Baroclinic energy ratio and deformation scale
= Baroclinic energy ratio and deformation scale
{title2=$A/K_{\rm bc}\sim(l/R_d)^2$}
Depth-weighted decomposition gives reduced depth $H_r=H_1H_2/(H_1+H_2)$ and internal radius $R_d^2=g\prime H_r/f_0^2$. On scale $l$, the ratio of interface <available potential energy> to baroclinic <kinetic energy> is of order $(l/R_d)^2$. Comparable depths recover $l^2f_0^2/(g\prime H_i)$; for strongly unequal depths the thinner layer sets the scale.