Geophysical fluid dynamics (GFD) — the unified theoretical framework for rotating, stratified fluids on a sphere, applied to atmosphere, ocean, and stellar/planetary interiors. Distinguished from general fluid dynamics by two additional…
geophysical-fluid-dynamics
QG vorticity scale: ζ_QG/f ≈ Ro
Quasi-geostrophic (QG) scaling: the relative vorticity ζ of a QG-approximated flow scales as ζ ≈ f·Ro, so the dimensionless ratio ζ/f ≈ Ro…
Rossby-wave dispersion: ω = -β·k/(k²+l²)
The dispersion relation for barotropic Rossby waves on a β-plane is ω = -β·k/(k²+l²), where β = df/dy = 2·Ω·cos(φ)/R is the latitudinal…
Baroclinic instability: σ ~ U·f/(H·N)
Baroclinic instability — the dynamical mechanism by which vertically-sheared rotating stratified flow spontaneously converts available…
QG breakdown: (ζ_QG/f)(Ro=1) = 1
Sympy-exact witness of the quasi-geostrophic breakdown anchor. Setup: ζ_QG/f = Ro as a one-symbol identity (the canonical QG scaling…
Rossby-wave limits: ω(k→0)=0; ω(l=0)=-β/k
Sympy-exact witness of the Rossby-wave dispersion-relation limiting cases. Setup: ω = -β·k/(k²+l²) as a three-symbol function. Identity 1…
Baroclinic growth doubling: σ(2U)/σ(U) = 2
Sympy-exact witness of the baroclinic-instability shear-doubling identity. Setup: σ = U·f/(H·N) as a four-symbol function. Identity:…