Anisotropy in Turbulent Flow over Two-Dimensional Fixed Bedforms with Downward Seepage

The investigation of bedform configurations and their migration manifest under varying flow conditions in alluvial channels remains a persistent challenge for engineers and researchers due to the intricate nature and lack of certainty associated with these formations. The study of turbulence characteristics of flow over a dune-shaped bedform can become a foundation for evaluating potential bedform migration and sediment transport behavior in an alluvial stream. Through the present study, effort has been made to demonstrate the variation in turbulent anisotropy associated with the flow over a 2D fixed dune-shaped bedform under the influence of downward seepage. Using an acoustic doppler velocimeter, measurements of flow velocities were taken over several sections of the dune-shaped bedform, in the presence and absence of downward seepage. Flow characteristics at these sections are then compared for both conditions to observe the change in turbulence behavior under the influence of downward seepage. The results reveal that, at the initial sections and lee side sections of the dune, the average contribution of streamwise and spanwise turbulent intensity to turbulent kinetic energy (TKE) along the depth of flow increases by $\sim 24\%–45\%$ and $\sim 7\%–39\%$ for 10% seepage and by $\sim 26\%–63\%$ and $\sim 25\%–45\%$ for 15% seepage, respectively, as compared with the no-seepage condition. The contribution of vertical turbulent intensities to the TKE is negligible as compared with the streamwise and spanwise turbulent intensities. Similarly, the contribution of Reynolds shear stress to TKE increases by $\sim 2\%–30\%$ for 10% seepage and $\sim 5\%–35\%$ for 15% seepage at the initial sections and lee side sections of the dune as compared with the no-seepage condition. The findings from the three anisotropy tensor eigenvalues indicate a significant rise in the strength of turbulent intensities in the streamwise direction with downward seepage primarily in the region near to the bedform surface and at the initial and lee sections of the dune. Analysis of the invariant function and plot of the anisotropic invariant map show that 1D anisotropy prevails in the initial and lee sections of the dune under the action of downward seepage. Downward seepage increases mass and momentum exchange near the bed zone of these sections, causing a significant increase in the contribution and strength of turbulent intensities in the streamwise direction. Additionally, comparative studies employing octant analysis of bursting events under seepage and no-seepage conditions demonstrate that, at the initial and lee side sections of the dune, the probability of occurrences of ejection and sweep events increases with an increase in the seepage percentage. The present investigation can form a basis for understanding the effects of downward seepage on flows over bedforms, which has not been, to our best knowledge, taken into account in the previous literature and may therefore facilitate more accurate prediction of the rate of sediment motion during the migration of bedforms in an alluvial stream.