Momentum balance in flows over mobile granular beds: application of double-averaging methodology to DNS data

This paper presents the application of the double-averaging methodology to actual data obtained for the mobile-bed conditions from direct numerical simulations using an immersed boundary method. The dimensions of the computational domain resemble those for open-channel flows with small relative submergence. The domain bottom is a plane covered with one layer of hexagonally packed, single-size spheres fixed to the bed. The fixed particles are covered by 2000 mobile particles of the same size that are free to move. Two simulation scenarios at distinctly different values of the Shields parameter are studied representing a fully mobilized and partially mobilized granular bed. The effects of the averaging time and the averaging domain size and shape on the double-averaged flow quantities are identified first. Then, the data analysis focuses on the detailed assessment of the key terms of the double-averaged momentum balance equation formulated for mobile-bed conditions. The paper demonstrates that the double-averaging methodology provides an efficient reduction of the massive datasets produced by the fully resolved simulations to a manageable number of physically meaningful double-averaged quantities, which should help devising closure strategies for modelling mobile-bed flows.