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Stochastic Lagrangian Modelling of Vertically Upward Sediment-Laden Buoyant Jets

Author(s): S. N. Chan; J. H. W. Lee

Linked Author(s): Joseph Hun-Wei Lee, Shu Ning Chan

Keywords: Buoyant jets; Sediment transport; Gravity current; Particle tracking model

Abstract: A vertically upward sediment-laden buoyant jet is an important flow phenomenon in geophysical science and engineering as it resembles the dynamics of volcanic eruptions, deep sea hydrothermal vents and wastewater discharge. In an upward buoyant jet, sediment particles are carried by the rising jet fluid until they reach the maximum height of rise or the water surface. Sediment fall-out occurs at the jet edge and/or from the radial spreading current and re-entrainment of sediment occurs. For the first time, a three-dimensional stochastic Lagrangian particle tracking model for predicting the deposition and dynamics of a vertical sediment-laden buoyant jet is developed. The model solves the governing equation of particle motion in a predetermined fluid velocity field superimposed with stochastic turbulent fluctuations. The three flow regimes involved in a buoyant jet-the turbulent jet flow, jet entrainment-induced external flow and surface spreading current, are modeled using validated semi-analytical methods: (1) the jet mean flow velocity is determined using a jet integral model; (2) jet-induced external irrotational flow field is computed by the point sink approach; (3) surface spreading current is predicted using an integral model accounting for the interfacial shear. Turbulent velocity fluctuations are modelled by an autocorrelation function that mimics the trapping of sediment particles in turbulent eddies. Root-mean-square (RMS) turbulence velocity and turbulent time scale are estimated from best-fitted self-similar profiles of turbulent kinetic energy and dissipation rate derived from a computational fluid dynamics solution of vertical buoyant jets. Model prediction shows excellent agreement with previous experimental data of bottom sediment deposition. Model prediction reveals the increase in sediment concentration due to sediment reentrainment which has important significance for the dynamics of vertical sediment jets.


Year: 2014

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