Effect of Transport Noise on Kelvin-Helmholtz instability

Abstract

The effect of transport noise on a 2D fluid may depend on the space-scale of the noise. We investigate numerically the dissipation properties of very small-scale transport noise. As a test problem we consider the Kelvin-Helmholtz instability and we compare the inviscid case, the viscous one, both without noise, and the inviscid case perturbed by transport noise. We observe a partial similarity with the viscous case, namely a delay of the instability.

Figures (9)

• Figure 1: $\nu=0$. (a): initial configuration, approximating a shear flow fluid dynamics; (b): iteration $t=50$, formation of macroscopic vortex structures; (c): iteration $t=100$, perfectly developed macroscopic vortex structures.
• Figure 2: $\nu>0$. (a): iteration $t=50$, preservation of strip profile; (b): iteration $t=100$, development of instability, formation of macroscopic vortex-like structures.
• Figure 3: environmental noise. (a): iteration $t=50$, diffusive behaviour of strip profile; (b): iteration $t=100$, degradation of profile, formation of macroscopic structures due to the stretch.
• Figure 4: environmental noise case, iteration $t=50$, diffusion of the strip is present for a short time with preserved configuration.
• Figure 5: environmental noise case, iteration $t=50$, low density ratio between fixed vortices and point vortices showing emergence of medium-scale structures.