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This is a photograph I took of the picture of Kolmogorov displayed at the 1989 conference in his honor the year after his death, Moscow, USSR. I gave the second talk, on "contributions of Kolmogorov to oceanography". Kolmogorov's 1941 universal similarity hypotheses are justified by the Navier-Stokes equations of momentum conservation when the inertial-vortex forces v x \omega have driven a non-linear, self-similar cascade of coupled eddy motions from scales larger than L_K to a much larger "Obukhov" or energy scale L_O. By definition, turbulence is confined to scales where v x \omega forces dominate. For cosmological purposes, L_O must be smaller than ct (the Hubble, or Horizon, scale of causal connection). Kolmogorov's third, or intermittency, hypothesis is a refinement of the first two to take into account the intermittent lognormality of the viscous dissipation rate epsilon which results from a wide range of scales in the non-linear, self- similar cascade of turbulence from small scales to large. The number density of primordial fog particles (the baryonic dark matter), initially found only within protoglobularcluster fragments, enters into a non-linear, self-similar, gravitational-accretion cascade to form stars a million times more massive, so that the number density of these dark matter particles becomes an intermittent lognormal with an enormous mean to mode ratio. Thus, PFPs are difficult to detect by star-microlensing, just as high Reynolds number turbulence patches in the ocean are difficult to detect by sparse vertical soundings.
astro-ph/9904269
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astro-ph/9908335
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astro-ph/9904330
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