Growth of Uncertainty in Decaying Isotropic Turbulence

Abstract

Computer simulators are made of the growth of the difference-velocity field for pairs of realizations of isotropic, three-dimensional turbulence at Reynolds number R&lambda≈40. The simulations involve full-scale integration of the Navier-Stokes equation in the Fourier representation. It is found that the difference-velocity variance (error energy) grows with time even when the initial difference-velocity is confined to wave numbers strongly damped by viscosity. The numerical integrations are compared with results of the direct-interaction approximation (DIA). It is found that the DIA gives reasonably satisfactory quantitative agreement for the evolution of the error energy and the error. energy spectrum. What discrepancies there are represent an underestimate of error energy growth by the DIA. This is explained by theoretical analysis of the approximation.