2021-03-12, Venuleo, Sara, Pokrajac, Dubravka, Tokyay, Talia, Constantinescu, George, Schleiss, Anton J., Franca, Mário J.

Rigorously derived shallow water equations (SWEs) are applied to results of large eddy simulation (LES) of a continuously fed gravity current in order to assess (1) sensitivity of current depth results to its definition; (2) coefficients in depth-averaged continuity and momentum equation due to the nonuniformity of density and velocity profiles; and (3) sensitivity of entrainment coefficient to definition of current depth. It is shown that using different definitions of the current depth may produce significantly different numerical results. The coefficients due to nonuniformity in the continuity equation are very close to unity, whereas the coefficients in the momentum flux and the pressure term in the momentum equation are different from unity by a margin that is very sensitive to the definition of current depth. The entrainment coefficient is more sensitive to the selected parameterization than to the definition of the current depth.

2019-12-31, Venuleo, Sara, Pokrajac, Dubravka, Schleiss, Anton J., Franca, Mário J.

We present the results of laboratory investigations of continuously-fed density currents that propagate first over a smooth horizontal bed and then over a porous substrate of limited length. Inflow discharge, initial excess density, and substrate porosities are varied. Density measurements, acquired through an image analysis technique, are performed above the porous layer simultaneously with quasi-instantaneous vertical velocity profiles. After a first phase in which the current sinks into the substrate, freshwater entrainment from the bed begins and, gradually, a mixing layer forms at the interface between the surface flow and the porous bed. Shear-driven and Rayleigh-Taylor instabilities rule the dynamics of this mixing layer. The porous boundary effects are observed in the vertical distributions of both density and velocity, especially in the near-bed region. Here, larger flow velocities are recorded over porous substrates. We argue that these are due to the presence of a longitudinal pressure gradient, which in turn is a consequence of the current mass loss. Its presence over the porous substrate is proved by the current interface longitudinal slope. However, other effects of the presence of the porous substrate, such as the relaxation of the no-slip boundary condition and the bed-normal momentum exchange, also affect the velocity field. The turbulent structure changes significantly over the porous substrate: while streamwise turbulence decreases, shear and bed-normal Reynolds stresses increase in large part of the current depth. Buoyancy instabilities further enhance the bed-normal momentum flux and, in the near-bed region, contribute to turbulent kinetic energy generation together with shear.

2017-07-31, Pokrajac, Dubravka, Venuleo, Sara, Franca, Mário J.

Gravity currents are often modelled by means of shallow water equations (SWEs). In these models, simplifications such as the consideration of a constant layer-averaged density are common. This note presents the complete and general derivation of a 2D depth-averaged momentum equation for gravity currents with density and velocity varying in the bed-normal direction. Special attention is given to the pressure term which is evaluated for constant, linear and exponential density profile. The shape of the density profile has implications for the momentum balance: the assumption of constant density leads to an overestimation of the driving force due to pressure gradient by a factor of 33% for linear density profile and up to 50% for an exponential profile. It also leads to an overestimation of celerity in numerical models based on traditional SWEs by factor of 22% and around 40% for linear end exponential density profiles respectively.