Organized structures, memory, and the decay of turbulence

Abstract

The rapid increase in computational power has led to an unprecedented enhancement of our ability to study the behavior of complex systems in the physical, biological, and social sciences. However, there are still many systems that are too complex to tackle. A turbulent fluid is the archetypal example of such a complex system. Its complexity is manifested as the appearance of organized structures across all of the scales available to a turbulent fluid. Thus, the task that a numerical analyst working on turbulence faces is to reduce the complexity of the problem into something manageable, which at the same time preserves the essential features of the problem. Although much knowledge about the Euler and Navier–Stokes equations has accumulated over the years (1–8), it has proven very difficult to incorporate this knowledge in the construction of effective models. The work of Hald and Stinis (9) in this issue of PNAS is an attempt toward the construction of an effective model that utilizes qualitative information about the structure of a turbulent flow. The work in ref. 9 rests on the idea that the organization of a fluid flow in vortices leads to "long memory" effects, i.e., the motion of a vortex at one scale is influenced by the past history of the motion of vortices in other scales. This line of thought first appeared in the work of Alder and Wainwright (ref. 10; see also ref. 11 for a recent review on memory and problem reduction).

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