Tailwater gravity currents and their connection to perfectly subcritical flow: laboratory experiments and shallow-water and direct numerical solutions

We report upon a series of laboratory experiments and complementary (two-dimensional) direct numerical simulations that explore the lock release of a fixed volume of dense fluid into a two-layer density-stratified ambient. By initial condition, the lock release experiments/simulations fall into one of two categories: full-depth and partial-depth. Our particular focus is on the "tailwaters" limiting case where the lock fluid density matches that of the lower ambient layer. In either case the front speed of the advancing lock fluid is less than that of the excited interfacial disturbances. Consequently, the internal front propagates at constant speed for less time than, say, the downstream-propagating interfacial disturbance, which we term the dense gravity current (or GC1). Complementing GC1, there is an analogue flow of light ambient fluid into the lock, and this we refer to as the light gravity current (or GC2). Measured speeds for GC1, GC2 and the internal front are compared against analogue predictions from shallow water (SW) theory. From this comparison, positive agreement is noted in the case of GC1 and the internal front. Meanwhile, the speed of GC2 post reflection from the lock end wall is under-predicted by 10-20% depending on the initial depth of dense fluid within the lock. This under-prediction is believed to result from a mismatch between where the SW prediction is made (immediately following GC2 reflection from the back of the lock) and where the experimental GC2 speed is measured, usually 0.5-2.5 lock lengths downstream by which point the GC2 height has decreased due to dispersion. Although the GC1 height also undergoes a dispersive decrease in height, generally more positive agreement is noted when comparing measured and predicted gravity current heights. The distance travelled by the internal front prior to being arrested by the reflected GC2 agrees robustly with SW theory. Laboratory and DNS experiments exhibiting a thick ambient interface are also reported upon. We observe that the speed of the internal front and the downstream distance it travels at a constant speed increase with interface thickness. The insights gained from this investigation can be applied to realistic environmental flows such as nocturnal thunderstorm outflows.