Mathematical modeling provides a particularly important tool for studying the
stream
runoff formation processes, and its role is enhanced in the case of a sparse,
obsolete monitoring
network characteristic of most regions of Siberia. When analyzing
spatio-temporal regularities of
the water and sediment runoff in river systems, serious problems are caused by
lack of the basic
hydrological model capable of handling real-time data of hydrological
measurements.
Calculations of unsteady flows in stream channels draw heavily on
one-dimensional numerical
models which are relatively easy to use and yield reliable results. Numerical
investigations into the
hydraulic regime of natural streams involve specific difficulties caused by the
presence of nonlinear
frictional forces in a turbulent flow, a variability in the channel geometry,
the braiding of flows, the
presence of floodplain depressions, riffles, etc. For especially complex
stretches of rivers, a onedimensional
approximation no longer fits the reality sufficiently adequately, so that the
planar flow
structure must be taken into account. For this purpose Saint Vennant's plane
system of equations
was used as the basis in order to develop further the numerical model due to
this author which
is intended for calculating the flow field, flow rates, levels, and impurity
concentrations in natural
water bodies of an arbitrary configuration or in a part of them. Fundamental
laws of fluid mechanics
are used as the basis for the model.
Spatial modeling of flows in complex regions necessitates reliable, consistent
methods providing
acceptable accuracy. As far as hydrological problems are concerned, the control
volume
method that allows the use of curvilinear grids was found to be the most
powerful tool for obtaining
the initial finite-difference relations.
This paper offers a number of examples illustrating the capabilities of the
planar model for
streams which is intended to resolve real problems arising at the design,
construction and operation stages of engineering structures in river channels
and floodplains.