Hydraulics of Rock Weirs (3D versus 1D Effects)
One-dimensional, 1D, numerical simulations model downstream changes in hydraulics while neglecting vertical and lateral variation. Two-dimensional, 2D, models incorporate lateral differences in velocity and water surface elevation, but neglect flow not perpendicular to the stream bed. Three-dimensional, 3D, modeling simulates the motion of water in all directions and most accurately captures flow patterns. Estimating structure performance with lower dimensional methods requires understanding the impact of representing a features with methods farther divorced from real world processes. A 3D numerical model of a rock weir was constructed to investigate multi-dimensional flow patterns and determine modeling needs. The U2RANS 3D model, developed by Dr. Yong Lai, has been used for all figures.
Plate 1 shows a U-Weir in the field and the corresponding water surface and velocity from a 3D numerical model. In the photograph, entrained air reveals areas of high velocity. The 3D model captured flow features including the draw down curve, hydraulic jump, and variations in velocity. Dry areas in the photograph, such as the protruding rocks in the upper right corner match the 3D model water surface. Plate 1 demonstrates the capability of three-dimensional numerical modeling to match field conditions.
Plate 2 shows a plan view with water surface elevation contours. The areas upstream and downstream of the structure show little lateral variation. The water surface drops rapidly over the structure and follows the weir crest topology. 1D modeling assumes gradually varied flow and constant water surface elevation across a transect. Methods to meet 1D water surface requirements include constructing cross sections tracing water surface elevation contours or coding multiple cross section perpendicular to the thalweg. Plate 2 shows the water surface elevation requirements for a 1D model. (click to enlarge)
Plate 3 shows surface velocity vectors. In the channel upstream and downstream of the structure water flows parallel to the banks. Over the weir, the flow paths rapidly converge and then slowly expand. A jet through the center of the channel creates abrupt lateral changes in velocity. 1D modeling requires cross section lines perpendicular to the velocity vectors. Modelers accommodate lateral variability through bending the cross section. Plate 3 shows the velocity conditions that must be met in a 1D representation. (click to enlarge)
Plate 4 shows a profile view for velocities in a slice cut along the thalweg. Water flows parallel to the bed upstream and downstream of the structure. The stream lines rapidly converge and diverge vertically through the structure. The velocity profile contains a jet midway through the water column rather than the logarithmic profile of a typical river section. Vertical velocity components in the scour pool show plunging flow. 1D modeling requires perpendicular velocity vectors in all directions, including vertical. Plate 4 shows the vertical velocity conditions that must be met in a 1D representation. (click to enlarge)
Plate 5 shows attempts to reconcile 1D requirement with field conditions. A cross section model can meet either water surface requirements or velocity requirements, but not both. Plate 5 demonstrates the need for 1D models to incorporate adjustments for multi-dimensional effects. HEC-RAS contains placeholders, but the magnitude of the adjustment is unknown for rock weirs. The adjustment will depend on the throat width, profile and plan arm angle, drop height, and more. (click to enlarge)
3D modeling directly captures the physics of the flow hydraulics and can provide adjustments defensible to funding sources and regulatory agencies. There are no 1D hydraulic guidelines for rock weirs, field work cannot quantify and capture detailed processes, and physical modeling is expensive and time intensive. Without accurate hydraulics, designers cannot address the failure mechanisms of structures.