Another look at rotational sampling of atmospheric turbulence with focus on the transference of energy from different frequency intervals of the Eulerian spectrum to the rotational spectrum

Abstract

Rotational sampling is of paramount importance in the loading of wind turbine blades due to wind turbulence We revisit the classical model of rotational sampling of the longitudinal component of a statistically stationary, homogeneous, isotropic turbulent velocity field experienced by a point rotating in a plane perpendicular to the mean velocity. As is well known, this is the simplest frame work, since it allows to determine the non-dimensional rotational spectrum in terms of the non-dimensional frequency and only two more non dimensional parameters, the non dimensional radial position of the rotating point and the non dimensional rotational speed. We systematize the parametric analysis of the rotational spectrum proposed independently by Connel in 1981 and Kristensen et al. in 1982, in terms of the aforementioned two non dimensional parameters. We propose a quantification of the transference of energy from different frequency intervals of the Eulerian spectrum to the rotational spectrum. We verify that regions of the Eulerian spectrum corresponding to different frequency intervals are transformed into contributions to the rotational spectrum that expand to the whole frequency range without preserving the variance. Certain frequency intervals of the Eulerian spectrum can lead to negative contributions to the rotational spectrum along certain frequency ranges.