Detrended Structure-Function in Fully Developed Turbulence

A detrended structure-function (DSF) method is proposed to extract scaling exponent by constraining the influence of large-scale structures. This is accomplished by removing a $q$th-order polynomial fitting within a window size $\tau$ before calculating the velocity increment. By doing so, the scale larger than $\tau$, i.e., $r\ge \tau$, is expected to be removed. The detrending process is equivalent to a high-pass filter. We first validate the DSF by using synthesized fractional Brownian motion for mono-fractal process and lognormal process for multifractal random walk process. When applying the DSF to a turbulent velocity obtained from a high Reynolds number wind tunnel experiment with $Re_{\lambda}\simeq 720$, the third-order DSF demonstrates a clear inertial range with $\mathcal{B}_3(\tau)\sim \tau$ on the range $0.001<\tau<0.1\,$sec, corresponding to a frequency range $10