Fractal scaling of the turbulence interface in gravity currents

Dominik Krug, Markus Holzner, Ivan Marusic, Maarten van Reeuwijk

Journal of Fluid Mechanics · 2017

Abstract

It was previously observed by Krug et al. ( J. Fluid Mech. , vol. 765, 2015, pp. 303–324) that the surface area $A_{\unicode[STIX]{x1D702}}$ of the turbulent/non-turbulent interface (TNTI) in gravity currents decreases with increasing stratification, significantly reducing the entrainment rate. Here, we consider the multiscale properties of this effect using direct numerical simulations of temporal gravity currents with different gradient Richardson numbers $Ri_{g}$ . Our results indicate that the reduction of $A_{\unicode[STIX]{x1D702}}$ is caused by a decrease of the fractal scaling exponent $\unicode[STIX]{x1D6FD}$ , while the scaling range remains largely unaffected. We further find that convolutions of the TNTI are characterized by different length scales in the streamwise and wall-normal directions, namely the integral scale $h$ and the shear scale $l_{Sk}=k^{1/2}/S$ (formed using the mean shear $S$ and the turbulent kinetic energy $k$ ) respectively. By recognizing that the anisotropy implied by the different scaling relations increases with increasing $Ri_{g}$ , we are able to model the $Ri_{g}$ dependence of $\unicode[STIX]{x1D6FD}$ in good agreement with the data.