Heated particle-laden gravity current

A heated particle-laden layer released along a bed forms a gravity current while $g^{\prime }=g(\gamma \varphi -\theta )>0$. In a gravity-current box model, heating can make $g^{\prime }$ vanish in finite time, whereas settling velocity alone can give finite runout length of a gravity current approached asymptotically.

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.