On the negative production in the cylinder wake using triple decomposition*

Two-dimensional and two-component velocity fields of cylinder wakes were measured through laboratory experiments using particle image velocimetry (PIV). Proper orthogonal decomposition (POD) was applied to the measured data to extract the unsteady coherent motion of the cylinder wakes. The combination of the first and the second modes was assumed to be the unsteady coherent motion of cylinder wakes, and the summation of the rest of the fluctuation components was denoted as turbulent fluctuation. Similarly, decomposing an original velocity into the time average, unsteady coherent motion, and turbulent fluctuation is a decomposition methodology called triple decomposition.

Based on the triple-decomposed kinetic energy equations, kinetic energy budgets have been investigated. By plotting the distribution of the three productions, negative production was observed in several limited regions. The dominant terms of the time-averaged momentum equation were compared with one another and analyzed in comparison to the sub-divided terms of production to interpret the mechanism of the negative productions. As a result, normal stresses by fluctuation and the divergence of mean velocity have been confirmed to be the main causes of the negative production.