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Short-term forecasts and scaling of intense events in turbulence

  • D. A. DONZIS (a1) and K. R. SREENIVASAN (a2) (a3)


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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Borgas, M. S. & Yeung, P. K. 2004 Relative dispersion in isotropic turbulence. Part 2. A new stochastic model with Reynolds-number dependence. J. Fluid Mech. 503, 125160.
Constantin, P. 1994 Geometric statistics in turbulence. SIAM Rev. 36, 7398.
Donzis, D. A., Yeung, P. K. & Sreenivasan, K. R. 2008 Dissipation and enstrophy in isotropic turbulence: scaling and resolution effects in direct numerical simulations. Phys. Fluids 20, 045108.
Eswaran, V. & Pope, S. B. 1988 An examination of forcing in direct numerical simulations of turbulence. Comp. Fluids 16, 257278.
Frisch, U. 1995 Turbulence. Cambridge University Press.
Gibbon, J. D. & Doering, C. R. 2005 Intermittency and regularity issues in 3d Navier–Stokes turbulence. Arch. Rat. Mech. Anal. 177 (1), 115150.
He, G., Chen, S., Kraichnan, R. H., Zhang, R. & Zhou, Y. 1998 Statistics of dissipation and enstrophy induced by localized vortices. Phys. Rev. Lett. 81, 46364639.
Lee, S. & Lee, C. 2005 Intermittency of acceleration in isotropic turbulence. Phys. Rev. E 71, 056310.
L'vov, V. & Procaccia, I. 1996 The universal scaling exponents of anisotropy in turbulence and their measurements. Phys. Fluids 8, 25652567.
Melbourne, T. I. & Webb, F. H. 2002 Precursory transient slip during the 2001 M w = 8.4 Peru earthquake sequence from continuous GPS. Geophys. Res. Lett. 29 (21), 2032.
Meneveau, C. & Sreenivasan, K. R. 1987 The multifractal spectrum of the dissipation field in turbulent flows. Nucl. Phys. B 2, 4976.
Nelkin, M. 1990 Multifractal scaling of velocity derivatives in turbulence. Phys. Rev. A 42 (12), 72267229.
Nelkin, M. 1995 Inertial range scaling of intense events in turbulence. Phys. Rev. E 52 (5), R4610R4611.
Nelkin, M. 1999 Enstrophy and dissipation must have the same scaling exponents in the high Reynolds number limit of fluid turbulence. Phys. Fluids 11, 22022204.
Rice, J. R. 2006 Heating and weakening of faults during earthquake slip. J. Geophys. Res. 111, B05311.
Rogallo, R. S. 1981 Numerical experiments in homogeneous turbulence. NASA Tech Rep. 81315.
Schumacher, J., Sreenivasan, K. R. & Yakhot, V. 2007 Asymptotic exponents from low-Reynolds-number flows. New J. Phys. 9, 89.
Shimamoto, T. 1986 Transition between frictional slip and ductile flow for halite shear zones at room temperature. Science 231, 711714.
Sreenivasan, K. R. 2004 Possible effects of small-scale intermittency in turbulent reacting flows. Flow Turbul. Combust. 72, 115131.
Sreenivasan, K. R. & Meneveau, C. 1988 Singularities of the equations of fluid motion. Phys. Rev. A 38, 62876295.
Yakhot, V. & Sreenivasan, K. R. 2005 Anomalous scaling of structure functions and dynamic constraints on turbulence simulations. J. Stat. Phys. 121, 823841.
Zeff, B. W., Lanterman, D. D., McAllister, R., Roy, R., Kostelich, E. J. & Lathrop, D. P. 2003 Measuring intense rotation and dissipation in turbulent flows. Nature 421, 146149.
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