With Gawedzki, he established " anomalous inertial range scaling of the structure functions for a model of homogeneous, isotropic advection of a passive scalar by a random vector field . " ( Kolmogorov's theory of homogeneous turbulence breaks down for a particular model .)
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For homogeneous turbulence ( i . e ., statistically invariant under translations of the reference frame ) this is usually done by means of the " energy spectrum function ", where is the modulus of the wavevector corresponding to some harmonics in a Fourier representation of the flow velocity field:
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