Mathematical modeling provides a particularly important tool for studying thestreamrunoff formation processes, and its role is enhanced in the case of a sparse,obsolete monitoringnetwork characteristic of most regions of Siberia. When analyzingspatio-temporal regularities ofthe water and sediment runoff in river systems, serious problems are caused bylack of the basichydrological model capable of handling real-time data of hydrologicalmeasurements.
Calculations of unsteady flows in stream channels draw heavily onone-dimensional numericalmodels which are relatively easy to use and yield reliable results. Numericalinvestigations into thehydraulic regime of natural streams involve specific difficulties caused by thepresence of nonlinearfrictional forces in a turbulent flow, a variability in the channel geometry,the braiding of flows, thepresence of floodplain depressions, riffles, etc. For especially complexstretches of rivers, a onedimensionalapproximation no longer fits the reality sufficiently adequately, so that theplanar flowstructure must be taken into account. For this purpose Saint Vennant's planesystem of equationswas used as the basis in order to develop further the numerical model due tothis author whichis intended for calculating the flow field, flow rates, levels, and impurityconcentrations in naturalwater bodies of an arbitrary configuration or in a part of them. Fundamentallaws of fluid mechanicsare used as the basis for the model.
Spatial modeling of flows in complex regions necessitates reliable, consistentmethods providingacceptable accuracy. As far as hydrological problems are concerned, the controlvolumemethod that allows the use of curvilinear grids was found to be the mostpowerful tool for obtainingthe initial finite-difference relations.
This paper offers a number of examples illustrating the capabilities of theplanar model forstreams which is intended to resolve real problems arising at the design,construction and operation stages of engineering structures in river channelsand floodplains.