We study the direct enstrophy cascade in a two-dimensional flow generated in an electromagnetically driven thin layer of fluid. Due to the presence of bottom friction, the energy spectrum deviates from the classical Kraichnan prediction k −3 . We find that the correction to the spectral slope depends on the thickness on the layer, in agreement with a theoretical prediction based on the analogy with passive scalar statistics.
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Boffetta et al. (2005) studied this question.