Flow separation and shear stress over angle-of-repose bed forms: A numerical investigation

Abstract

Large asymmetric bed forms commonly develop in rivers. The turbulence associated with flow separation that develops over their steep lee side is responsible for the form shear stress which can represent a substantial part of total shear stress in rivers. This paper uses the Delft3D modeling system to investigate the effects of bed form geometry and forcing conditions on flow separation length and associated turbulence, and bed form shear stress over angle-of-repose (30 lee side angle) bed forms. The model was validated with lab measurements that showed sufficient agreement to be used for a systematic analysis. The influence of flow velocity, bed roughness, relative height (bed form height/water depth), and aspect ratio (bed form height/length) on the variations of the normalized length of the flow separation zone, the extent of the wake region (where the turbulent kinetic energy (TKE) was more than 70% of the maximum TKE), the average TKE within the wake region and the form shear stress were investigated. Form shear stress was found not to scale with the size of the flow separation zone but to be related to the product of the normalized extent of the wake region (extent of the wake region/extent of water body above the bed form) and the average TKE within the wake region. The results add to understanding of the hydrodynamics of bed forms and may be used for the development of better parameterizations of smallscale processes for application in large-scale studies.

Three‐Dimensional Flow Above River Bedforms: Insights From Numerical Modeling of a Natural Dune Field (Río Paraná, Argentina)

“…At lab scale, a value of 0.000001 m 2 /s or lower should be used. As already identified in the 2‐D model (Lefebvre, Paarlberg, & Winter, ), the results are strongly influenced by the horizontal and vertical resolutions, which need to be fine enough to resolve flow separation and recirculation over the bedform lee. The layer size should be small near the bed in order to successfully capture processes relevant to 3‐D flow above bedforms and may be gradually increased toward the water surface.…”

“…The nonhydrostatic Delft3D modeling system has already been successfully used to set up a 2‐D vertical numerical model to simulate horizontal and vertical velocities, turbulent kinetic energy (TKE), and water levels above fixed bedforms. The model has been calibrated and validated against the laboratory flume experiments of McLean et al () and proved to correctly reproduce horizontal and vertical velocities (including flow separation), turbulence, and shear stress over idealized, angle‐of‐repose bedforms under unidirectional flow conditions (Lefebvre, Paarlberg, & Winter, ). Further confirmed against field data, the model also showed to correctly simulate velocities, TKE, and water levels in a tidal environment over natural bedforms (Lefebvre, Paarlberg, Ernstsen, et al, ).…”

“…It has also been used to carry out systematic experiments to constrain the influence of lee side angle on bedform roughness (Lefebvre & Winter, ) and to characterize the effect of natural bedform morphology on flow (Lefebvre et al, ). Details of the 2‐D model setup, calibration, and validation, including specifics on the turbulence closure scheme and sensitivity to grid size and roughness length, can be found in Lefebvre, Paarlberg, Ernstsen, et al (), Lefebvre, Paarlberg, & Winter ().…”

“…For each point at the bed where a negative stream‐wise velocity is found, the height of the FSZ is calculated as the distance above the bed at which the net discharge per unit width is zero (Figure c). In other words, the height of the FSZ is situated where the integral of the negative velocity between the bed and the zero‐velocity point is compensated by the integral of the positive velocity between the zero‐velocity point and the height of the flow separation (Lefebvre, Paarlberg, & Winter, ; Paarlberg et al, ).…”

“…Numerical models have been used to simulate the interaction of bedforms and hydrodynamics (El Kheiashy et al, ; Khosronejad & Sotiropoulos, ; Lefebvre, Paarlberg, & Winter, ; Omidyeganeh & Piomelli, ; Stoesser et al, ). They compensate for limitations in field and flume measurements as they allow simulations of high‐resolution near‐bed flow fields, provide estimate of turbulence, and can be used with a variety of boundary conditions.…”