Investigation of the fluctuating velocity in a single-cell tornado-like vortex based on coherent structure extraction

Fluctuating velocity plays an essential role in tornadic winds and the induced transient loads, while its characteristics are rarely considered in existing tornado models. Based on the coherent structure extraction technology, this study investigates the characteristics of the fluctuating velocity in a single-cell tornado-like vortex (TLV) and proposes a unified wind spectrum formula accordingly. First, the performance of proper orthogonal decomposition (POD) and dynamic mode decomposition is compared and validated using synthetic vortices. A single-cell TLV is then generated by large eddy simulation. The relationship between the fluctuating velocity and the coherent structures is analyzed. Finally, a wind spectrum formula is obtained from the fluctuating velocity reconstructed by the first two POD modes that are almost unchanged with height. Thus, it is a unified formula suitable for different heights. The results show that at a lower height in the single-cell TLV, more than 90% of the velocity fluctuation is induced by vortex wandering and size variation. The first two POD modes can accurately reconstruct the fluctuating velocity with an error of less than 8%. The power spectral density of the reconstructed fluctuating velocity agrees well with the Kaimal wind spectrum in the low-frequency subrange and the proposed formula in the high-frequency subrange.