Investigating the dynamics of particle-laden gravity currents using two-fluid simulations

Particle-laden gravity currents are extremely important in geophysical flow applications. They are the major pathway of sediments in subaqueous environments such as deep lakes and oceans and, to some extent, in the shallower seas of the continental shelves [1]. Various approaches have been developed to model these currents with different complexities ranging from box models, shallow water models, single-phase and two-phase flow models. The starting point of the present analysis is based on Gadal et al. [2] who investigated the role of non-dimensional parameters such as the bed slope (α), the Reynolds number (Re), the Stokes number (St), and the volume fraction (φ) on the dynamics of the front velocity at the early stage of the current propagation using both experimental and numerical approaches. The front velocity at short time scales as the square root of the reduced gravity times the initial lock-height. Overall, it is an increasing function of the bed slope and a decreasing function of the initial volume fraction (for φ>0.45). It is also shown that the duration of the initial constant velocity regime decreases with the particle settling velocity or Stokes number at small bed slope angles. The 2D two-fluid simulations performed with sedFOAM [3] have been shown to reproduce almost quantitatively these trends however a comprehensive description of the detailed underlying physical mechanisms is still missing. In this contribution, we propose to use the two-fluid model to address this question. To achieve this goal, 3D two-fluid simulations have been performed and the numerical results have been depth-averaged over the current shape. The mass balance is used to quantify the entrainment at the current interface and the various terms entering in the momentum balance are extracted from the simulation results. These analysis are used to understand the origin of the current dynamics attenuation such as fluid viscous and turbulent stresses, particle-particle interactions, and fluid-particle interactions.

References:

[1] Meiburg, E. and Kneller, B. (2010). Turbidity currents and their deposits. Annual Review of Fluid Mechanics, 42(1):135–156.

[2] Gadal C., Mercier M. J., Rastello M., and Lacaze L. (2023). “Slumping regime in lock-release turbidity currents”,. J. Fluid Mech., 974:A4,

[3] Chauchat, J., Cheng, Z., Nagel, T., Bonamy, C., and Hsu, T.-J. (2017). Sedfoam- 2.0: a 3-d two-phase flow numerical model for sediment transport.    Geoscientific Model Development, 10(12):4367–4392.