On the problem of turbulent flows in pipes at very large Reynolds numbers (reply to comment by I I Vigdorovich [Phys. Usp. 58 196 (2015); Usp. Fiz. Nauk 185 213 (2015)] on “Turbulent flows at very large Reynolds numbers: new lessons learned” [Phys. Usp. 57 250 (2014); Usp. Fiz. Nauk 184 265 (2014)])

The problem of turbulent flow in pipes, although at first sight of purely engineering interest, has since the 1930s been the subject of much attention by mathematicians and physicists, including such outstanding figures as Th von Kármán, L Prandtl, and L D Landau. It has turned out that despite — or perhaps due to — the seemingly simple formulation of this problem, research on it has revealed new aspects of the still very mysterious phenomenon of turbulence. Reference [1] briefly summarizes our work over the last twenty years on the problem. Some of our results strongly disagree with commonly accepted views which, unsurprisingly, makes them difficult to accept. This is well exemplified by letter [2], so its analysis here may hopefully be of interest to UFN's (Physics –Uspekhi) readers.