Author(s): D. Pokrajac; S. Venuleo; T. Tokyay; G. Constantinescu; M.J. Franca
Linked Author(s): George Constantinescu, Mário Franca
Keywords: Shape factor; Shallow water equations; Gravity currents; Pressure term; Non-uniform density profile
Abstract: Gravity currents are often modeled by means of shallow water equations (SWEs). These models commonly assume a constant (top-hat) density profile. This paper presents the analysis of the effect of non-uniform density profile on the pressure term in SWEs. Layer-averaged equations can be used either as a basis for numerical simulation models, or for a large-scale description of gravity currents. The layer thickness (current depth) appearing in these equations can be defined in several ways. A 'notional' current depth proposed by Ellison & Turner (1959) is based on both volume and momentum fluxes integrated from the bed level to infinity. Alternatively, the depth can be 'physically' defined, based for example on a density threshold (e.g. Hacker et al. 1995). Layer-averaged equations (or Shallow Water Equations, SWEs) are subsequently obtained by integrating Navier-Stokes equations either between the bed level and either infinity (Parker et al. 1987) or the physical top of the current (Chu et al. 1979, Pokrajac et al. 2017). In either case integration of the non-uniform current density and velocity profiles produces coefficients usually called shape factors. Although the shape factors have been acknowledged for very long time, the SWE-based numerical models still do not incorporate them (e.g. Chu et al. 1979, Ungarish 2009, Adduce et al., 2012). This has motivated an investigation of the shape factor in the pressure term of the layer-averaged momentum equation, carried out using results of numerical simulation of a gravity current. The values of the pressure coefficient are reported for a physical definition based on the density threshold, Ellison & Turner's notional definition, and the combination of the two.
DOI: https://doi.org/10.3850/978-981-11-2731-1_212-cd
Year: 2018