The real butterfly effect (Q2924833)

In this nice paper, the historical background for the well-known expression ``butterfly effect'' is discussed. The authors argue that ``Lorenz did not intend the phrase to characterize `mere' sensitive dependence on initial conditions in low-order chaos. Rather, he intended it to characterize an absolute finite-time barrier to predictability in certain multi-scale dynamical systems.'' They present results from an idealized nonlinear simulator of three-dimensional turbulence which provide some evidence for the finite-time loss of predictability described by Lorenz. Discussing the evidence for whether the effect about which Lorenz speculated is a provable property of the three-dimensional Navier-Stokes equations, the authors conclude that this is still an open question. They point out that ``using ensemble forecasting methods to flag the intermittent poor forecasts \textit{a priori}, it should be possible to improve weather forecasts further by reducing initial effort.'' This can be achieved ``not only by improving the quality and density of atmospheric observations, but also by improving the quality and resolution of the models into which these observations are assimilated. This latter aspect requires further investment in supercomputing.''