# Solenoidal scaling laws for compressible mixing

## TL;DR

This paper investigates how passive scalar mixing in compressible turbulence deviates from classical scaling laws, revealing that solenoidal components follow incompressible-like spectra despite significant dilatational effects.

## Contribution

It demonstrates that solenoidal spectra in compressible turbulence can exhibit incompressible scaling laws when analyzed appropriately, even with strong dilatational influences.

## Key findings

- Solenoidal energy spectrum follows incompressible scaling.
- Passive scalar spectrum assumes incompressible form.
- Scalar gradient aligns with the most compressive eigenvalue.

## Abstract

Mixing of passive scalars in compressible turbulence does not obey the same classical Reynolds number scaling as its incompressible counterpart. We first show from a large database of direct numerical simulations that even the solenoidal part of the velocity field fails to follow the classical incompressible scaling when the forcing includes a substantial dilatational component. Though the dilatational effects on the flow remain significant, our main results are that both the solenoidal energy spectrum and the passive scalar spectrum scale assume incompressible forms, and that the scalar gradient aligns with the most compressive eigenvalue of the solenoidal part, provided that only the solenoidal components are used for scaling in a consistent manner. Minor modifications to this statement are also pointed out.