A Philosophy of Turbulence Modeling

Based on our experience and passion for the subject, we attempt a lucid description of the activity called Turbulence Modeling, its motivation, its rules, its unwritten principles, its sources of information, and sadly its many fallacies. Modeling is an essential enabler for CFD, and most of the time the model constitutes a gift to the community by the individuals and their institutions, whether government, industry, or university. Prestige is a motivation, but progress is its own reward. We contrast Intuitive and Constructed models. Rules begin with dimensional analysis, but include proper behavior at the edge of a turbulent region. Debatable guiding principles include the requirement for the Partial Differential Equations to be local, and the relationship with the exact Reynolds-Stress transport equations. Information comes from experiments and Direct Numerical Simulations, in both simple and complex flows. All the classical models are shown to suffer a "Structural Limitation" expressed by a General Law of the Wall which is physically incorrect. Fallacies include the idea that the Boussinesq approximation returns an isotropic stress tensor, the importance of realizability, the distinction between normal and off-diagonal Reynolds stresses, and of course the idea that one-equation models don't work.