On a continuum-mechanical theory for turbulence


We discuss a continuum-mechanical formulation and generalization of the Navier–Stokes-𝛼 equation based on a comprehensive framework for uidynamical theories with gradient dependencies (Fried & Gurtin 2006). Our ow equation entails two additional material length scales: one energetic, the other dissipative. In contrast to Lagrangian averaging, our formulation delivers boundary conditions — involving yet another length scale — and a complete structure based on thermodynamics applied to an isothermal system.

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Turbulence; Hypertraction and hyperstress; Virtual power; Boundary conditions

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