Abstract

Numerical hydrodynamic model of current in natural water streams based on two-dimensional Saint-Venant equations is presented. The model is designed to calculate the fields of velocity, discharges and levels in channels and floodplains of complex morphology. Mathematical task is enclosed by initial and edge conditions. Equations for transport of suspended and drawn sediments are formulated within a concept of dispersoid and form an interconnected system with hydrodynamic equations. Equations for sediment mass balance are written in the form of conservation law and contain the equation of suspension transport and the equation of channel deformation. Parameter reflecting a probability of exceeding of non-eroding values velocity is introduced for description of suspended and drawn sediments mass exchange. Equations of solid admixture concentration in the water are written for polydisperse suspension composition. Equations of channel deformation contain source summands entering with opposite signs towards the equation for suspension, hence a componentwise sum of these equations gives a conservation law of sediment pooled mass having a clear physical sense. To parameterise a vector of drawn sediments the range of known semi-empirical relations is used (Van Rijn; Graf, Bagnold; Grishanin and others). To illustrate the model resources the current and sediment transport were calculated for 30-km extent of Novosibirsk water reservoir near Zavjalovo village where the sand and pebble deposit is developed with suction dredge.

Keywords: Numerical modelling, channel currents, suspended current