Animated upper-layer potential-vorticity field from a baroclinic instability life cycle, tiled across a wide banner, growing from a smooth wave into a tilted, breaking pattern

Baroclinic instability life cycle — Ch. 16

An interactive Geophysical Fluid Dynamics Textbook

A graduate GFD course where every model runs in your browser. The text derives each minimal model; the embedded marimo notebook lets you turn the knob and watch the balance break — no installation required. Symbols and sign conventions are fixed on the notation page.

Start reading — Ch. 1 → How these notebooks work

Part 1 — Foundations

The two ideas every later chapter leans on without saying so: the material derivative, and rotation's own kinematics.

Part 2 — Balance & Adjustment

How a rotating, stratified fluid finds its balance — thermal wind, geostrophic adjustment, and the PV-inversion algorithm that drives nearly everything after it.

Part 3 — Quasi-Geostrophy

The workhorse approximation of the whole subject: QGPV, Rossby-wave ray paths, and the two-layer split into barotropic and baroclinic modes.

Part 4 — Stratified Flow & Waves

Vertical structure and internal waves — normal modes of a stratified column, and how a wave leaves a lasting mark on the mean flow it rides.

Part 5 — Instabilities

Where the energy for storms and eddies actually comes from — barotropic shear, baroclinic instability (the book's centerpiece), and the faster mechanisms at fronts.

Part 6 — Turbulence & Circulation

From an unstable jet to the general circulation: geostrophic turbulence, eddy mixing, wind-driven gyres, and buoyancy-driven overturning.

Part 7 — Structure optional

A closing retrospective through Hamiltonian and wave–mean-flow structure — point vortices, non-acceleration, and the slow manifold that quietly justifies every balanced model in the book.

Not sure where to start? See the full chapter dependency map →