= Stratified mixing energy budget
{title2=$\dot K=F-B-\epsilon,\quad\dot A=B-M$}
With boundary fluxes suppressed, let $B$ transfer <kinetic energy> to <potential energy>, $M$ transfer <available potential energy> irreversibly to <background potential energy>, and $W$ transfer <internal energy> to potential energy. Then $\dot P=B+W$, $\dot P_b=M+W$, $\dot A=B-M$, and $\dot K=F-B-\epsilon$. The internal reservoir has $\dot I=\epsilon-W$, conserving total energy apart from forcing $F$. The distinction between reversible buoyancy exchange and irreversible mixing is essential outside a quasi-steady negligible-$A$ regime.
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