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INTRODUCTION 25 Though there exists a set of deterministic diﬀerential equations (NSE) probably containing (almost) all of turbulence, most of our knowledge about turbulence comes from observations and experiments (laboratory, ﬁeld and later numerical)11 . N. Kolmogorov: I soon understood that there was little hope of developing a pure, closed theory, and because of absence of such a theory the investigation must be based on hypotheses obtained on processing experimental data (see Tikhomirov, 1991)12 .
An example of a turbulent mixing layer. Top – side view, bottom – (half) plan view, both shadowgraph. 8 m/s. From Konrad (1976) All the quantities exhibit apparently random temporal patterns, though quite diﬀerent. Similar diﬀerences occur in the spatial variations of these quantities. We will return to these diﬀerences and many other related issues in the subsequent chapters. , without mathematics. It is natural to use the qualitative manifestations of turbulent ﬂows as a ﬁrst step to ‘deﬁne’ what is turbulence.
Second, dealing with conceptual aspects of turbulence research leads necessarily to addressing misconceptions which have arisen during more than a century of turbulence research attempting to achieve some physical understanding/picture of this enigmatic phenomenon. Chapters 2 to 7 and chapter 9 are concluded by a brief summary. The former chapter 9 became chapter 10. It is devoted to the recapitulation of some main points with somewhat diﬀerent emphasis, and to the discussion of issues of general nature not addressed in previous chapters.