Inertial range scaling of the scalar flux spectrum in two-dimensional turbulence

TL;DR

This paper investigates the inertial range scaling of the scalar flux spectrum in two-dimensional isotropic turbulence with a uniform scalar gradient, using dimensional analysis and numerical simulations to validate predictions.

Contribution

It provides new dimensional scaling predictions for the scalar flux spectrum in 2D turbulence and confirms them through direct numerical simulations.

Findings

Good agreement between theoretical scaling and numerical results

Scaling laws differ in inverse cascade and enstrophy cascade ranges

Validates dimensional arguments for scalar flux spectrum in 2D turbulence

Abstract

Two-dimensional statistically stationary isotropic turbulence with an imposed uniform scalar gradient is investigated. Dimensional arguments are presented to predict the inertial range scaling of the turbulent scalar flux spectrum in both the inverse cascade range and the enstrophy cascade range for small and unity Schmidt numbers. The scaling predictions are checked by direct numerical simulations and good agreement is observed.