On the classification of the laminar-turbulent transition process using the methods of nonlinear dynamics: general analysis and the future

Abstract

Abstract The definition of a turbulent flow is still not mathematically defined. Different methods exists that provide different definitions resulting in different approaches and classifications of the laminar-turbulent transition as well as the fully developed turbulent flows. The paper includes the analysis of different stages of turbulence development, specific methods that are used in each stage and possible methods of unification of these methods based on the nonlinear-dynamical approach. Results are demonstrated for some characteristic fluid dynamics problems. Future highlights on the path to possible unification are discussed.