On the Prediction of the Kurtosis of Velocity Derivatives in a Turbulent Field

The prediction of the values of non-dimensional fourth-order moment (kurtosis) of the velocity derivative in a turbulent field is made under the assumption that the values of kurtosis depend on both the turbulence Reynolds number and the intermittency factor. The method consists of modeling a suitable probability density of the variable in a given turbulence Reynolds number and the intermittency factor. A crude model of the probability density function is derived, and the numerical calculations based on the model show excellent agreement with many of the experimental data. The analysis shows that the values of kurtosis depend strongly on the intermittency factor, and that depending on the value of the intermittency factor, it is entirely possible to have values of kurtosis as low as five in a flow with a turbulence Reynolds number of 5000.