Appendix. Essential Quotations

Abstract

Along with a relatively limited number of intext citations we bring a small collection of citations in this Appendix, more is found in Tsinober (An informal conceptual introduction to turbulence, 2009). In this reference one of the aims was an extensive treatment of the dialog in the turbulence community with an emphasis on problems of a conceptual nature.

Here we put more emphasis on the pretty early recognition in the community of the fundamental difficulties as concerns the theoretical aspects of the problem and as a consequence the absence of theory based on first principles and inadequate tools to handle both the problem and the phenomenon of turbulence. This rather peculiar state of matters exists along with a set of deterministic differential equations, the Navier–Stokes equations probably containing all of turbulence, so that most of our knowledge about turbulence comes from observations and experiments, laboratory, field and later numerical, which is unfortunate as theory is supposed to guide and gives meaning to observation.

Along with absence of genuine theory there is no consensus on what is (are) the problem(s) of turbulence and what would constitute its (their) solution. Neither is there agreement on what constitutes understanding which can be brought only by a genuine theory.

This state of matters was understood long ago by many outstanding people, Kolmogorov, von Neumann, Wiener and many other as quoted below. Related issues concern the multitude of “approaches” and the continuing diversity of opinions on what is important, what are the main questions and similar.