Two-layer internal deformation radius ($R_d^2=g\prime H_1{H}_2/[f_0^2(H_1+H_2)]$)

The two-layer quasi-geostrophic potential vorticity coupling defines $R_d^{-2}=F_1+F_2$. With $F_i=f_0^2/(g\prime H_i)$ this gives the stated radius. The baroclinic energy ratio and deformation scale depends on $(l/R_d{)}^2$, so the thinner layer matters when the depths are strongly unequal.