Fractal characteristics of turbulent–non-turbulent interface in supersonic turbulent boundary layers

Abstract

The turbulent–non-turbulent interface (TNTI) of supersonic turbulent boundary layers is a fundamental but relatively unexplored physics problem. In this study, we present experimental results from fractal analysis on the TNTI of supersonic turbulent boundary layers, and test the applicability of the additive law for these flows. By applying the nanoparticle-tracer planar laser scattering (NPLS) technique in a supersonic wind tunnel, we obtain data covering nearly three decades in scale. The box-counting results indicate that the TNTI of supersonic turbulent boundary layers is a self-similar fractal with a fractal dimension of 2.31. By comparing data sets acquired from two orthogonal planes, we find that the scaling exponent does not depend on direction, consistent with the validity of the additive law for the TNTI of turbulent boundary layers in a scale range with the large-scale limit not exceeding approximately $0.05\unicode[STIX]{x1D6FF}$.

Reynolds number dependence of the turbulent/non-turbulent interface in temporally developing turbulent boundary layers

“…As the Reynolds number increases, D f also increases. These values of the fractal dimension are slightly smaller than D f ≈ 7/3 found in previous studies (de Zhuang et al 2018) for Reynolds numbers higher than in the present DNS, namely Re θ 13 000. However, Wu et al (2020) have reported D f ≈ 2.2 at a low Reynolds number (Re τ = 483), and Borrell & Jiménez (2016) also showed that the fractal dimension is approximately 2.1-2.2 for Re τ = 1000-2000.…”

“…2013; Zhuang et al. 2018) for Reynolds numbers higher than in the present DNS, namely . However, Wu et al.…”

The effect of the geometric features of the turbulent/non-turbulent interface on the entrainment of a passive scalar into a jet

“…According to Mandelbrot, 64 this results in a 2D fractal dimension of D 2 = 1.32 ± 0.01, which resides well inside the accepted range of D 2 = 1.3-1.4, as previously found by recent studies. 22,36,37,39,40…”

Experimental investigation of supersonic boundary-layer tripping with a spanwise pulsed spark discharge array

“…By recording the scattered light intensity, which is in proportion to the local particle concentration, NPLS to some extent reflects the density variation of the flow field (Zhao et al 2009) and is specialized to the visualization of fine flow structures. Due to its noticeable advantages of high spatial-temporal resolution and high signal-to-noise ratio, the NPLS method has been successfully applied by several super/hypersonic researchers (Zhuang et al 2018a(Zhuang et al , 2019 in recent years, and its working principle and technical validation have been demonstrated in detail by Zhao et al (2009).…”