Determining the Velocity Fine Structure by a Laser Anemometer in VAD operation

The theoretical basis for determining the dissipation ε, by measuring the velocity structure function with a CW-laser anemometer has been derived in the case of calm wind conditions. If there is a well defined mean wind speed the structure function can be obtained by having the laser beam pointing in one direction and measure a time series of the Doppler wind velocity component along the beam. Applying Taylor’s hypothesis the structure function can be calculated. This technique was discussed by Kristensen et al. (2011). Taylor’s hypothesis cannot, however, be used if there is no mean wind.Then it is necessary to “create” a mean wind by turning the laser beam. Since the instrument is not moved the beam will describe a cone which could be a VAD-scanning. In any case the measured velocity components will not be parallel and this implies that the measured structure function will contain a term which is proportional to the total variance. The theoretical expression for the line-filtered structure function is derived in two equivalent ways, one in physical space and one in wave-number space, of which the last can be reliably evaluated by numerical integration. Also a practical approximate equation, derived in the physical space, is presented.