A similarity transformation for inviscid non–Boussinesq gravity currents

Summary.

We propose a similarity transformation to investigate the motion of inviscid gravity currents in the similar phase. With this similarity transformation, the shallow water equations can be solved without needing to consider the front condition Eq. (1) downstream of the gravity current, and the parameter β of Eq. (1) becomes a part of the similarity solutions. It is shown that the resultant similarity solutions are in good agreement with the experimental results of both the dam-break and the lock-exchange non-Boussinesq currents, which have a density much larger than the ambient fluid.