An identification of coherent structures in an inhomogeneous turbulence

This study proposes a proper scaling of a vortex indicator for practical identification of coherent structures (CS) from an inhomogeneous wall turbulence at the Reynolds numbers of $Re_{\tau}=180$ and $400$. The Laplacian of the pressure, $\Theta$, is scaled by its time-space average $\Theta_{ave}$ and root-mean-square value $\Theta_{rms}$ to obtain a proper scaling for effective identification of CS, $\hat\Theta=\left(\Theta-\Theta_{ave}\right)/\Theta_{rms}$. Numerical turbulent flow realizations with a wall and a gas-liquid interface obtained by a direct numerical simulation technique are employed to confirm suitability of the proposed scaling. The results of this study exhibit that the probability density function (PDF) of $\hat\Theta$ is very similar without respect to the distance from the wall, unlike PDF of unscaled $\Theta$. Because of this statistical similarity, identification of CS based on $\hat\Theta$ is shown advantageous to separate all the essential CS from disorganized turbulent background using a unique threshold level, especially in the region adjacent to the wall and the gas-liquid interface. Several turbulent flow signatures at the gas-liquid interface suggest that a threshold of $1\le\Theta\le 2$ is preferable to identify all the essential CS in the whole of the turbulent flow domain, without ``contamination'' caused by misidentification of meaningless structures.