The solution of the one-dimensional unsteady flow problem in the Lena river delta



The research into the hydrological regime of the river estuaries conventionally concerns the distribution of the flow across their channels and branches.

There is a known hydraulic method for calculating the hydrological regimes in the river deltas [1]. It is based on a system of the balance equations for branching nodes and uses the hydraulic formulas to describe the free surface level gradient in stationary conditions.

In [2-5] the complex river channel systems are simulated by the numerical solution of the Saint-Venant equation system using a variety of implicit difference schemes. The unsteady flows in the channels are described using a one-dimensional model. At the points of branching, the conjugation conditions are formulated. To solve the arising equations, the authors employ a stable sweeping algorithm which accounts for the tree-like graph structure. Altogether, these constitute the approach to solving the Saint-Venant equation system.

It should be noted that to apply the numerical solution of the Saint-Venant equation system to natural watercourses, one needs to prepare a representative and consistent dataset. This would ensure the accuracy of the solution to be.

This paper considers the mathematical model of the complexly braided Lena estuary. The model describes the hydrological regime of the river starting at the Kusur gauging station and ending at the outlets.

Also, this paper investigates the hydrological regime of the navigable Bykovskaya branch. The digital terrain model required in the equations of motion is obtained using the Google Earth Application.