Gravity currents produced by constant and time varying inflow in a circular cross-section channel: Experiments and theory

We investigate high-Reynolds number gravity currents (GC) in a horizontal channel of circular cross-section. We focus on GC sustained by constant or time varying inflow (volume of injected fluid ∝ tα, with α=1 and α > 1). The novelty of our work is in the type of the gravity currents: produced by influx/outflux boundary conditions, and propagation in circular (or semi-circular) channel. The objective is to elucidate the main propagation features and correlate them to the governing dimensionless parameters; to this end, we use experimental observations guided by shallow-water (SW) theoretical models. The system is of Boussinesq type with the denser fluid (salt water) injected into the ambient fluid (tap water) at one end section of a circular tube of 19 cm diameter and 605 cm long. The ambient fluid fills the channel of radius r* up to a given height H*=βr* (0 < β < 2) where it is open to the atmosphere. This fluid is displaced by the intruding current and outflows either at the same or at the opposite end-side of the channel. The two different configurations (with return and no-return flow) allow to analyze the impact of the motion of the ambient fluid on the front speed of the intruding current. For Q larger than some threshold value, the current is expected theoretically to undergo a choking process which limits the speed/thickness of propagation. Two series of experiments were conducted with constant and time varying inflow. The choking effect was observed, qualitatively, in both series. The theory correctly predicts the qualitative behavior, but systematically overestimates the front speed of the current (consistent with previously-published data concerning rectangular and non-rectangular cross-sections), with larger discrepancies for the no-return flow case. These discrepancies are mainly due to: (i) the variations of the free-surface of the ambient fluid with respect to its nominal value (the theoretical model assumes a fixed free-slip top of the ambient fluid), and (ii) mixing/entrainment effects, as shown by specific measurements of the open interface level and velocity profiles.