Water Surface Drag and Vertical Grid¶
Available from version 2.0.20261007
Overview¶
In ADCP measurements during floods, the velocity near the water surface is often lower than the logarithmic law predicts (the velocity dip). FreeBird can represent such profiles by combining a water surface drag coefficient, which applies a shear stress at the surface, with a vertical grid refined at both the bed and the surface.
| Feature | Location | Default |
|---|---|---|
Water surface drag coefficient cs_surf |
Calculation Conditions → Bed roughness and Bank(Wall) friction | 0 (no surface resistance) |
Vertical grid dividing method j_zgrid |
Calculation Conditions → Geometric and computational Parameters | Equal spacing |
Water Surface Drag Coefficient¶
A quadratic shear stress is applied at the water surface:
where \(C_s\) is the surface drag coefficient and \(\boldsymbol{u}_s\) is the horizontal velocity at the surface. The stress acts against the flow and reduces the near-surface velocity.
- With 0 (default) no surface resistance is applied, and the results are identical to earlier versions.
- With a value greater than 0, the surface shear velocity
SurfaceShearVelocity_cellis added to the 2D output.
Typical values
In a comparison with ADCP measurements at river scale (depth about 5 m), \(C_s\) = 0.65–1×10⁻³ reproduced the measured velocity profile. The best value depends on the size of the vertical cells near the surface, so calibrate it against your own measurements.
Difference from wind shear
The wind stress in the "Wind Driven Flow" tab is an external force given by the wind speed and direction. The surface drag coefficient represents the resistance acting on the surface flow itself (due to waves and surface turbulence). The two can be set independently.
Vertical Grid Dividing Method¶
Select how the σ-coordinate is divided in the vertical direction.
| Option | Description | Additional parameters |
|---|---|---|
| Equal spacing | The depth is divided equally by the number of vertical grids | None |
| Specify bottom grid size | The bottom cell is refined and cells grow geometrically toward the surface | Ratio to the water depth of the bottom grid cell size dz1 |
| Refine both bottom and surface | Cells grow geometrically from both the bed and the surface toward mid-depth | dz1 and Ratio to the water depth of the surface grid cell size dzs |
With "Refine both bottom and surface", the growth ratio is determined automatically so that the cells add up to the water depth. A warning is shown when the ratio between neighbouring cells exceeds 1.3. In that case, increase the number of vertical grids or enlarge dz1 and dzs.
When using surface drag
The surface drag acts on the flow through the surface cell, so a coarse surface cell does not represent its effect correctly. When surface drag is used, select "Refine both bottom and surface" to refine the cells near the surface.
Non-uniform grids
From 2.0.20261007, the vertical diffusion of u and v and the coefficients of the non-hydrostatic pressure equation are written for non-uniform grids. Results on an equally spaced grid are unchanged. The advection terms (CIP / upwind) keep the previous approximation.
Example¶
Settings for a flood velocity profile with a depth of about 5 m:
| Parameter | Value |
|---|---|
| Numbers of Grid in Z-direction | 20 |
| Vertical grid dividing method | Refine both bottom and surface |
| Ratio to the water depth of the bottom grid cell size | 0.01 |
| Ratio to the water depth of the surface grid cell size | 0.01 |
| Water surface drag coefficient | 0.0008 |