Experimental and Theoretical Modelling of 3D Gravity Currents

Abstract

When two liquid bodies with different density come in contact in non-equilibrium conditions, a flow is caused, known as gravity or density current. In the environment, as well as in the industrial framework, this kind of flow is very common and the scientifictechnical interest of the investigation on it is very high. The paper of Huppert (2006) and the book of Ungarish (2009b) give excellent reviews on the state of the art of the topic, while a huge collection of artificial, as well as natural, gravity currents and a qualitative description of their key features is given in the book of Simpson (1997). The investigation on gravity currents dates back to several decades ago (first important works are those of Von Karman, 1940; Yih, 1947; Prandtl, 1952 and Keulegan, 1957), nevertheless many aspects still need a better understanding. These aspects should be investigated in order to widen the knowledge on the considered phenomenon and are generally related to the geometry of the fluid domain and the use of particular fluids, like e.g. mixtures of liquid and sediments. Early studies on gravity currents were based on analytical and experimental methods and were concerned with 2D gravity currents: i.e. gravity currents whose description can be made in a vertical x-z plane. The seminal work of Benjamin (1968) formulates a fundamental theory, based on the perfect-fluid hypothesis and simple extensions of it (like the classical theory of hydraulic jumps), which gives a relationship between the thickness of the gravity current and the velocity of the front. The Benjamin’s theory is a milestone and analytical investigations on gravity currents, even the most recent (Shin et al., 2004; Lowe et al., 2005; Ungarish & Zemach, 2005; Ungarish, 2008; Ungarish, 2009) cannot disregard it. Laboratory gravity currents can be realized in very different ways (Simpson, 1997), depending on which features have to be investigated. The basic experimental setup, which permits to investigate the propagation’s features of the gravity current, is the lock exchange release experiment. This experiment consists in leaving two liquid bodies of different density in non-equilibrium condition, typically removing a sliding gate which originally separated them. The consequence is a flow of heavier liquid (the gravity current) under the