Energy transfer mechanisms and resolvent analysis in the cylinder wake

Bo Jin, Sean Symon, Simon J. Illingworth

Published 2020-04-30Version 1

Energy transfer mechanisms for vortex shedding behind a 2D cylinder at a Reynolds number of Re=100 are investigated. We first characterize the energy balances achieved by the true cylinder flow---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. Nevertheless, nonlinear energy transfer plays a critical role in the transfer of energy across temporal frequencies. Suitable energy conservation laws reveal that while nonlinear energy transfer mechanisms neither produce nor consume energy overall, they nevertheless account for an important transfer of energy between temporal frequencies. We then compare the energy balance for DNS to that predicted by resolvent analysis. Although a suitable energy balance is achieved for each harmonic, resolvent analysis does not respect the conservative nature of the nonlinear terms and fails to model nonlinear energy transfer between temporal frequencies. This lack of nonlinear energy transfer helps to explain the excess energy of the leading resolvent mode observed in the far wake.