Scale interactions and energy transfer in the turbulent wake of a bluff body

Abstract

Turbulent bluff-body wakes exemplify the coexistence of large-scale coherent structures and fine-scale turbulence -- two ends of a wide dynamical range of scales connected through the turbulent cascade. In this work, we study the multiscale dynamics in the high-Reynolds-number wake behind a circular disk. One-point and two-point statistics are first examined, including the budget and spectra of the turbulent kinetic energy (TKE). Streamwise advection is found to contribute the most to the TKE balance, while the dissipation rate does not follow the classical equilibrium scaling ($\varepsilon \nsim \mathcal{U}^3/\mathcal{L}$). The largest scales are represented by the three-dimensional coherent modes extracted using spectral proper orthogonal decomposition, whereas the TKE and Reynolds shear stress spectra exhibit inertial-range scalings. A filtering-based triple decomposition further separates the fluctuations into large- and small-scale components and partitions the kinetic energy, with respective spatial transports at each scale and an inter-scale transfer in between. The inter-scale fluxes indicate a statistical forward cascade and follow the classical $\mathcal{U}^3/\mathcal{L}$ scaling, while their radial profiles become self-similar. The disequilibrium between inter-scale flux and dissipation is shown to arise from non-negligible streamwise advection at the sub-filter scale. Finally, the observed anti-correlation between the dissipation coefficient and the local Taylor Reynolds number, $C_\varepsilon = \varepsilon \mathcal{L}/\mathcal{U}^3 \sim Re_\lambda^{-1}$, is shown to originate from a similar correlation in the coarse-grained, locally averaged statistics. The results suggest that the instantaneous cascade-dissipation disequilibrium is intrinsic to turbulence and becomes apparent when large-scale unsteadiness and length-scale growth prevent statistical equilibrium.