The First Turbulence

Abstract

Chaotic, eddy-like motions dominated by inertial-vortex forces begin immediately at Planck scales in a hot big-bang cosmological model. This quantum-gravitational-dynamics epoch produced not only the first space-time-energy of the universe but the first large Reynolds number turbulence and turbulent mixing with Kolmogorov and Batchelor-Obukhov-Corrsin velocity and temperature gradient spectra. Strong-force-freeze-out and inflation produced the first fossil temperature turbulence by stretching the fluctuations beyond the horizon scale ct of causal connection at light speed c in time t. The spectrum increases toward a maximum at the smallest (fossilized Planck) scales, contrary to either the flat Harrison-Zel'dovich form usually assumed or Tilted forms with maxima at large (fossilized strong-force) scales used to explain observed plasma epoch temperature fluctuations as acoustic. A second transition to turbulence was inhibited by buoyancy forces from the first structures, as indicated by observations that dT/T in the cosmic microwave background radiation is only 10^-5 except at the spectral peak and increases smoothly as wavenumber k^1/6. The peak is therefore due to gravitational structure not sound.