With baroclinic (e.g. midlatitude systems) energetics, you get kinetic energy extracted from the potential energy of the mean flow (which itself has two components -- internal potential energy and that from gravity). However, not all potential energy can be converted over to kinetic energy...in fact, the percentage of such is pretty low. Even less of the total potential energy can be converted over to available potential energy.

Getting to the math behind all of this is very complex...it's entry-level graduate dynamics in meteorology. But, skipping that, the conversion term to get between potential and kinetic energy is directly related to the thermal wind, which itself is a measure of the vertical difference in the winds between two levels, and vertical motion processes. In that respect, the thermal wind is not a true wind shear, but is in many respects similar to one. Generation of potential energy that can be converted to kinetic energy comes out of heating processes. Ultimately, the kinetic energy goes back to potential energy as the system evolves and matures, leading to dissipation.

The big thing about weather systems is that they occur to restore stability to an unstable situation. They grow out of instability -- it is required to even get to this whole debate on energetics -- but serve as facilitators to return the atmosphere to a stable state.