A new numerical methodology to follow the time-decay of turbulence

Homogeneous isotropic turbulence in time decay has longly been a paradigm in turbulence. Since the very first investigations it clearly appeared that certain scaling laws characterize the time decay, i.e. the turbulent kinetic energy decreases in time as a power law with exponent 𝑛(𝑘=𝐴𝑘(𝑡−𝑡0)−𝑛) n ( k = A k ( t − t 0 ) − n ) From experiments [2] it immediately appeared that the values of n are strongly sensitive to the specific forcing and to the geometry of the apparatus. Ever since, there are been a number of attempts to understand this dispersion of data, under the assumption that the value of n should be universal. The theory described in [1] states that the decay exponent n is strongly affected by initial conditions and for large Reynolds number it assumes the value n = 1. Under this respect DNS simulations in triperiodic box ([5],[6]), are highly influenced by initial conditions i.e. by the spectrum of the velocity field. In particular it is strongly affected by the behavior of the spectrum near k = 0. Recent experiments [3] with space-filling square fractal grids show that the generated turbulence is characterized by the property that the Taylor scale remains constant during the decay. George [4] theoretically derived under the assumption of a constant characteristic scale that the turbulence described in [3] decays with an exponential law instead of the classical power law decay. He also states that this exponential solution in not restricted to low Reynolds number but its valid also for finite Reynolds number.