Short-term forecasts and scaling of intense events in turbulence

Large fluctuations in complex systems from earthquakes to financial markets, though infrequent, are particularly important because of their disproportionate impact. Our ability to forecast them is quite poor at present. Large fluctuations occur also in intermittent features of turbulent flows. Some dynamical understanding of these features is possible because the governing equations are known and can be solved exactly on a computer. Here we particularly study large-amplitude events of turbulent vorticity using results from direct numerical simulations of isotropic turbulence in conjunction with the vorticity evolution equation. We show that the advection of vorticity is the dominant process by which an observer fixed to the laboratory frame perceives it, and that the growth of squared-vorticity during large excursions is quadratic in time when normalized appropriately. This result is consistent with the multifractal description but simpler for present purposes. Computational data show that the peak in the viscous contribution can act as the precursor for the upcoming peak in vorticity, forming a reasonable basis for forecasts on short timescales that can be estimated simply. This idea might apply more broadly to forecasting other extreme quantities, e.g., in seismology.