A theoretical approach is developed for solving for the Reynolds stress in turbulent\nflows, and is validated for canonical flow geometries (flow over a flat plate, rectangular\nchannel flow, and free turbulent jet). The theory is based on the turbulence momentum\nequation cast in a coordinate frame moving with the mean flow. The formulation\nleads to an ordinary differential equation for the Reynolds stress, which can\neither be integrated to provide parameterization in terms of turbulence parameters\nor can be solved numerically for closure in simple geometries. Results thus far indicate\nthat the good agreement between the current theoretical and experimental/DNS\n(direct numerical simulation) data is not a fortuitous coincidence, and in the least it\nworks quite well in sensible ways in canonical flow geometries. A closed-form solution\nfor the Reynolds stress is found in terms of the root variables, such as the mean\nvelocity, velocity gradient, turbulence kinetic energy and a viscous term. The form of\nthe solution also provides radically new insight on how the Reynolds stress is generated\nand distributed.
Loading....