The effects of large-scale sweeping velocity on the turbulent cascade to small scales are examined for two problems: the advection of a passive scalar by a multivariate-Gaussian velocity field and incompressible Alfvén-wave turbulence. In both cases, the sweeping produces anisotropy and reduces the strength of cascade. If the direction of the sweep velocity varies with time, a balance is reached between this anisotropy and isotropizing effects associated with the change of direction.
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Chen et al. (1997) studied this question.