Turbulent windsTurbulent wind for tropical cyclonesTropical cyclone and thunderstormThunderstorm eventsPower spectral density function areTurbulent wind frequentlyTropical cyclone modeledThunderstorm as a uniformly modulated evolutionary process with time-invariant or time-varying mean wind speed. We argue that the use of uniform modulation is insufficient, and the amplitude- and frequency-modulated evolutionary stochastic process should be considered for such turbulent windsTurbulent wind. We provide some theoretical basis for such a consideration. The theoretical derivation is based on the concept of time transformation and the instantaneous power spectrumSpectrum representation and amplitude and frequency modulation. We also give the time–frequency decompositionTime-frequency decomposition results for the recorded wind from tropical cyclonesTropical cyclone and thunderstormThunderstorm events. These results are used to further support the argument that the fluctuating wind component for such wind events should be modeled as the amplitude- and frequency-modulated evolutionary stochastic process. Furthermore, we discuss whether the wind time history for the fluctuating wind should be modeled as Gaussian or non-Gaussian and its implications for its simulation.