The Fractal Turbulence and the Origin of Large Scale Structure

We have suggested a scenario of fractal turbulence which might explain the origin of galaxies and the observed large scale structure of the universe (Liu and Deng, 1987). Under the condition of the early universe, the cosmic fluid can be regarded as incompressible. If we assume that the density perturbations in the early universe are adiabatic and have the scale-free Zeldovich spectrum, we may obtain the spectrum of the velocity perturbations. Perturbations with scales less than horizon will undergo dissipative process by Thomson scattering. So, the cosmic fluid can be considered as a viscous fluid (Peebles, 1971). We can find the largest and smallest scale of the perturbations in the cosmic fluid by taking account of the Reynold's number on given scale and the scale of horizon. Using the present values of Hubble constant and the mean density of matter, we have found that on the scale of horizon the Reynold's number is just the order of 102. This result shows that perturbations with scale a little smaller than horizon may produce Karman vortices before recombination and the vortices might form fractal turbulence due to Thomson drag.