Experimental study of gravity current propagation over rough tilted surfaces

Numerous previous studies have been done to understand the physics of gravity currents. Some considered the propagation over smooth or rough horizontal surfaces (Tokyay et al. (2014), Zhou et al. (2017)), and others studied inclined surfaces without any roughness. What about the more complex situation of inclined rough surfaces? We have studied, experimentally, how a finite volume of heavy fluid (salted water with a clay suspension) rushing down a slope (20° & 30°) is affected by the multiple obstacles it counters on its way. Our setup is a classic volume release configuration in a 2D flume immersed in a 20 m³ water tank at INRAE Grenoble. The study tests (352 experiments per tilt) different initial conditions of the released flow (volume and density) and various surface conditions from smooth to rough:

• For the initial conditions: the experiments show that the front velocity is monotonically related to its initial volume and density. Although the initial mass of the flow is the product of its density times volume, the mass effect on the flow front velocity cannot come in replacement of both volume and density effects, as it was found that the front velocity is non-monotonically related to its initial mass.
• For the surface conditions: besides testing the smooth case, we have covered a wide range of roughness configurations using obstacles with different shapes, heights, and spacings. Walls or barriers blocking the whole width of the flume have been used (see Fig.1-a). Testing various heights and spacings shows that higher barriers decrease the flow front velocity, while non-monotonic relations were found when the spacing between successive barriers in the flow direction is changed. Flow propagation over and through an array of obstacles has also been studied with various obstacles arrangement (in-line and staggered) and different obstacles' cross-sections (rectangular and circular). For circular obstacles, the (x_𝑓-t) curve is no longer smooth but takes the shape of stairsteps, and they are found to be more efficient in decelerating the flow (see Fig.1-b).

Studying both 20° and 30°-flume tilts enables us to look through the slope effect. The analysis shows that, in general, increasing the slope results in higher front velocity values. Nevertheless, the degree of influence is dependent on diverse factors (volume, density, bed surface conditions). In addition, we have studied the effect of the initial flow parameters on the flow height just after the lock release (at an accurate predetermined distance from the lock chosen based on 252 experiments). This height depends only on the initial volume and density effect is negligible. Determination of this height is essential for our non-dimensional analysis: to study the temporal evolution of the non-dimensional front position (𝑥_𝑓−𝑥_o)/𝑥_o versus the non-dimensional time (t_𝑓/t_o). Indeed, it will enable us to avoid using the initial flow depth at the lock that is highly dependent on the inclination angle, or an estimated virtual height after the lock that would be less representative (see Fig.1-c).

Fig. 1: