How much does wind speed change in an area/over time?

Question

I am currently planning to implement wind force into a physics simulation and have a hard time figuring out how to best approach the problem. My main concern here is how consistent wind speed is. How much does wind speed normally variate over a distance of 100 meters high above ground for example? What factors cause such variation? How could this fluctuation be represented in a map? Are these changes between two points with gradual change or are they more abrupt? Is there a reasonably simple way of guessing the windspeed at a predetermined point in certain environments like a forest or an urban area? How about wind speed over time? How significant are they and can they be predetermined in any way? Is there any rythm to such changes to at least make realistic randomization possible? I want to make the simulation at least somewhat more precise than just using a static speed for an entire map, but have no idea how to go about it.

It would also be great if anyone could link me the necessary reference material on the subject I am seemingly unable to find.

Answer 1

There's a lot of questions here, I'd start by saying that modelling wind is hard. You're dealing with a turbulent flow across length scales varying from potentially tens of kilometres down to the microscale. The best modelling approach will depend on the length scales and time period you're interested in.

One approach is to ignore the fluctuating component of the velocity and just use an average velocity profile. This is what is commonly used for generating pressure coefficients around a building for building services modelling for example. We require a measured or estimated wind speed from the site, typically taken at 10m in open terrain. This is then fed into the formula

$$ U_H = U_{met}\left(\frac{\delta_{met}}{H_{met}}\right)^{a_{met}}\left(\frac{H}{\delta}\right)^a, $$

where $U_{met}$ is the measured velocity at height $H_{met}$ and $U_H$ is the velocity we want to find at height $H$. The exponents $a_{met}$ and $a$ are empirical constants associated with the environment of the measured and modelled data and $\delta_{met}$ and $\delta$ are the boundary layer thicknesses of the measured and modelled data. Values for $a$ and $\delta$ for different environments, such as open ground, wooded and urban areas and cities can be found in ASHRAE Fundamentals. This method still allows for time-dependent behaviour to be modelled, but hour by hour rather than second by second. It also can't account for the local variations due to a complex local topography.

If a higher temporal resolution is required than you'll need to use Computational Fluid Dynamics. Direct Numerical Simulation is computationally very expensive because the Reynolds numbers could of the order of $10^5$ for the flow around a tall building, therefore Large Eddy Simulation is typically used. This paper gives a good summary of the challenges of modelling the flow around buildings, many of which are shared with modelling wind in general.