Higher-order moments with turbulent length-scales and anisotropy associated with flow over dune shapes in tidal environment

Abstract

The purpose of this research paper is to investigate the third-order moments of velocity fluctuations, turbulent kinetic energy (TKE) fluxes, turbulence dissipation rate, turbulent length scales, and Reynolds stress anisotropy in the wake regions over two artificial upstream-facing bed forms. For the structure having a smaller flow-facing slope (slanting forward-facing structure, named as SFFS), the maximum flow intermittency is 0.6% with a maximum flow reversal frequency of 0.24 Hz, whereas for the greater flow-facing sloped structure (vertical forward-facing structure, named as VFFS), up to 70% flow intermittency is noticed just downstream of the corresponding crest location with a maximum of 28 Hz flow reversal frequency. A strong negative M30 (stream-wise flux of stream-wise normal stress) and a strong positive M03 (vertical flux of vertical normal stress), implying the occurrence of ejection events, take place above the flow separation region along the generated shear layer. However, near the lee-surface, positive M30 and negative M03 imply the presence of sweep events. For both the cases, maximum of normalized TKE (κ) is generated in the vicinity of crest location, which spread over the retarding flow region near-bed of the trough and wake-flow region downstream of the crest. The production of turbulence is mainly concentrated at the interface of intense ejection and sweep dominated zones over the trough region for the VFFS case, and for the other bed form, i.e., SFFS case, maximum turbulence production is concentrated at the near-bed crest location. Near the bed, the length-scale of eddies in the inertial sub-range decreases substantially compared to that in the upstream. It is seen that in the region of negative kinetic energy production, local maximum anisotropy is found, especially for b11,22,33S and b11,22,33V components. Interestingly, at the corresponding crest points for SFFS and VFFS, maximum affinity toward the one-component isotropy is measured almost throughout the vertical height. However, a clear increasing trend in the affinity to a better isotropy; i.e., the three-dimensional isotropy is identified as the vertical height increases up to z ≈ 3 cm above the bed when a fair downstream location for the VFFS case is considered. A special look toward the investigation of possible connection of the flow region with negative TKE production with the stream anisotropy shows that a substantial increase in the degree of anisotropy (Ad) in the anisotropy invariant maps of the negative TKE production takes place for both the cases, when compared to that for the positive TKE production region.