Heated gravity-current runout

In a constant-volume gravity-current box model without settling, $\varphi ={\varphi }_0$ and $g^{\prime }=g{\varphi }_0(\gamma -\beta t)$. A constant Froude number then gives finite runout length of a gravity current at the neutral-buoyancy time $\gamma /\beta$. Further motion requires a different physical model once the stable density stratification is lost.