APPROXIMATION OF THE LONGITUDINAL PROFILE OF RIVER DUNES USING SINE WAVE BRANCHES

mathematical model of the longitudinal profile of river dunes is proposed, based on the approximation of the stoss and lee sides of the dune by two sine wave branches with identical amplitudes but different periods and phase shifts. Unlike the triangular approximation, this model ensures profile smoothness (С1-continuity) at all characteristic points – at the crest and in the troughs – eliminating the singularity problem in hydrodynamic calculations. Analytical expressions are obtained to describe the profile both as a piecewise function and as a unified analytical function defined over the entire abscissa axis, which is convenient for use in theoretical models and numerical simulations. It is shown that the areas under the sine wave branches are exactly equal to the areas of the corresponding triangles formed by chords, allowing for the use of simple estimates for dune volume characteristics. For arc lengths expressed through elliptic integrals, numerical calculations were performed across a wide range of steepness and asymmetry parameters. It was established that the relative excess of the «sinusoidal» profile length over the «triangular» one is 2–4%, which can be significant in calculations of hydraulic resistance and sediment transport. Families of parametric plots describing the main geometric characteristics of the «sinusoidal» dune are constructed. The results obtained can be used for riverbed relief modeling, channel resistance assessment, and bedload discharge calculations.

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