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.

Figures (22)

• Figure 1: Density fluctuations in the Poiseuille flow in the absence of the van der Waals effect. Left -- starting time, right -- at 0.05 seconds.
• Figure 2: Density fluctuations in the Poiseuille flow in the presence of the van der Waals effect. Upper-left -- at 0.01 seconds, upper-right -- at 0.02 seconds, lower-left -- at 0.03 seconds, lower-right -- at 0.05 seconds.
• Figure 3: Divergence fluctuations in the Poiseuille flow in the presence of the van der Waals effect. Upper-left -- at 0.01 seconds, upper-right -- at 0.02 seconds, lower-left -- at 0.03 seconds, lower-right -- at 0.05 seconds.
• Figure 4: Vorticity fluctuations in the Poiseuille flow in the presence of the van der Waals effect. Upper-left -- at 0.01 seconds, upper-right -- at 0.02 seconds, lower-left -- at 0.03 seconds, lower-right -- at 0.05 seconds.
• Figure 5: Tracer streaks in the Poiseuille flow in the presence of the van der Waals effect. Left -- starting time, right -- at 0.05 seconds.