Probability Density Function of Longitudinal Velocity Increment in Homogeneous Turbulence

Naoya Takahashi; Tsutomu Kambe; Tohru Nakano; Toshiyuki Gotoh; Kiyoshi Yamamoto

doi:10.1143/jpsj.68.86

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arXiv · chao-dyn/9803010

Probability Density Function of Longitudinal Velocity Increment in Homogeneous Turbulence

Naoya Takahashi·Tsutomu Kambe·Tohru Nakano·Toshiyuki Gotoh·Kiyoshi Yamamoto

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Abstract

Two conditional averages for the longitudinal velocity increment u_r of the simulated turbulence are calculated: h(u_r) is the average of the increment of the longitudinal Laplacian velocity field with u_r fixed, while g(u_r) is the corresponding one of the square of the difference of the gradient of the velocity field. Based on the physical argument, we suggest the formulae for h and g, which are quite satisfactorily fitted to the 512^3 DNS data. The predicted PDF is characterized as (1) the Gaussian distribution for the small amplitudes, (2) the exponential distribution for the large ones, and (3) a prefactor before the exponential function for the intermediate ones.

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Naoya Takahashi, Tsutomu Kambe, Tohru Nakano, Toshiyuki Gotoh, Kiyoshi Yamamoto. 1998-03-09. Probability Density Function of Longitudinal Velocity Increment in Homogeneous Turbulence. https://doi.org/10.1143/jpsj.68.86

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