Accuracy wind set-up formula for irregularly shaped lakes with a strong varying water depth

Abstract

This document includes a survey whether the wind set-up formula is valid and accurate in case of irregularly shaped lakes with a strong varying water depth. The formula is designed for a pure theoretical situation, the question is whether the formula is valid in situations that differ a lot from the theoretical one. The research is carried out with data (wind speed, wind direction and water depth), from the Grevelingenmeer (Netherlands, province Zeeland). First several assumptions are made with respect to the relevant wind directions and speeds for the different measure stations. Wind set-up won’t be generated when the wind speed is very low. The relevant wind speeds are the mean values per hour above 13 meter per second. The relevancy of the wind directions does depend on the location of the measure station. The mean values of all the data are calculated in order to correct for the setting time of the lake, to arrive at a more or less stationary situation. The fetch is defined as the length of the lake parallel to the wind direction. It is not easy to model the water depth, shallow water does give a higher value for wind set-up in comparison to deep water. However, the water depth of the Grevelingenmeer is strongly varying, so an assumption had to be made. The mean value of the water depth is assumed, in order to balance the varying base of the lake. It is a rough assumption, but possible errors in this approximation are compensated by the friction coefficient kappa. The conclusion of the main research is that the wind set-up formula is valid and relatively accurate. The order of magnitude of the wind set-up is 10 centimeter, the standard deviation is in the order of 1 centimeter. The dispersion of the wind set-up is independent of the wind speed. Using the original wind set-up formula gives the mean value of the wind set-up. In order to compute the design value of the wind set-up, depending on the allowed probability of exceedance, there has to be added an additional value of wind set-up. So, the dispersion is not caused by a scatter of kappa.