The logarithmic wind profile describes how wind speed increases with height above the ground in the atmospheric boundary layer, specifically following a logarithmic function. This profile indicates that at lower altitudes, wind speeds are significantly affected by surface roughness and stability, while at higher altitudes, the influence of these factors diminishes, leading to a more uniform increase in wind speed. Understanding this profile is essential for analyzing the structure of the planetary boundary layer and applying Monin-Obukhov similarity theory in meteorological studies.
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The logarithmic wind profile can be expressed mathematically as $$U(z) = \frac{u_*}{\kappa} \ln \left(\frac{z}{z_0}\right)$$, where $$U(z)$$ is the wind speed at height $$z$$, $$u_*$$ is the friction velocity, $$\kappa$$ is the von Kármán constant, and $$z_0$$ is the roughness length.
The profile shows that wind speed increases logarithmically with height due to frictional forces acting on airflow near the surface.
Roughness length ($$z_0$$) is influenced by surface features like trees and buildings, which can modify local wind speeds.
The logarithmic wind profile applies best under neutral stability conditions; deviations from this profile occur during stable or unstable atmospheric conditions.
Monin-Obukhov similarity theory extends the logarithmic wind profile by incorporating stability effects, allowing for predictions of wind profiles under different thermal stratifications.
Review Questions
How does the logarithmic wind profile relate to the characteristics of the planetary boundary layer?
The logarithmic wind profile is fundamental to understanding the dynamics within the planetary boundary layer because it illustrates how wind speed changes with height due to surface roughness and turbulence. In this layer, frictional forces from ground surfaces play a significant role in shaping wind behavior. As you move higher up in the boundary layer, these effects diminish, resulting in a more uniform increase in wind speed that is captured by the logarithmic function.
Discuss how Monin-Obukhov similarity theory builds upon the concept of the logarithmic wind profile and its implications for atmospheric research.
Monin-Obukhov similarity theory builds upon the logarithmic wind profile by integrating stability considerations into its framework. While the logarithmic profile primarily addresses neutral conditions, Monin-Obukhov similarity accounts for stable and unstable atmospheric stratifications. This allows researchers to model how temperature gradients and atmospheric stability influence wind profiles and turbulence characteristics, providing a more comprehensive understanding of atmospheric processes.
Evaluate how changes in surface roughness impact the logarithmic wind profile and what that means for local weather forecasting.
Changes in surface roughness significantly affect the logarithmic wind profile by altering the roughness length ($$z_0$$), which modifies how quickly wind speeds increase with height. For example, urban areas with tall buildings will have different roughness characteristics than open fields. Understanding these changes is critical for local weather forecasting as it can influence predictions of wind patterns and turbulence, affecting everything from pollution dispersion to storm development.
Related terms
Planetary Boundary Layer: The lowest part of the atmosphere, typically extending from the surface to a height of about 1-2 kilometers, where turbulent mixing occurs and surface influences are significant.
Shear Stress: The force per unit area exerted by the wind on the surface, which is crucial for determining how wind speed varies with height.