Dissipation scaling in the transition region of turbulent mixing layer

Abstract

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, Cϵ. The scaling law suggested by Goto and Vassilicos [Phys. Rev. E 94, 053108 (2016)], Cϵ∼Reλ−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 Cϵ takes a constant value in the further downstream region, where Reλ 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 Cϵ 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 Cϵ is a constant.