 Buoyancy fraction of total turbulent sinks

With positive stable buoyancy destruction $B$ and positive dissipation $ϵ$, this normalized sink fraction need not equal the Flux Richardson number $B/P$ away from equilibrium. If $R=(B+ϵ)/P$, then $J={\mathrm{Ri}}_f/R$. In the fixed-correlation equilibrium model for stratified turbulence, a minimum of $R=a/q+bq$ has $B=ϵ$, hence $J=1/2$. The actual flux Richardson number there is $R_{\min }/2$ and equals $1/2$ only when that minimum also satisfies the equilibrium condition $R=1$.