What Is the Turbulence Problem, and When May We Regard It as Solved?

Abstract

Turbulent motion of fluids is often thought of as a grand problem, but what exactly is this “turbulence problem”? Because it has often been proclaimed as very difficult and unsolved, when can we claim that it is solved? How does this situation in turbulence compare with other complex problems in physical sciences? Addressing these questions is not trivial because everyone has their favorite idea of what is required of the “solution.” The answers range from being able to calculate the pressure drop in turbulent pipe flow to being able to calculate anomalous scaling exponents to answering the regularity problem of the Navier–Stokes equations. Taking an absolute position on the basis of any of these, or other similar examples, is incomplete at best and potentially erroneous at worst. We believe that it is beneficial to have an open discussion of this topic for the advancement of the research agenda in turbulence. This article is an attempt to address the question of what constitutes the turbulence problem, its place in the scientific enterprise as a whole, and how and when one may declare it as solved.