The perturbations extract their energy from the potential energy stored in the system of sloping density surfaces. The energetics of the baroclinic instability are therefore quite different than those of the Kelvin-Helmholtz instability

• For baroclinic instability, the perturbation Reynolds stress $\overline{u'w'}$ extracts energy from the vertical shear
• Baroclinic instability is not a shear-flow instability because the Reynolds stresses are too small due to the small $w'$ in quasi-geostrophic large-scale flows

The energetics of baroclinic instability can be studied using the equation for perturbation kinetic energy $$ \frac{d}{dt} \left( \rho_0 \int (u'^2 + v'^2) \, dx \, dy \, dz \right) = \frac{dKE}{dt} = -g \int w' \rho' \, dx \, dy \, dz $$ For instability, $dKE/dt > 0$, which requires $$ \int w' \rho' \, dx \, dy \, dz < 0 $$ Denote the volume average as $\overline{w'\rho'}$. A negative $\overline{w'\rho'}$ means lighter fluid rises and heavier fluid sinks, lowering the system’s potential energy.

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