Dissipation scaling in the transition region of turbulent mixing layer

Direct numerical simulation is conducted for a spatially developing shear mixing layer to investigate the spatial transition of the dissipation coefficient of the turbulent kinetic energy, C_ϵ. The scaling law suggested by Goto and Vassilicos [Phys. Rev. E 94, 053108 (2016)], C_ϵ∼Re_λ ⁻¹, holds over a wide area in the upstream region (0.3 ≤ x/L₀ ≤ 1.9, where x is the streamwise direction and L₀ is the height of the computational domain), and C_ϵ takes a constant value in the further downstream region, where Re_λ is the turbulent Reynolds number based on Taylor's microscale. Proper orthogonal decomposition (POD) analysis is performed to investigate the distributions of the streamwise length of the large-scale energy-containing structure, which is estimated from the cycle of the zero-crossing point of the time-series data composed of the sum of the POD modes until the cumulative energy rate exceeds 60 %. It is shown that C_ϵ becomes a constant when the distributions of the length of the large-scale structure reach a self-similar state. This result suggests that it is necessary to satisfy the self-similarity of the distribution of the length of the large-scale energy-containing structure in order to apply the condition that C_ϵ is a constant.