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 stream..