Plunging and entrainment dynamics of an unconfined hyperpycnal plume over a sloping bed

The flow of a hyperpycnal river plume into a lake with a sloping bed and without any lateral confinement is a common occurrence in nature. A characteristic example of such geophysical fluid flow system is the inflow of river Rhone in Llake Geneva. In this work, we study the near-field plunging dynamics of an unconfined hyperpycnal plume at laboratory scale, over an idealized bed, with a slope that is similar to the one of the natural system. The study is based on large-eddy simulation of the Navier-Stokes equations in the Boussinesq approximation. We focus on the effect of varying the inflow conditions and in particular the densimetric Froude number, Frd, which is the nondimensional parameter describing the ratio between inertial and buoyancy forces acting on the plume. Three simulations were performed at different values of Frd, within the range encountered in the natural system. Similarly to previous works, we are able to identify lateral slumping as the main mechanism that leads to plunging of the dense river water and the formation of the characteristic triangular pattern at the lake surface. We are able to further identify the formation of a wake downstream of the vertex plunge point, due to the transport of mixed river-ambient water from the converging mixing layers across the plunge curve on both sides of the plume. The extent of both the wake and the overall plunge region increases significantly with increase of Frd. This mechanism can be associated to the changes of the surface patterns of the plume observed in the field. In addition, we compute the total entrainment, E, of ambient lake water as the streamwise increase of volumetric flow rate downstream of the river mouth. E is found to increase with distance from the mouth, as the plume continuously entrains ambient lake water. We find that for the same distance from the river mouth, E is larger for lower Frd. This increase of E with decreasing Frd is attributed to two mechanisms. First, in the plunge region, lower Frd leads to greater lateral spread and therefore increased interface area between plume and ambient water. Second, in the underflow region, lower Frd results in higher mean streamwise plume velocity, enhancing entrainment intensity.