Forecasting Turbulence

Abstract

Fluid turbulence is one of the greatest unsolved problems of classical physics (and the subject of a million dollar mathematical (Millenium) challenge). Centuries of research--including Leonardo da Vinci’s observations of “la turbolenza” and the best efforts of numerous physicists (Heisenberg, Kelvin, Rayleigh, Sommerfeld, ...)--have failed to yield a tractable predictive theory. However, recent theoretical and computational advances have successfully linked recurring transient patterns (coherent structures) within turbulence to unstable solutions of the equations governing fluid flow (the Navier-Stokes equations). The solutions describing coherent structures provide a geometrical structure that guides the evolution of turbulence. We describe laboratory experiments where the geometry of key coherent structures is identified and harnessed to construct a roadmap to forecast the behavior of weakly turbulent flows.