| Abstract |
Understanding of the structure of wall-bounded turbulent flows up to an infinite Reynolds number Re matters because of several reasons, for example, in regard to the validation of theory, computational methods, and experimental studies. However, our ability to obtain such insight is rather limited because of resolution requirements of simulations and experiments at very high Re which cannot be met. Technically, there are two ways to address these questions. One way is the use of simulation methods capable of providing reliable predictions of very high Re flows. This approach can be applied to realistic, complex, wall-bounded turbulent flows. Another way is the analytical prediction of the asymptotic structure of turbulent flows, which is feasible for canonical wall-bounded turbulent flows. The meaningfulness of both approaches depends on whether the methods applied are proven to be in line with physical requirements. The latter was recently shown in regard to the simulation methods that are applicable to address these questions. The meaningfulness of the analytical approach relates essentially to the questions about the universality of the model considered, including in particular the universality of the law of the wall. First, the paper presents an analysis of concepts used to derive controversial conclusions in regard to the law of the wall. It is shown that nonuniversality is a consequence of simplified modeling concepts, which leads to unrealizable models. On the other hand, realizability implies universality: models in consistency with physical requirements do not need to be adjusted to different flows. Second, the universal analytical model obtained is used to derive detailed conclusions about the asymptotic structure of canonical wall-bounded turbulent flows. Third, these conclusions are contrasted with corresponding conclusions about complex wall-bounded turbulent flows obtained on the basis of numerical prediction methods having significant reliability advantages compared to existing methods. |
