The effects of large-scale sweeping velocity on the turbulent, cascade
to small scales are examined for two problems: the advection of a pas
sive scaler by a multivariate-Gaussian velocity field and incompressib
le Alfven-wave turbulence. In both cases, the sweeping produces anisot
ropy and reduces the strength of cascade. If the direction of the swee
p velocity varies with time, a balance is reached between this anisotr
opy and isotropizing effects associated with the change of direction.