Fluctuations of energy dissipation rate and 1D dissipation surrogate in isotropic turbulence

Kinetic energy dissipation rate is a quantity of central interest in turbulence research. The fluctuations around the mean increase with decrease of the scale, the intermittency. The full dissipation rate consists of 9 terms of the squared velocity gradients and is difficult to access. Instead, a one-dimensional (1D) dissipation surrogate ϵ1 equal to 15υ((∂u_1)⁄(∂x_2 ))^2 is measured under the assumption of local isotropy. The right tail of the PDF P1(ϵ1) is always longer than that of P3(ϵ), implying the stronger intermittency of ϵ1 than that of ϵ. In this talk I will describe a transformation formula between two PDFs and explain that the difference in the tails of two PDFs arises from the difference in the number of terms contributing to the 1D or full dissipation. The arguments are further extended to the PDFs of the locally averaged 1D or full dissipation and their scaling exponents in the inertial range in Kolmogorov’s 1962 theory.