Rough bed hydrodynamics under wave-current interactional flow field: double averaging approach

The effect of surface wave on the double-averaged (DA) current-only flow properties is examined over two different types of rough beds comprising hemispherical elements with regular and staggered arrangements. For each case, the relative roughness spacing of p/r = 4 is maintained, where p = pitch distance and r = hemisphere height. The changes in turbulence characteristics against the water depth are analysed for superimposed surface waves propagating along the current with 1 and 2 Hz frequencies. The effect of regular and staggered roughness arrangements on different turbulence characteristics is explored. Results demonstrate that the DA stream-wise velocity decreases and increases at the outer region and within the roughness region, respectively, due to wave propagation. Owing to the surface wave, the DA intensity and form-induced intensity increase above the roughness layer and decrease within the bottom boundary layer. The values of form-induced intensities are smaller (greater) than the DA turbulence intensities at each considered flow depth within the roughness (outer) layer. For the entire flow depth, the values of DA Reynolds stress decrease due to wave interactions along a steady current. Again, the turbulence is observed to be close to isotropic for the current-only flow at the outer zone, while the flow transits to an anisotropic state with wave imposition on current. Further, the computed values of the turbulence indicator and dispersion functions are used for the identification of the level of turbulence and dispersion at each flow depth for the locations upstream and downstream of a hemisphere in the hemispherical bed.