Physical mechanism of turbulence attenuation by polymers from a timescale perspective
To elucidate the physical mechanism of turbulence attenuation by polymers at each scale, we conduct direct numerical simulations of homogeneous isotropic turbulence in dilute polymer solutions. We model polymers as FENE dumbbells and simulate them using Brownian dynamics. By visualising the hierarchical structures of coherent vortices, we demonstrate that as the Weissenberg number increases, polymers progressively suppress vortices from smaller to larger scales, attenuating their turbulent energy. While inspired by Lumley's theory, we propose a novel timescale-based framework for analysing this attenuation process using the scale decomposition. We define a scale-dependent Weissenberg number, $\mathrm{Wi}_{\mathrm{sd}}(k)$, as the ratio of the polymer relaxation time to the turnover time of multiscale vortices at each wave-number. We reveal that when expressed in terms of $\mathrm{Wi}_{\mathrm{sd}}(k)$, the energy attenuation rate at each scale collapses onto a single curve that rises at $\mathrm{Wi}_{\mathrm{sd}}(k) \gtrsim 1$, proving that $\mathrm{Wi}_{\mathrm{sd}}(k)$ successfully describes both the onset and the degree of turbulence attenuation at any given scale $k^{-1}$. Furthermore, the scale decomposition uncovers that polymers preferentially align with the turbulent stretching direction at the scale satisfying $\mathrm{Wi}_{\mathrm{sd}}(k) \approx 1$. Based on these results, we establish a physical picture of the polymer--turbulence interaction and explicitly link it to the statistics in turbulence attenuated by polymers.