We investigate energy transfer mechanisms for vortex shedding in the two-dimensional cylinder wake at a Reynolds number of $\text{Re}=100$. In particular, we focus on a comparison of the energy transfer in the true flow field to that predicted by resolvent analysis. The energy balances achieved by the true cylinder flow are first characterized—both for the flow as a whole and for each of its most energetic harmonic frequencies. It is found that viscous dissipation balances production when each is considered over the entire flow field and therefore that linear mechanisms achieve an energy balance on their own, thus respecting the Reynolds–Orr equation. Suitable energy conservation laws reveal that while nonlinear mechanisms neither produce nor consume energy overall, they nevertheless account for an important transfer of energy to higher frequencies. The energy balance for DNS is compared to that predicted by resolvent analysis. Although a suitable energy balance is achieved for each harmonic, resolvent analysis does not correctly model nonlinear energy transfer between temporal frequencies since it only models interactions between the mean flow and fluctuations. The impact of the neglected nonlinear energy transfer on the resolvent mode shapes is also made clear by analyzing the spatial distribution of the energy transfer mechanisms. We then investigate the detailed roles of energy transfer from the viewpoint of nonlinear triadic interactions by considering a finite number of harmonic frequencies. It is shown that interfluctuation interactions play a critical role in the redistribution of energy to higher harmonic frequencies. We observe not only an energy cascade from low frequencies to high frequencies, but also a considerable inverse cascade from high frequencies to low frequencies. The true energy pathways observed among harmonic modes provide additional constraints that could help to improve the modeling of nonlinear energy transfer in the cylinder flow.

• Received 18 August 2020
• Accepted 4 February 2021

DOI:https://doi.org/10.1103/PhysRevFluids.6.024702