Fractal scaling of the turbulence interface in gravity currents

Abstract

It was previously observed by Krug et al. (J. Fluid Mech., vol. 765, 2015, pp. 303-324) that the surface area Aη 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 Rig. Our results indicate that the reduction of Aη is caused by a decrease of the fractal scaling exponent β, 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 lSk = k1/2/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 Rig, we are able to model the Rig dependence of β in good agreement with the data.