Short-term forecasts and scaling of intense events in turbulence
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abstract
Extreme events such as intense tornadoes and huge floods, though infrequent, are particularly important because of their disproportionate impact. Our ability to forecast them is poor at present. Large events 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 with good accuracy on a computer. Here, we 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 is the dominant process by which an observer fixed to the laboratory frame perceives vorticity evolution on a short time scale and that the growth of squared vorticity during large excursions is quadratic in time when normalized appropriately. This result is not inconsistent with the multifractal description and is simpler for present purposes. Computational data show that the peak in the viscous term of the vorticity equation can act as a precursor for the upcoming peak of vorticity, forming a reasonable basis for forecasts on short time scales that can be estimated simply. This idea can be applied to other intermittent quantities and, possibly, more broadly to forecasting other extreme quantities, e.g. in seismology.
