Analyzing, modelling, and simulating nonstationary thunderstorm winds in two horizontal orthogonal directions at a point in space

Thunderstorm winds in the horizontal plane are time-varying, resulting in the time-varying alongwind direction and mean wind speed in the alongwind direction. The fluctuating winds in the alongwind and crosswind directions are time-varying as well. The characterization of the mean and fluctuating winds for their simulation in two horizontal orthogonal directions are incomplete or unavailable in the literature. In the present study, we analyze and model the thunderstorm winds with respect to their time- and directional-variation of the alongwind speed and direction, as well as the fluctuating wind components in the alongwind and crosswind directions. For the analysis, we use the continuous harmonic wavelet. We show that the power spectral density (PSD) functions of the fluctuating winds depend on the time-varying mean wind speed. Based on the time-frequency spectral analysis, we propose the PSD functions and lagged coherence functions for the fluctuating thunderstorm winds in the alongwind and crosswind directions. We also present new empirical models for the time-varying alongwind direction and mean wind speed in the alongwind direction. Finally, we suggest the steps to simulate the wind speed in the alongwind and crosswind directions with time-varying directions and provide numerical examples to illustrate the effectiveness of our proposed models.