Power spectra via the van der Waals effect in the two-dimensional Poiseuille and Couette flow

TL;DR

This study numerically investigates the spectral properties of two-dimensional laminar flows with van der Waals effects, revealing that density and velocity divergence primarily influence the power spectra, independent of vorticity.

Contribution

It demonstrates that the power spectra dynamics in such flows are mainly governed by density and velocity divergence, not vorticity, providing new insights into flow physics with van der Waals effects.

Findings

Power spectra decay observed in small flow fluctuations.

Flow remains laminar despite complex spectral dynamics.

Vorticity's role is secondary to density and velocity divergence.

Abstract

We numerically simulate the two-dimensional inertial flow with the van der Waals effect in a straight periodic channel around the Poiseuille and Couette stationary states. Even though the flow remains laminar macroscopically, we observe complex dynamics and power decay of the Fourier spectra of small fluctuations of the density, velocity divergence, vorticity and kinetic energy of the flow near their respective stationary background states. Remarkably, pinning the vorticity to its background state, and leaving only the density and velocity divergence as the variables, results in the dynamics and power decay of the Fourier spectra qualitatively similar to those of the full system. This strongly indicates that the underlying physics of the power spectra reside primarily in the density and velocity divergence variables, and are not directly related to the vorticity of the flow.