Experimental and numerical simulation of three dimensional
gravity currents on smooth and rough bottom
Michele La Roccaa, Allen Bateman Pinzonb, Giampiero Sciortinoa, Claudia Adducea
In this paper the dynamics of a 3D gravity current is investigated both experimentally and numerically. The gravity current is realised in a rectangular tank by means of a lockexchange release experiment with fluid bodies of different salinity. The bottom of the tank can be both smooth and rough. The bottom roughness is realised by gluing diments of different granulometry. Five different granulometries (0.0-0.7-1.0-1.6-3.0 mm) and two different salinity conditions (1015-1025 kgm-3) are considered.
The mathematical model is defined in the framework of the shallow water theory of two immiscible fluid layers. Assuming that the free surface is constant with respect to both space and time, the athematical model can be simplified, becomes strictly hyperbolic and can be put in conservative form. As a consequence the numerical algorithm can be defined in the finite volumes method framework. The Godunov ormulation, together with the Roe’s approximate Riemann solver is adopted. The main problem with the mathematical model is that lighter layer equations become independent from heavier layer ones and cannot evolve from zero initial conditions. The lighter layer velocity field is then calculated by applying the mass conservation equation and verified by momentum equations. The computational procedure, as a whole, is quite new, to the authors’ knowledge. Comparisons between numerical and experimental results show in general a satisfactory
agreement and typical stages of gravity current evolution are ighlighted both numerically and experimentally. A systematic discrepancy is shown between numerical and experimental results in first two stages of gravity current evolution. Such a discrepancy is attributed to the
absence of entrainment in mathematical model. Indeed, by means of a simplified gravity current integral model, it is shown that the consideration of entrainment enhances the agreement between experimental and numerical results. An interesting result is connected with the influence of the roughness and consists both in shortening the duration of first two stages of gravity current evolution and with the smoothing of differences between numerical and experimental results during such first two stages. The roughness influence characterisation in 3D gravity currents is an aspect of the present paper, which is innovative on the authors’ opinion.