Effects of finite arithmetic precision on large-scale direct numerical simulation of box turbulence by spectral method

The effects of finite arithmetic precision on direct numerical simulations (DNS) of three-dimensional box turbulence using a spectral method were studied by comparing single and double precision at Taylor-scale Reynolds numbers R${}_{\ensuremath{\lambda}}$ = 170 and 268. At R${}_{\ensuremath{\lambda}}$ = 268, significant differences appeared after about 1.6 eddy turnover times, especially in extreme-event statistics such as the maxima and high-order moments of local energy dissipation and enstrophy. In contrast, differences at R${}_{\ensuremath{\lambda}}$ = 170 were negligible. These results suggest that in high-Reynolds-number DNS, round-off errors from limited precision could significantly affect extreme-event statistics over long simulation times.