Turbulence modeling using body force potentials

Reynolds averaged Navier–Stokes (RANS) turbulence models are usually concerned with modeling the Reynolds stress tensor. An alternative approach to RANS turbulence modeling is described where the primary modeled quantities are the scalar and vector potentials of the turbulent body force—the divergence of the Reynolds stress tensor. This approach is shown to have a number of attractive properties, most important of which is the ability to model nonequilibrium turbulence situations accurately at a cost and complexity comparable to the widely used two-equation models such as $\mathrm{k-\epsilon .}$ Like Reynolds stress transport equation models, the proposed model does not require a hypothesized constitutive relation between the turbulence and the mean flow variables. This allows nonequilibrium turbulence to be modeled effectively. However, unlike Reynolds stress transport equation models, the proposed system of partial differential equations is much simpler to model and compute. It involves fewer variables, no realizability conditions, and removes the strong coupling between the equations. A detailed analysis of the turbulent body force potentials and their physical significance reveals that they represent the relevant information contained in the Reynolds stress tensor and are fundamental turbulence quantities in their own right. Model predictions for a number of basic turbulent flows are presented including: Channel flow at various Reynolds numbers, mixing layer, rotating channel flow, adverse pressure gradient boundary layers, low Reynolds number backward facing step, and transition to turbulence in channel flow.