Characterizing turbulent mixing and entrainment in gravity currents sustained by constant inflow

Sustained gravity currents driven by the continuous supply of dense fluid into a lighter ambient are ubiquitous in natural and engineering contexts. Although lock-release configurations have been extensively studied, gravity currents sustained by constant inflow remain less understood, particularly regarding turbulent mixing, entrainment, and the influence of inlet conditions. High-resolution numerical simulations and depth-averaged models are employed to investigate these aspects. Intense turbulent mixing is observed where the depth-averaged gradient Richardson number falls below a critical value, accompanied by Kelvin–Helmholtz (KH) billows. A high inlet Froude number induces the sustained formation of KH billows downstream of the inlet, while a high inlet mass flux causes KH vortices formed at the front to lag and lose coherence with it. Scaling laws governed by turbulent entrainment are derived analytically and validated by simulation results. Head dynamics influenced by turbulent mixing and entrainment are analyzed. In most cases, new heads continuously form at the leading edge and grow in height, leading to deceleration, and at high inlet mass flux, eventual detachment from the front occurs. However, when the inlet Froude number is high and the inlet mass flux is low, the head closely follows the front and propagates steadily at a shock speed, preventing the formation of new heads. The increase in head height results from recirculation and turbulent entrainment. At low inlet mass flux, turbulent entrainment dominates, while at high inlet mass flux, the two mechanisms are initially comparable, but recirculation weakens over time, leaving turbulent entrainment as the main contributor.