Appearance of the −5/3 scaling law in spatially intermittent flows with strong vortex shedding

Our previous investigations “Extreme events and non-Kolmogorov -5/3 spectra in turbulent flows behind two side-by-side square cylinders,” J. Fluid Mech. 874, 677–698 (2019); “Energy transfer in turbulent flows behind two side-by-side square cylinders,” J. Fluid Mech. 903, A4 (2020) revealed that an extended −5/3 energy spectrum can be found in the highly intermittent flow accompanied by strong vortex shedding (i.e., composed of both large-scale laminar and turbulent motions). To shed light on the emergence of the −5/3 energy spectra, we perform direct numerical simulations of a single-cylinder wake. In the highly intermittent upstream region, albeit a significant −5/3 scaling law can be found, the energy spectra and the corresponding Kolmogorov constant Ck are distinctly different from those in the downstream almost turbulent region and the case of grid turbulence with a similar local Reynolds number. However, the conditional Kolmogorov constant acquires the expected value and the conditional energy spectra are in good agreement with those in the far downstream region. Ck is found to have a power-law dependence on the intermittency factor γ, C k ∼ γ 1 / 3. This study, the first of its kind, demonstrates that in the highly intermittent flow, the composed turbulent motions are responsible for the emergence of the −5/3 scaling law, which implies the characteristics of the composed turbulent motions resemble those in the fully turbulent flow.