Turbulence compressibility reduction with helicity

TL;DR

This study numerically investigates how helicity influences the compressibility of isotropic turbulence, revealing power-law behaviors in spectral ratios and potential applications in flow control and noise reduction.

Contribution

It provides new insights into the spectral effects of helicity on turbulence compressibility using numerical simulations with a finite difference scheme.

Findings

Spectral ratios follow power laws at large wavenumbers.

A consistent difference of 11/15 in spectral exponents between helical and nonhelical turbulence.

Implications for flow control and turbulence noise reduction discussed.

Abstract

Numerical test of isotropic turbulence compressibility reduction with helicity in a cyclic box is performed. The ratios of compressibility-relevant-mode spectra over those of kinetic energy present power laws at large wavenumbers in the dissipation range, indicating a common difference of $11/15$ in the exponents of the algebraic prefactor of the nonhelical power spectra over those of helical ones. Our results being not derived from the shapes of the spectra themselves, the implied information about the helicity effect on the complex singularities of the discretized dynamical system can still be of reasonable value for insights of the Navier-Stokes equation, although the high-order finite difference scheme used for computation may not be as accurate in dissipation range as the state-of-the-art of incompressible turbulence with pseudo-spectral method. Possible applications in controlling flows, for the purposes of, say, decreasing turbulence noise, are also discussed according to the spectral fluctuations.