The problem of the stability of the sand bed surface in a rectangular closed conduit with respect to spatially one-dimensional perturbations is formulated. The bed-form stability problem is solved using an analytical formula of bed load which takes into account the effect of bottom pressure on bed-load transport. An analytical dependence of the bed wavelength on hydrodynamic flow parameters and sediment particle diameter is obtained and compared with experimental data.
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Krat et al. (2016) studied this question.
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