Lock-exchange problem for Boussinesq fluids revisited: Exact shallow-water solution

An exact solution to the lock-exchange problem, which is a two-layer analogue of classical dam-break obtained in shallow-water (SW) approximation for two immiscible fluids with slightly different densities. The problem solved by method characteristics using analytic expressions Riemann invariants. solution, represents an inviscid high-Reynolds-number limit, is, general, discontinuous containing up three hydraulic jumps are due either multivaluedness or instability continuous SW solution. Hydraulic resolved applying Rankine–Hugoniot conditions mass and generalized momentum conservation equations. latter contains free parameter α defines relative contribution each layer interfacial pressure gradient. We consider α=0, corresponds both layers affecting gradient equal weight coefficients. This compared solutions resulting from application Benjamin's front condition as well circulation condition, correspond α=−1 α→∞, respectively. reproduces all principal features 2D numerical viscous fluids. gravity current speed found agree experimental results when acquires largest stable height occurs at α=5−2. show that equations can describe waves self-contained way without external closure conditions.