baroclinic instability: one construct, many systems

Baroclinic instability is the process by which the sloping temperature (density) surfaces of a rotating, stratified fluid store available potential energy that small disturbances can tap, so that waves grow by sinking cold air and lifting warm air across the slope. Charney's 1947 The dynamics of long waves in a baroclinic westerly current and Eady's 1949 Long waves and cyclone waves showed mathematically that the midlatitude westerlies are unstable in just this way, which is why extratropical cyclones and their frontal waves form and amplify. The referent is the growth of disturbances that convert the potential energy of a tilted thermal gradient into the kinetic energy of eddies, the same mechanism that appears in the ocean.[1][2]

Unit

The growth rate and preferred wavelength of the fastest-growing disturbance

Recovery means

Not applicable

Measured by

Characterised by the perturbation growth rate, the most-unstable wavelength, and the deformation (Rossby) radius that sets the eddy scale

In the ocean the identical construct governs how large-scale currents shed eddies: where density surfaces slope across a current, the flow is baroclinically unstable and spawns mesoscale eddies that transport heat and momentum, just as the atmosphere spawns cyclones. Gill's Atmosphere–ocean dynamics treats the shared theory, deriving the same energy conversion and the deformation radius that here is far smaller, so ocean eddies are tens of kilometres across rather than thousands. It is the same instability of a tilted density gradient in a rotating fluid, realised in seawater and measured by eddy scales and growth rather than by synoptic weather waves.[3]

Unit

The growth rate and scale of the mesoscale eddies the instability produces

Recovery means

Not applicable

Measured by

Assessed through eddy kinetic energy, the baroclinic conversion rate, and the ocean deformation radius that sets eddy size