The significance of two-way coupling in two-dimensional, dusty turbulence

Abstract

The significance of small-scale forcing of particles on the carrier two-dimensional turbulent flow has been shown [Pandey, Perlekar, and Mitra, Phys. Rev. E, 100, 013114 (2019)] to influence the spectral scaling properties of the carrier fluid. We investigate possible consequences of such two-way coupling in a turbulent suspension of inertial particles in one and two-point Eulerian and Lagrangian statistics. In particular, we find signatures of a possibly enhanced intermittency in the vorticity distributions. We characterize the changes in the (small-scale) geometry of the flow via the Okubo-Weiss parameter. Finally, we examine the scaling properties of the second-order (vorticity) structure functions and find a non-trivial form of scale-invariance at finite mass-loading. This suggests that a dual-scale forcing mechanism on the two-dimensional Navier-Stokes equation may be an effective model to mimic the role of particle feedback in turbulence.

Figures (7)

• Figure 1: A representative plot of the fluid kinetic energy vs time (non-dimensionalised by $\tau_\eta$) for various mass loading $\phi_m$. The shaded region indicates the time when the system has reached a statistically steady state.
• Figure 2: Representative pseudo-color plots of the vorticity fields mass loading (a) $\phi_m = 0$ and (b) $\phi_m = 0.125$ with $N_p=2.5\times10^{5}$ particles of Stokes numbers $St = 0.67$. (c) The probability distribution functions (PDF) of $\omega ({\bf x})$, normalized with its variance, for different $\phi_m$; The black dashed Gaussian curve is a guide to the eye. (Inset) A plot of the kurtosis $\kappa$ of these distributions as a function of $\phi_m$. The error bars on $\kappa$ are obtained via bootstrapping.
• Figure 3: (a) A log-log plot of the second-order structure function $S_2 (r)$ vs $r/\eta$ for different $\phi_m$; the pair of vertical lines indicates the region where a dominant scaling range with $r^{\zeta_2}$ emerges. (Inset) The second-order structure function exponents $\zeta_2$ vs $\phi_m$. (b) PDFs of vorticity increments for two different $\phi_m$ and separations with their scale-dependent kurtosis $\kappa$ shown in panel (c) for different $\phi_m$. In the inset of (c), we show the behaviour of $\kappa$, calculated at $r^*/\eta = 4.55$ and $r^*/\eta = 72.72$ as a function of $\phi_m$.
• Figure 4: PDFs of the Okubo-Weiss parameter $\Lambda$ for a suspension with St = 0.67 and calculated along Lagrangian (tracer: St = 0) trajectories for different $\phi_m$. The corresponding skewness $\gamma$ is shown in the inset as a function of $\phi_m$. The error bars on $\gamma$ are obtained via bootstrapping.
• Figure 5: PDFs of the Okubo-Weiss parameter $\Lambda$ for a suspension with St = 0.67 and calculated along the St = 0.67 particle trajectories for different $\phi_m$. The corresponding skewness $\gamma$ is shown in the inset as a function of $\phi_m$. The error bars on $\gamma$ are obtained via bootstrapping.