Scaling of diffusivity: prediction of growth rates and distance-neighbour functions for sub-ranges encountered in atmospheric turbulence

Torben Mikkelsen
Wind Energy Department, Risř National Laboratory, Denmark

Turbulence, as we encounter in the atmosphere or in plasmas, is known to contain distinct subranges. The subranges are governed by scaling parameters and distinguished by scale.

In the atmosphere, for instance, the most known and studied subrange is the Inertial subrange. Turbulence here is characterized by being 3-dimensional, isotropic, and is governed by a single controlling scaling parameter, the dissipation rate.

At larger scales or closer to the ground, however, the atmospheres turbulence is no longer isotropic, and strong shear driven turbulence can be encountered. Here, the constant shear stress velocity u* rather than the dissipation rate seems the appropriate scaling parameter. Dimensional analysis leads to the prediction of a ~ u*2 k-1 spectral subrange for wave numbers with a wavelength larger than the height above ground.

In the free atmosphere high above the surface layer on the contrary, turbulence at ~10 km scale and larger has been observed to be semi two-dimensional, within a distinct Enstrophy subrange, with spectral energy dependence of ~k-3.

Similarly, one-dimensional turbulence in confined drift-wave plasmas has been predicted to contain distinct: Production (k-3), Coupling (k-3), and Inertia (k-2) energy subranges, Tchen et al (1980).

However, diffusion rates for growth of a puff of trace particles are also known to differ according to scale and subrange:

In this talk, a new and simple scaling method for a puff's diffusion, that is, its scale and time dependent diffusivity, K(y,t), is presented. The scaling seems to unify all hitherto observed subrange-specific growth-rate and distance-neighbour functions encountered in the atmospheres surface layer.

If the scaling is universal it can be further applied to growth-rates and distance-neighbour function prediction for subranges encountered in turbulent plasmas and fluids.


  1. C.M. Tchen, H.L. Pécseli, and S.E. Larsen, "Strong Turbulence in Low-beta Plasmas", Plasma Phys. 22, 817-829 (1980).