Interpretation and prediction of the three-dimensional coherent structure and its dynamics of tornado-like vortex via delayed proper orthogonal decomposition

This study proposes a three-dimensional mode-based surrogate framework to predict the tornado-like vortex (TLV) derived from the fuzzy neural network and delayed proper orthogonal decomposition method. First, near-break-down TLV is simulated via large-eddy simulation, and its mean, fluctuating and statistical flow feature is analyzed. Then, three-dimensional spatiotemporal features of coherent structure are extracted and interpreted. Next, the capability of the proposed framework to predict the future state of an unsteady chaotic TLV flow field is systematically evaluated, including the spatiotemporal variation of velocity, pressure, and vorticities as well as flow statistics. Finally, parametric analysis is also conducted to investigate the influence of three key parameters [i.e., Fuzzy rules of the state network or output network (K1 or K2), time delayed embedding number (d)] contained in the framework and the step number of forward prediction (K) on the predicted accuracy. Results show that for near-break-down TLV, vortex wandering effect largely affects its dynamical feature, and its three-dimensional characteristics are distinct, exhibiting the essence of the swirling jet flow. 3D mode-based surrogate model can correctly predict the tornado-like vortex with a relative error of less than 2% for the radial, tangential, and vertical velocity component. It is found that fuzzy rules and time-delayed embedding number has great effect on prediction accuracy. Thus, to achieve optimal predicting effect, it is suggested that d is taken as 8, K1, and K2 are taken as 18, and when making multi-step predictions, the largest K should not exceed 7.