Turbulent Kinetic Energy Budget in the Far Field of a Square Cylinder Wake

Abstract

In this paper, the transport equation for the turbulent kinetic energy (TKE) is tested in the far field of a square cylinder wake (hereafter denoted SC). It is found that the physical mechanism for transporting TKE along the axis is different from that in a circular cylinder (hereafter denoted CC) wake. For the SC wake, the \(\overline{{q^2}} \) diffusion term is negligible compared to advection term along the axis and the advection and energy dissipation terms dominate the budget. However, in the CC wake, aside from the advection and energy dissipation terms, the \(\overline{{q^2}} \) diffusion term also contributes significantly to the budget. At the region close to the centreline, the gain of the energy due to the contributions from the advection and diffusion terms is equal to the loss due to the isotropic dissipation, indicating that the isotropic dissipation rate \({\overline{\varepsilon }_{iso}}\) is a good surrogate of the mean TKE dissipation rate \({\bar{\varepsilon }}\).