Universality Of Modal Time Correlation Functions In Medium Scale

We investigate the universality of modal time correlation functions using a closure equation for the normalized dimensionless time correlation function. As a candidate for a new universal function for turbulence, we propose a solution to the closure equation in the case of the critical value of the wavenumber, at which the decay form of the time correlation function changes from exponential to oscillatory exponential. The solution is compared with the normalized dimensionless time correlation functions obtained from numerical results for one-dimensional turbulence, such as the Kuramoto-Sivashinsky equation and that obtained from the direct interaction approximation for three-dimensional Navier-Stokes turbulence. As a result of the comparison, we provide evidence to show that the normalized dimensionless time correlation function is universal in the case of the critical value of the wavenumber.