Gravity Currents from Instantaneous Sources Down a Slope A. Dai 1 ; C. E. Ozdemir 2 ; M. I. Cantero 3 ; and S. Balachandar 4 Abstract: Gravity currents from instantaneous sources down a slope were modeled with classic thermal theory, which has formed the basis for many subsequent studies. Considering entrainment of ambient fluid and conservation of total buoyancy, thermal theory predicted the height, length, and velocity of the gravity current head. In this study, the problem with direct numerical simulations was re-investigated, and the results compared with thermal theory. The predictions based on thermal theory are shown to be appropriate only for the acceleration phase, not for the entire gravity current motion. In particular, for the current head forms on a 10° slope produced from an instantaneous buoyancy source, the contained buoyancy in the head is approximately 58% of the total buoyancy at most and is not conserved during the motion as assumed in thermal theory. In the deceleration phase, the height and aspect ratio of the head and the buoyancy contained within it may all decrease with downslope distance. Thermal theory relies on the increase in the mass of the current head through entrainment as the major mechanism for deceleration and, therefore, tends to underpredict the front velocity in the deceleration phase. DOI: 10.1061/(ASCE) HY.1943-7900.0000500. © 2012 American Society of Civil Engineers. CE Database subject headings: Slopes; Thermal factors; Currents; Hydraulics. Author keywords: Buoyancy-driven flows; Gravity currents; Sloping boundary; Thermal theory. Introduction Gravity currents, also known as density currents, are buoyancy- driven flows caused by a density difference. The density difference may be due to dissolved or suspended materials and temperature differentials. Gravity currents on slopes are commonly encountered in geophysical environments, for example, powder-snow ava- lanches and turbidity currents off the continental shelf, but they are also of interest in engineering applications mostly related to industrial safety and environmental protection. Readers are referred to Allen (1985), Fannelop (1994), and Simpson (1997) for more details about gravity currents and their relevance in natural science and engineering applications. The interest in gravity currents has initiated a substantial amount of research using theoretical, experimental, and numerical methods. Much work has focused on gravity currents produced by instanta- neous, finite buoyancy on a horizontal boundary, that is, lock- exchange flows (Benjamin 1968; Huppert and Simpson 1980; Marino et al. 2005; Huppert 2006). For gravity currents on a slope, the buoyancy source may be continuously maintained (Britter and Linden 1980; Parker et al. 1986) or released instantaneously with finite buoyancy (Beghin et al. 1981; Rastello and Hopfinger 2004). The focus here is on the gravity currents produced by a finite amount of buoyancy instantaneously released on a slope. Such gravity currents were experimentally studied and theoretically modeled with thermal theory in Beghin et al. (1981), which has formed the basis for many subsequent studies. For example, Dade et al. (1994) extended the theory to a gravity current on a slope with decreasing buoyancy because of particle settling; Rastello and Hopfinger (2004) studied a case in which the buoyancy increases as a result of resuspension of sediment. Apart from classic thermal theory, Webber et al. (1993), Tickle (1996), and Ross et al. (2002) alternatively used a shallow water model for an instantaneous re- lease of buoyancy on a uniform slope. Birman et al. (2007) numeri- cally investigated Boussinesq and non-Boussinesq gravity currents on sloping boundaries using two-dimensional simulations and found agreement with experiments designed to minimize three- dimensional dynamics. However, here it is shown that a three- dimensional configuration is warranted to accurately capture the different phases of gravity current motion, and the use of two- dimensional simulations is limited (Cantero et al. 2007). The thermal theory developed by Beghin et al. (1981) for grav- ity currents follows the spirit of the famous Morton et al. (1956) in that the total released buoyancy is assumed to be contained in the gravity current head, into which the ambient fluid is entrained. The gravity current head was assumed to have a self-similar, semiellip- tical shape as it moves downslope. The acceleration and deceler- ation phases of gravity current on a slope were qualitatively described by thermal theory, and in particular, the height and length of the current head were predicted to increase linearly with down- slope distance. Recently, Maxworthy and Nokes (2007) reexamined the gravity current produced by an instantaneous bouyancy source that is com- posed of a slender body of dense fluid, where the lock length is twice as long as the lock height. It was found in such a case that the gravity current head does not contain the total released 1 Dept. of Water Resources and Environmental Engineering, Tamkang Univ., Taiwan (corresponding author). E-mail: hdai@mail.tku.edu.tw 2 Dept. of Civil and Environmental Engineering, Univ. of Delaware, Newark, DE 19716. 3 National Council for Scientific and Technological Research, Bariloche Atomic Center, Bustillo 9500, San Carlos de Bariloche, Rio Negro, Argentina; Institute Balseiro, National Univ. of Cuyo—National Commis- sion of Atomic Energy, Bustillo 9500, San Carlos de Bariloche, Rio Negro, Argentina. 4 Dept. of Mechanical and Aerospace Engineering, University of Flor- ida, Gainesville, FL 32611. Note. This manuscript was submitted on August 30, 2010; approved on August 18, 2011; published online on August 20, 2011. Discussion period open until August 1, 2012; separate discussions must be submitted for individual papers. This paper is part of the Journal of Hydraulic Engineer- ing, Vol. 138, No. 3, March 1, 2012. ©ASCE, ISSN 0733-9429/2012/3- 237–246/$25.00. JOURNAL OF HYDRAULIC ENGINEERING © ASCE / MARCH 2012 / 237 Downloaded 01 Apr 2012 to 163.13.134.11. 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