-driven-circulation: beta v = (1/rho_0) curl(tau); modern Stommel-1948 western-boundary-current intensification adds…
Argo (2000)
International Argo program 2000; modern 4000+ profiling-floats + 0-2000m T/S; revolutionized global-ocean observation; underpins reanalysis…
Internal waves (Garrett-Munk 1972)
C Garrett-W Munk 1972 GM-spectrum; oceanic-internal-wave-field universal shape; modern McComas-Bretherton 1977…
Sea level (Cazenave 2010)
Cazenave-Llovel 2010 satellite-altimetry + GRACE; modern 4.5 mm/yr 2014-2024; thermal + ice-sheet contributions; coastal-flood-risk mapping.
Submesoscale (McWilliams 2016)
J McWilliams 2016 'Submesoscale Currents in the Ocean'; 0.1-10 km scale; modern observations + LES/DNS reveal vertical heat +…
Ekman (1905)
V Ekman 1905 Ekman-spiral wind-driven; modern modern foundational text + 2024 ocean-mixed-layer ML-driven Argo-floats.
Sverdrup (1947)
H Sverdrup 1947 + Stommel 1948 + Munk 1950 wind-driven gyres; modern modern foundational + 2024 ocean-circulation eddy-rich climate models.
Thermohaline (Broecker 1991)
W Broecker 1991 great-ocean-conveyor; modern modern foundational text + AMOC + 2024 IPCC-AR6 weakening evidence Caesar 2018-2024.
Argo (2000)
Argo-program 2000 + 2024 4000+ floats global-T/S; modern modern foundational text + Deep-Argo + BGC-Argo nutrient O2 satellite synergy.
Internal waves (Garrett-Munk 1972)
C Garrett-W Munk 1972 GM-spectrum; modern modern foundational text + 2024 mixing-tide internal-tide DIMES dissipation.
ATOC (Munk 1995)
W Munk 1995 ATOC acoustic-thermometry-of-ocean-climate; modern modern foundational text + RAFOS-floats + 2024 SOFAR-channel ocean-warming.