A simple model for the bottleneck effect in homogeneous isotropic turbulence based on Kolmogorov's hypotheses

We propose a model for the bottleneck effect, 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. All the model parameters are either derived from asymptotic behaviors of the structure function or are universal constants fitted from direct numerical simulation (DNS) and experimental data. The model has a simple form without empirical parameters. From the model, the height of the spectral bump in the compensated spectrum has a power law R_λ^-0.0426, 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_λ. 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_λ.