Lagrangian modeling of a non-homogeneous turbulent shear flow: Molding homogeneous and isotropic trajectories into a jet

TL;DR

This paper introduces an efficient Lagrangian model that transforms homogeneous turbulence data into accurate predictions of non-homogeneous turbulent jet statistics, capturing complex phenomena like intermittency.

Contribution

The novel model effectively maps homogeneous turbulence signals into inhomogeneous jet trajectories, enabling high-accuracy predictions of complex turbulent flow statistics.

Findings

Model achieves remarkable agreement with experimental data across all scales.

Accurately captures intermittency phenomena in inhomogeneous turbulence.

Simple transformation allows extensions to other complex flows.

Abstract

Turbulence is prevalent in nature and industry, from large-scale wave dynamics to small-scale combustion nozzle sprays. In addition to the multi-scale nonlinear complexity and both randomness and coherent structures in its dynamics, practical turbulence is often non-homogeneous and anisotropic, leading to great modeling challenges. In this letter, an efficient model is proposed to predict turbulent jet statistics with high accuracy. The model leverages detailed knowledge of readily available velocity signals from idealized homogeneous turbulence and transforms them into Lagrangian trajectories of a turbulent jet. The resulting spatio-temporal statistics are compared against experimental jet data showing remarkable agreement at all scales. In particular the intermittency phenomenon is accurately mapped by the model to this inhomogeneous situation, as observed by higher-order moments and velocity increment probability density functions. Crucial to the advancement of turbulence modeling, the transformation is simple to implement, with possible extensions to other inhomogeneous flows such as wind turbine wakes and canopy flows, to name a few.