= Convective cooling under the four-thirds heat-transfer law
{title2=$\theta(t)=[\theta_0^{-1/3}+Kt/3]^{-3}$}
A well-mixed layer of depth $h$ losing heat through an unstable cold upper boundary has bulk excess temperature $\theta=T-T_0$. With <four-thirds convective heat-transfer law> flux $q=Ck[g\beta/(\nu\kappa)]^{1/3}\theta^{4/3}$, its heat capacity per area is $kh/\kappa$. Thus $\dot\theta=-K\theta^{4/3}$ with $K=C\kappa[g\beta/(\nu\kappa)]^{1/3}/h$, giving the displayed cooling law. It excludes the initial conductive transient and the late low-Rayleigh conduction regime.
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