Hydrostatic vs. non-hydrostatic modelling of density currents developing two dimensionally on steep and mild slopes

Abstract

Salinity and turbidity currents developing two dimensionally on steep and mild slopes are simulated numerically. An application of the process-based model Delft3D-Flow is presented that is able to capture the dynamics of subaqueous dense underflows by solving the two dimensional over the vertical (2DV) Reynolds-averaged Navier–Stokes equations under hydrostatic (H) and non-hydrostatic (NH) pressure assumptions. The development of conservative density currents that plunge in fresh water as a result of an upstream input of denser salty water and turbidity currents flowing down a fixed sandy bed with uniform slope are thoroughly investigated. Down-slope evolution of the modelled density currents is characterised by water entrainment coefficients that fall within the range of laboratory data. Vertical profiles of both velocity and excess density conform with previous experimental measurements. NH solutions, differently from their H counterparts, are shown to capture in detail time-dependent stages of dense undercurrents, such as the dynamics of their fronts, the passage of their heads as well as the development of Kelvin–Helmholtz (KH) instabilities at their interfaces with the ambient fluid resulting in the velocity pulsing of their bodies. Nonetheless, the H application of Delft3D-Flow predicts fairly well the steady state of salty and turbid undercurrents, thus representing a computationally cost-effective alternative for the modelling of field-scale density currents.