Double-averaged kinetic energy budgets in flows over mobile granular beds: insights from DNS data analysis

The equations for double-mean, form-induced and spatially averaged turbulent energy budgets are employed to analyse data from direct numerical simulations of turbulent open-channel flows over transitionally rough mobile beds with intermediate flow submergence. Two scenarios were considered related to (i) near-critical bed condition, and (ii) fully mobile bed condition. The bed was composed of a layer of mobile spherical particles moving on the top of one layer of fixed particles of the same size. Data analysis showed the leading energy exchanges between double-mean, form-induced, turbulent flow field contributions as well as particle motions. Above the fixed particles tops, the turbulent flow receives kinetic energy directly from the mean flow as well as from moving bed particles, which in turn also receive energy from the mean flow. For near-critical bed condition, particle aggregations enhanced mean-flow heterogeneity, strengthened turbulent stresses and their effects on the flow, while at increased bed-mobility, energy transport mechanisms became weaker and conversions induced by viscous stresses and pressure became stronger.