Cosserat fluids and the continuum mechanics of turbulence: A generalized Navier-Stokes-alpha equation with complete boundary conditions

摘要: We here develop a continuum-mechanical formulation and generalization of the Navier– Stokes-α equation based on general framework for fluid-dynamical theories involving gradient dependencies (Fried & Gurtin 2005). That entails two additional material length scales: one energetic origin, other dissipative origin. In contrast to Lagrangian averaging, our delivers boundary conditions — yet another scale complete thermodynamics applied an isothermal system. As application, we consider classical problem turbulent flow in plane, rectangular channel with fixed, impermeable, slip-free walls make comparisons results obtained from direct numerical simulations. For this problem, only scales involved enters final solution. When associated is signed ensure satisfaction second law at theory solutions that agree neither quantitatively nor qualitatively observed features plane flow. On contrary, find excellent agreement when sign parameter violates law. discuss implication result.