A sufficient condition for Gaussian departure in turbulence

TL;DR

This paper investigates how a gradient in turbulent kinetic energy influences turbulence properties, showing that such a gradient can induce intermittency and deviations from Gaussian behavior, with implications for understanding turbulence in inhomogeneous flows.

Contribution

The study demonstrates that a turbulent energy gradient alone can cause Gaussian departure and intermittency, providing a minimal condition for non-Gaussian turbulence behavior.

Findings

Turbulent energy gradients induce intermittency.

Pressure transport is significant during mixing.

Maximum turbulent penetration reaches 1.2 times the mixing layer width.

Abstract

The interaction of two isotropic turbulent fields of equal integral scale but different kinetic energy generates the simplest kind of inhomogeneous turbulent field. In this paper we present a numerical experiment where two time decaying isotropic fields of kinetic energies $E_1$ and $E_2$ initially match over a narrow region. Within this region the kinetic energy varies as a hyperbolic tangent. The following temporal evolution produces a shearless mixing. The anisotropy and intermittency of velocity and velocity derivative statistics is observed. In particular the asymptotic behavior in time and as a function of the energy ratio $E_1/E_2 \to \infty$ is discussed. This limit corresponds to the maximum observable turbulent energy gradient for a given $E_1$ and is obtained through the limit $E_2 \to 0$. A field with $E_1/E_2 \to \infty$ represents a mixing which could be observed near a surface subject to a very small velocity gradient separating two turbulent fields, one of which is nearly quiescent. In this condition the turbulent penetration is maximum and reaches a value equal to 1.2 times the nominal mixing layer width. The experiment shows that the presence of a turbulent energy gradient is sufficient for the appearance of intermittency and that during the mixing process the pressure transport is not negligible with respect to the turbulent velocity transport. These findings may open the way to the hypothesis that the presence of a gradient of turbulent energy is the minimal requirement for Gaussian departure in turbulence.