By Tsinober, A. (1937-)

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There is no consensus whether two-dimensional chaotic flows even with many degrees of freedom should be qualified as turbulence. The main reason is that such flows lack the mechanism of vorticity and strain amplification. This issue is discussed in chapter 8. 8 The common view of turbulence dynamics involves the Richardson-Kolmogorov cascade of energy (the famous poem by Richardson). g. in all spatially developing turbulent flows. All the examples given in the previous section on the partly turbulent flows are such, both free and wall-bounded.

This is because the equations for the fluctuations (unresolved scales) contain as coefficients the mean (resolved) field. This means that in turbulent flows point-wise flow independent ‘constitutive’ relations analogous to real material constitutive relations for fluids (such as stress/strain relations) can not exist, though the ‘eddy viscosity’ and ‘eddy diffusivity’ are frequently used18 as a crude approximation for taking into account the reaction back of fluctuations (unresolved scales) on the mean flow (resolved scales).

An overview of turbulent flows under various influences and physical circumstances, some of which serve also as sources of energy for sustaining the turbulence, is given in chapter 8. These include shear, buoyancy, rotation, CHAPTER 1 26 (electro) magnetic field, compressibility and additives. For obvious reasons the material of this chapter is limited by only the most important essential features and changes in turbulent flows under the various influences. Chapters 2 to 7 are all concluded by a brief summary.

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An informal introduction to turbulence by Tsinober, A. (1937-)

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