Flows in natural bodies of fluid often become turbulent, with eddy-like motions dominated by inertial-vortex forces. Buoyancy, Coriolis, viscous, self-gravitational, electromagnetic, and other force constraints produce a complex phase space of wave-like hydrodynamic states that interact with turbulence eddies, masquerade as turbulence, and preserve information about previous hydrodynamic states as fossil turbulence. Evidence from the ocean, atmosphere, galaxy and universe are compared with universal similarity hypotheses of Kolmogorov (1941, 1962) for turbulence velocity u, and extensions to scalar fields θ like temperature mixed by turbulence. Universal u and θ spectra of natural flows can be inferred from laboratory and computer simulations with satisfactory accuracy, but higher order spectra and the intermittency constant u of the third Kolmogorov hypothesis (1962) require measurements at the much larger Reynolds numbers found only in nature. Information about previous hydrodynamic states is preserved by Schwarz viscous and turbulence lengths and masses of self-gravitating condensates (rarely by the classical Jeans length and mass), as it is by Ozmidov, Hopfinger and Fernando scales in hydrophysical fields of the ocean and atmosphere. Viscous-gravitational formation occurred 104 -105 y after the Big Bang for supercluster, cluster, and then galaxy masses of the plasma, producing the first turbulence. Condensation after plasma neutralization of the H-4 He gas was to a primordial fog of sub-solar particles that persists today in galactic halos as dark matter. These gradually formed all stars, star clusters, etc (humans!) within.