TY - JOUR
T1 - Short-term forecasts and scaling of intense events in turbulence
AU - Donzis, D. A.
AU - Sreenivasan, K. R.
N1 - Funding Information:
It is a pleasure to dedicate this paper to Professor S. H. Davis who, through personal research, leadership and mentoring, has immensely influenced the fluid dynamics community of his times. We appreciate helpful collaboration with P. K. Yeung on the simulations. This work was supported by the National Science Foundation grant CTS-0553602 to the University of Maryland.
PY - 2010/3/25
Y1 - 2010/3/25
N2 - 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.
AB - 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.
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U2 - 10.1017/S0022112009993600
DO - 10.1017/S0022112009993600
M3 - Article
AN - SCOPUS:77952339460
SN - 0022-1120
VL - 647
SP - 13
EP - 26
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -