  We investigate the large-scale influence of numerical noises as tiny
artificial stochastic disturbances on a sustained turbulence. Using the
two-dimensional (2D) turbulent Rayleigh-B\'enard (RB) convection as an example,
we numerically solve the NS equations, separately, by means of a traditional
algorithm with double precision (marked by RKwD) and the so-called clean
numerical simulation (CNS). The numerical simulation given by the RKwD is a
mixture of the "true" physical solution and the "false" numerical noises that
is random and can be regarded as a kind of artificial stochastic disturbances:
unfortunately, the "true" physical solution is mostly at the same level as the
"false" numerical noises. By contrast, the CNS can greatly reduce the
background numerical noise to any a required level so that the "false"
numerical noises are negligible compared with the "true" physical solution and
thus the CNS solution can be used as a "clean" benchmark solution for
comparison. It is found that the numerical noises as tiny artificial stochastic
disturbances could indeed lead to large-scale deviations of simulations not
only in spatio-temporal trajectories but also even in statistics. Especially,
these numerical noises (as artificial stochastic disturbances) even lead to
different types of flows: the shearing convection occurs for the RKwD
simulations, and its corresponding flow field turns to a kind of zonal flow
thereafter, however the CNS benchmark solution always sustains the non-shearing
vortical/roll-like convection during the whole process of simulation. Thus, we
provide a rigorous evidence that numerical noises as a kind of small-scale
artificial stochastic disturbances have quantitatively and qualitatively
large-scale influences on a sustained turbulence, i.e. the 2D turbulent RB
convection considered in this paper.
