A novel forcing technique to reproduce scalar mixing of turbulent jets in a 3D periodic box

For most numerical simulations of passive scalars in 3D periodic boxes, a forcing technique is required to sustain the scalar energy. However, the existing forcing techniques are not based on physics, but rather arbitrary numerical methods that sustain the scalar energy. In this current investigation, we aim to develop a forcing technique to simulate a realistic turbulent mixing process inside a 3D periodic box. The target flow is an axisymmetric jet with passive scalars on its centerline. The velocity and scalar information of turbulent jets on the centerline is applied to the scalar transport equation via a Reynolds decomposition. The result is a combination of three terms in the scalar equation: a mean scalar gradient term, a linear forcing term, and a velocity-scalar non-linear term. These new forcing terms are derived to replicate the scalar mixing properties of jets in a triply periodic DNS. A set of DNS has been performed with the new forcing terms, and various turbulent parameters, such as the scalar variance and velocity-scalar correlation, are compared against experiments.