Simple model for the bottleneck effect in isotropic turbulence based on Kolmogorov's hypotheses

We propose a simple model for the bottleneck effect in homogeneous isotropic turbu-lence as a bump in the compensated energy spectrum, based on Kolmogorov's hypotheses (of 1941 and 1962). The model of the longitudinal structure function consists of two quadratic functions representing large-and small-scale motions. The model parameters are derived from the asymptotic behavior of the structure function. The Kolmogorov and intermittency constants are fitted from direct numerical simulation (DNS) and experimental data. From the model, the height of the spectral bump in the compensated spectrum has a power-law R-0.0426 lambda , and the bump location scaled by the Kolmogorov scale is 0.153, which generally agree with various DNS results at moderate and large Reynolds numbers R lambda. Moreover, we derive that the incorporation of the intermittency exponent into the model leads to the decaying power law of the bump height with R lambda.