Atmospheric Boundary Layer Profile Calculator

The Logarithmic Law (Log Law) is the fundamental model, derived from the theory of turbulent flow over a rough surface. It states that wind speed increases logarithmically with height.

Where:
$U(z)$ = Wind speed at height $z$ (m/s).
$u_*$ = Friction velocity (m/s), a scaling speed for turbulence.
$\kappa \approx 0.41$ = von Kármán constant.
$z_0$ = Roughness length (m), a measure of terrain roughness. It's the height where the wind speed theoretically becomes zero.

The Power Law is a simpler, empirical alternative often used in older building codes. It assumes wind speed increases as a power of height.

Where:
$U_{ref}$ = Known wind speed at a reference height $z_{ref}$ (m/s).
$\alpha$ = Hellman exponent, which depends on terrain roughness. Over open water, $\alpha$ is low (~0.1); over cities, it's high (~0.3).
The exponent $\alpha$ is not a fundamental property like $z_0$, but a convenient fitting parameter.

Wind Turbine Siting and Energy Yield: This is the primary use. Engineers use these profiles to predict the wind speed at a turbine's hub height (often 80-120m) based on measurements from a shorter meteorological mast. A small error in the profile can lead to a multi-million dollar mistake in estimated energy production.

Structural Wind Load Design: Skyscrapers, bridges, and stadiums must be designed for wind loads that vary with height. Building codes specify wind profiles (often using the Power Law) to determine the pressure distribution up the face of a tall building.

CFD Simulation Inflow Conditions: When simulating airflow around a new building or an entire city district, you must define realistic wind entering the simulation domain. The ABL profile, defined by $U_{ref}$ and $z_0$, provides this crucial "inflow boundary condition."

Pollution Dispersion Modeling: How far and fast pollutants from a factory stack spread depends on the wind speed and turbulence in the boundary layer. Accurate profiles are essential for environmental impact assessments and emergency planning.

When you start using this tool, there are a few key points to keep in mind. First, selecting the "Surface Roughness" is critical to the simulation. For instance, even within the same "urban area," wind flow patterns differ completely between low-rise residential districts and areas densely packed with skyscrapers. The tool's classifications are only representative values, so make a habit of carefully choosing the closest class based on actual site photos or land-use data. An incorrect choice can lead to wind speeds significantly lower (or higher) than expected, potentially ruining your design.

Next, understand that "the power law exponent α is not a universal constant". This tool uses α values converted from the log law, but in reality, this α varies slightly depending on the height range. For example, approximating the range from 10m to 100m above ground with a single α can lead to significant errors, especially when surface roughness is high. This is precisely why building codes often "specify different α values for different vertical segments." Before directly applying the tool's results to your design, always verify the definitions in the applicable standards or guidelines.

Finally, remember that "this profile represents the 'neutral' state, a specific condition". The real atmosphere becomes unstable due to solar heating during the day or forms stable layers at night. For example, on a clear afternoon, thermal convection can cause the low-altitude wind speed profile to deviate from the log law. This tool calculates the fundamental "reference state." In practice, you must separately account for the effects of atmospheric stability due to season and time of day.