Model analysis of aspects of the flow field ahead of a density current (Q5942632)

The author proposes a two-dimensional model for density currents. The density current or gravity current is the motion of a fluid in another one, governed by the difference in hydrostatic pressures caused by the density difference between the fluid in the flow and ambient fluid. Such currents are encountered in geophysical applications, in atmospheric gravity currents, and in other technical applications. The model consists in an arrangement of two-dimensional point sources in a plane, which stems from an important gravity flow in an infinite channel. This system of two-dimensional sources allows to introduce the complex potential of the flow, to determine the streamlines or the separation line between two fluids, and to calculate the velocity at large distances in the gravity current. To substantiate these theoretical results, due to the lack of boundary conditions for the current flow, the author uses experimental results of G. V. Middleton, published in 1966 and quoted in the references list. NEWLINENEWLINENEWLINEAnother important problem appearing in the study is the presence of the end wall ahead of the front, which is modeled by the introduction of two arrays of sources moving towards each other. In such a manner, the influence of this end wall can be determined. The results obtained by the author from this model are validated by direct numerical simulations of viscous density currents in plane channels of finite length.