# relation of vortex street structure to Stroudhal & Reynolds Numbers

While on an expedition to a lake, it was noticed that the wind speeds gusted violently in seemingly periodic wakes and the proposed explanation was Von Karman vortex shedding off of nearby mountains that the lake was in the lee of.

Therefore I am attempting to calculate the amount of influence that a Karman vortex street would have on some wind speed readings obtained during that time in order to see if I can detect the influence in wind speed readings collected during that time that the observation of intense gusts was made.

From some lengthy research into this topic I have found a cadre of equations which I think give me the desired results of the frequency and maximum wind speed within the Karman vortexes all based solely upon wind speed readings from the lake.I however have come across an issue in the calculations which reduces all parameters to either constants or to be exactly directly proportional to the presumed oncoming wind speed, a highly unlikely and illogical occurrence.

The problem rests in the fact that the laboratory calculated kinematic viscosity of air doesn't hold up to large scale observations of vortex street formation, thus necessitation a new parameter as stated in this article. This new parameter is β and is defined as $$β=St/Re$$ with $Re$ being the Reynolds number and $St$ being the Strouhal number.

Due to the fact that I don't have the shedding frequency but need to calculate it, I cannot calculate St except through the formula $$St = .212(1-\frac{21.2}{Re})$$ as found in this article. However, doing this and substituting into the parameter of $β$ yields a relationship between the constant $β$ and $Re$, which makes $Re$ constant and in turn $St$ constant as $St$ is defined in terms of $Re$ only.

This causes all the parameters that I have to be either linear with respect to any oncoming flow velocity or constant, something obviously wrong. Although I have everything that I need after this point in order to obtain maximum wind speed and shedding frequency, this initial step has stopped me dead in my tracks due to the fact that every author whom I have seen on this subject had a picture to work with to calculate the distances between the vortices and use that and an assumed wind speed to calculate shedding frequency, plug that in to find Strouhal number and then use the $β$ parameter to calculate Reynolds number.

All those working in lab tests similarly calculated shedding frequency and recorded it by video taping or counting the eddy shedding process. I, however, only have the wind speed to work with and so have problems by reducing out too many variables.

My question therefore becomes how do I define a either a variable $β$ parameter or redefine either my $St$ or $Re$ number so that one can be calculated independently with the limited information at my disposal of only the wind speeds and the ability to assume other parameters such as landmass dimensions etc.