Calculator Inputs
Formula Used
Friction velocity (u*) is a velocity scale that represents the intensity of turbulent momentum transfer near a surface. The calculator supports three common approaches:
- Shear stress method: u* = √(τ / ρ), where τ is surface shear stress (N/m²) and ρ is air density (kg/m³).
- Log wind profile method (neutral, above roughness sublayer): u* = κ U(z) / ln((z − d) / z₀), where κ is the von Kármán constant, z is measurement height, d is displacement height, and z₀ is roughness length.
- Reynolds stress method: u* = √(|u′w′|), using the covariance of turbulent fluctuations (m²/s²).
How to Use This Calculator
- Select the method that matches your available measurements.
- Enter values in consistent units, then press Calculate.
- Review u* and the input summary shown above the form.
- Use Download CSV or Download PDF for reporting.
- For wind-profile estimates, ensure z − d > z₀ and conditions are suitable.
Example Data Table
| Scenario | Inputs | Estimated u* (m/s) |
|---|---|---|
| Light breeze over grass | U=4.0, z=10, z₀=0.03, d=0 | 0.24 |
| Moderate stress case | τ=0.60, ρ=1.20 | 0.71 |
| Eddy-covariance snapshot | u′w′=-0.09 | 0.30 |
Friction Velocity (u*) in Practice
1) What friction velocity represents
Friction velocity (u*) is a wind‑shear scaling speed that links surface stress to turbulence near the ground. It is defined from shear stress τ as u* = √(τ/ρ), where ρ is air density. Because τ is small, u* is usually much lower than the mean wind speed.
2) Why u* matters in boundary layers
In the surface layer, u* controls the strength of turbulent mixing and vertical exchange. Larger u* generally means stronger eddies, higher near‑surface fluxes, and faster dilution of pollutants. Many micrometeorology, dispersion, and deposition models use u* as a primary input.
3) Typical magnitudes and benchmarks
Over smooth water, u* may be around 0.05–0.15 m/s in light winds. Over short grass in moderate winds, values near 0.15–0.40 m/s are common. Rough urban terrain or storms can push u* toward 0.6–1.0 m/s, depending on stability.
4) From stress measurements to u*
If you have measured τ (for example, from eddy covariance), the τ/ρ method is the most direct. Use τ in pascals (Pa) and ρ in kg/m³. As a check, τ = 0.10 Pa with ρ = 1.20 kg/m³ gives u* ≈ 0.289 m/s.
5) Estimating u* from a logarithmic wind profile
Under near‑neutral conditions, the log‑law gives U(z) = (u*/κ) ln((z−d)/z₀), where κ ≈ 0.41, z is measurement height, z₀ is roughness length, and d is displacement height. Choose realistic z₀ values: very smooth surfaces are <0.01 m, while built‑up areas can exceed 0.5 m.
6) Using Reynolds stress components
With turbulent wind components, a stress‑based u* can be computed as u* = ( (u′w′)² + (v′w′)² )^(1/4). This combines along‑wind and cross‑wind momentum flux and is common in research datasets.
7) Stability and surface‑condition cautions
The log‑profile option is best for neutral or weakly stratified flow. Strong daytime convection or stable nights can violate log‑law assumptions and change u*. For tall canopies or cities, include d and keep (z−d) positive and comfortably above z₀.
8) Interpreting results and sanity checks
u* should normally be much smaller than U(z). If u* looks too large, recheck units, roughness length, and heights. For the τ method, confirm τ is in Pa; for log‑law, ensure (z−d) > z₀.
FAQs
1) Is friction velocity an actual wind speed?
No. It is a scaling speed derived from surface stress. It summarizes turbulence intensity near the surface and is usually far below the mean wind speed at the same height.
2) Which method should I choose in this calculator?
Use τ/ρ if you have shear stress and air density. Use the log‑profile option for neutral conditions with known roughness and height. Use Reynolds stress when you have u′w′ and v′w′ data.
3) What air density should I use if I don’t know it?
A common near‑sea‑level estimate is 1.20 kg/m³. Density decreases with altitude and increases in colder air. If you have temperature and pressure, use a density calculation for better accuracy.
4) What happens if displacement height is ignored?
For tall canopies or urban sites, ignoring d can bias u* because the effective wind‑profile origin shifts upward. Including d helps represent flow over vegetation or buildings more realistically.
5) Can I use the log‑law during stable nights?
Use caution. Strong stability often violates neutral log‑law assumptions and can reduce turbulence. If you must estimate u*, consider stability‑corrected similarity approaches or use direct stress measurements.
6) What units does the calculator output?
u* is reported in meters per second (m/s). Internally, τ should be in pascals (N/m²) and density in kg/m³. Heights and roughness lengths should be in meters.
7) Why do my results look too high or too low?
Most issues come from unit mix‑ups (cm vs m), unrealistic z₀, or an invalid (z−d) term. Recheck each input and compare with typical u* ranges for your terrain and wind conditions.