Inverse versus direct cascades in turbulent advection

@article{Chertkov1998InverseVD,
  title={Inverse versus direct cascades in turbulent advection},
  author={Michael Chertkov and Igor V. Kolokolov and M. Vegrassola},
  journal={Physical Review Letters},
  year={1998},
  volume={80},
  pages={512-515}
}
A model of scalar turbulent advection in compressible flow is analytically investigated. It is shown that, depending on the dimensionality d of space and the degree of compressibility of the smooth advecting velocity field, the cascade of the scalar is direct or inverse. If d . 4 the cascade is always direct. For a small enough degree of compressibility, the cascade is direct again. Otherwise it is inverse; i.e., very large scales are excited. The dynamical hint for the direction of the cascade… 
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The growing importance of knowledge and innovations for modern organisations (Davenport, DeLong, & Breers, 1998; Drucker, 1998; Nonaka, 1998; Stewart, 1997), and increasing demands for new skills and
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