Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 345 / 3 / d / Solution

The energy-conserving full-depth lock-exchange flow is symmetric between the cold lower current and warm upper return current, soPart (b) then gives $u_2=\sqrt{g^{\prime }H}$ and the laboratory front speedDuring one opening, the cold current displaces the volumeThe same volume of warm air exits in the upper layer.