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キーワード:
turbulence; extreme events; intermittency; direct numerical simulations
要旨:
Fully turbulent flows are characterized by intermittent formation of very localized and intense velocity gradients. These gradients can be orders of magnitude larger than their typical value and lead to many unique properties of turbulence. Using direct numerical simulations of the Navier-Stokes equations with unprecedented small-scale resolution, we characterize such extreme events over a significant range of turbulence intensities, parameterized by the Taylor-scale Reynolds number (R-lambda).Remarkably, we find the strongest velocity gradients to empirically scale as tau(-1)(K) R-lambda(beta), with beta approximate to 0.775 + 0.025, where T-K is the Kolmogorov time scale (with its inverse, T-K(-1), being the rms of velocity gradient fluctuations). Additionally, we observe velocity increments across very small distances r <= eta, where yis the Kolmogorov length scale, to be as large as the rms of the velocity fluctuations. Both observations suggest that the smallest length scale in the flow behaves as eta R-lambda(-alpha), with alpha = beta - 1/2, which is at odds with predictions from existing phenomenological theories. We find that extreme gradients are arranged in vortex tubes, such that strain conditioned on vorticity grows on average slower than vorticity, approximately as a power law with an exponent gamma < 1, which weakly increases with R-lambda. Using scaling arguments, we get beta = (2 - gamma)(-1), which suggests that beta would also slowly increase with R. We conjecture that approaching the mathematical limit of infinite R-lambda, strain and vorticity would scale similarly resulting in gamma = 1 and hence extreme events occurring at a scale eta R(lambda)(-1/2)corresponding to beta = 1.
