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

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.