In the present study, mesopycnal flows are investigated using Direct Numerical Simulations (DNS). In particular, intrusive density- and particle-driven gravity currents
in the lock exchange set-up are simulated with the high-order finite-difference framework Xcompact3d. To account for the settling velocity of particles, a customised
Fick’s law for the particle-solution species is used with an additional term incorporating a constant settling velocity proportional to the concentration of particles. A
general energy budget equation is presented, for which the energy can migrate across
the domain’s boundaries. The relevant main features of intrusive gravity currents,
such as front velocity, energy exchanges, sedimentation rate, deposit profile, and
deposit map are discussed with comparison between two and three-dimensional simulations. In particular, the influence of the Grashof number, the interface thickness,
the energy exchanges, the sedimentation process, and how the presence of more than
one particle fraction may change the flow dynamics are investigated. The results are
in good agreement with previous experiments and theoretical work, in particular for
the prediction of the front velocity. For the particle-driven case, the suspended mass
evolution along with the sedimentation rate suggests the occurrence of three different
stages. In the first stage after the lock release, the particle mixture tends to suspend
itself due to gravitational forces. Once most of the particle-mixture mass is suspended, the current intrudes while increases its velocity, reaching its kinetic energy
peak. In the last stage, the particles are deposited at a nearly constant sedimentation
rate. As a results, the front velocity constantly decelerates.