Detection of the irrotational boundary using machine learning methods

Abstract

Four machine learning methods, i.e., self-organizing map (SOM), Gaussian mixture model (GMM), eXtreme gradient boosting (XGBoost), and contrastive learning (CL), are used to detect the irrotational boundary (IB), which represents the outer edge of the turbulent and non-turbulent interface layer. To accurately evaluate the detection methods, high-resolution databases from direct numerical simulations of a temporally evolving turbulent plane jet are used. It is found that except for the SOM method, the general contour of the IB appears to be effectively captured using the GMM, XGBoost, and CL methods, which indicate the turbulent and non-turbulent regions can be roughly recognized. Furthermore, the intrinsic features of the detected IB using the GMM, XGBoost, and the CL methods are quantitatively evaluated. Unlike the conventional vorticity norm method, the three machine learning methods do not rely on a single threshold of vorticity magnitude to separate the turbulent and non-turbulent regions. A small part of the detected IB using the three machine learning methods is characterized by the rotational motions, which are expected to be only found inside the turbulent sublayer and turbulent core region. Compared to the vorticity norm and XGBoost methods, the fractal dimensions of the IB detected by the GMM and CL methods are relatively small, which are related to the missing detection of some highly contorted elements. With the three machine learning methods, a large part of the detected IB is characterized by a convex shape, similarly as with the vorticity norm. However, the probability density function profiles of the local curvature of the detected IB differ greatly between the three machine learning methods and the vorticity norm. A mild variation of the mean conditional distributions of the vorticity magnitude can be observed across the detected IB by the three machine learning methods. This study first implies that using the machine learning methods the turbulent and non-turbulent regions can be roughly distinguished, but it is still challenging to obtain the intrinsic features of the detected IB.