Intermittency suppression in turbulence via forced light particles

Abstract

We investigate how turbulence is reshaped by the presence of externally forced light particles, using high-resolution direct numerical simulations with four-way coupling. The particles are subject to an oscillatory force that in turn locally affects the fluid flow through momentum exchange at the position of the particles. Since the light particles preferentially concentrate in high vorticity regions, this leads to an intricate preferential turbulence modulation. We show that through this modulation, the forced light particles strongly reduce the intermittency of the flow, shedding new light on the delicate relationship between vortex filaments and turbulence intermittency.

Figures (9)

• Figure 1: Problem setup. (a) 2D slice of the enstrophy field $\Omega^2$ with particles in black, showing preferential concentration in high-enstrophy regions. (b) Pressure field at fixed $z$. (c) Forces on a trapped particle: Stokes drag $f_D$, added mass and pressure gradient $f_P$, and external forcing $f_E = a_e \sin(\omega t) \hat{\mathbf{e}}_x$. We compare three cases: 1-way coupling (particles advected by the flow, no feedback), 4-way coupling without forcing (includes momentum exchange and collisions), and 4-way coupling with external particle forcing. (d,g,j): 3D particle distributions. Clustering is strongest in the 1-way case, where particles collapse into vortex filaments; in the 4-way cases, collisions limit accumulation, and forcing enables escape, leading to more diffuse distributions. (e,h,k): slices of the pressure field, illustrating how particle positions relate to pressure minima in each regime. (f,i,l): particle velocity components, highlighting the effects of collisions and forcing.
• Figure 2: Ratio of enstrophy sampled by particles, $\Omega^2_{\text{samp}}$, to the Eulerian enstrophy, $\Omega^2$, plotted against the Stokes number $St$. Results are presented for 1-way coupling and 4-way coupling with and without external forcing on the particles. We are interested in $St \approx 1$, where light particles preferentially concentrate in vortex filaments (regions of high enstrophy). The 4-way coupling simulations are performed at 1% volume fraction. For the forced case, the following parameters are used: $a_e = 64 a_{\eta}$ and $\omega = 3.2 \tau_{\eta}^{-1}$.
• Figure 3: Intermittency suppression. Eulerian flatness $F_{\ell}^{(p)}$ ($p = 4$ and $p = 6$ considered) for 1-way coupling and 4-way coupling with external forcing acting on the particles. The upper right inset plots show the excess flatness divided by the one with no particles, $\tilde{F}^{(p)} = (F^{(p)} - F^{(p)}_{\text{Gaussian}})/(F^{(p)}_{\text{no particles}} - F^{(p)}_{\text{Gaussian}}))$. The results for the forced cases are presented at two different resolutions: $256^3$ ($Re_{\lambda}=87$) and $512^3$ ($Re_{\lambda}=168$). The 4-way coupling simulations are performed at 1% volume fraction and with the following external forcing parameters: $a_e = 64 a_{\eta}$ and $\omega = 3.2 \tau_{\eta}^{-1}$.
• Figure 4: Forcing amplitude and resonance effects. Eulerian flatness $F_{\ell}^{(4)}$ for (a). Different particle forcing amplitudes $a_e \in [4, 96]a_{\eta}$, at a fixed frequency $\omega = 3.2/\tau_{\eta}$, (b). Different forcing frequencies $\omega \in [0.8, 12.8]/\tau_{\eta}$ at a fixed amplitude $a_e = 64a_{\eta}$. The upper right insets show the excess flatness of selected cases with forced particles divided by the one with no particles, $\tilde{F}^{(4)} = (F^{(4)}-3)/(F^{(4)}_{\text{no particles}}-3)$.
• Figure 5: Fourth-order Eulerian flatness $F^{(4)}_{\ell}$ for different Stokes numbers. The case $St=1$ yields preferential concentration in vortex filaments (see \ref{['fig:samp_oo']}), which can be observed to produce significant suppression of intermittency.