Non-equilibrium Turbulent/non Turbulent Interface velocity scaling in turbulent planar jets

We investigate the turbulent/non-turbulent interface (TNTI) of a turbulent planar jet using stereo-PIV and HWA. Following Zhou \& Vassilicos (JFM 2017) we derive an expression for the entrainment velocity $\frac{d}{dx} \langle \int_{{A}_{T}}udydz\rangle =$$\mathcal{L}$ $v_{n} $, where $x$ is the streamwise coordinate, $u$ is the streamwise velocity, $\mathcal{A}_{T}$ is the area of the turbulent region in a plane orthogonal to the mean flow, and $\mathcal{L}$ is the length of the TNTI in this plane. $\mathcal{L}$ can be expressed as $\mathcal{L}$$\sim\delta(\eta_I/\delta)^{1-D}$, where $\delta(x)$ is the jet width at $x$, $\eta_I\sim\nu/v_n$ (Corrsin 1955) is a characteristic interface thickness and $D$ is the line interface's fractal dimension. Non-equilibrium dissipation self-similar jet theory (Cafiero \& Vassilicos PRSA 2019) predicts that $v_n/v_{\eta}$ (where $v_{\eta}$ is the Kolmogorov velocity) is a decreasing function of $x$, which is at odds with the classical Corrsin scaling $v_n \sim v_{\eta}$. Our experimental results confirm Corrsin's $\eta_I\sim \nu/v_n$ but also show that $v_n/v_{\eta}$ is indeed a decreasing function of $x$. Our measurements support the scaling $v_n \sim v_{\lambda}$ (=\nu/\lambda$, being $\lambda$ the Taylor scale) predicted by our theory.