Classical turbulence remains a mystery. This is in part responsible by the large number of data points needed to solve the numerical equations of motion. Reasonably it takes at least 100,000 points for a volume of 1 cubic centimeter, about 1/8 the size of a sugar cube. Predicting climatic turbulence of hundreds cubic kilometers would be impossible even by the use of parallel supercomputers. However, human ingenuity allows the use of time-average analysis making turbulence manageable in a controlled environment.

The phenomena of turbulence can be observed in enclosed pipe flows, e.g. human blood flowing in capillary systems; open channels and rivers; tropical cyclones and hurricanes; and on the galactic scale, the eddies of giant whirlpool galaxy. More complex turbulences requiring knowledge of magnetohydrodynamics (MHD) are the prominences of stellar systems.

In controlled studies, a dimensionless quantity known as Reynolds number (R) has been determined to characterize the onset of turbulence. For R ≤ 2000 the flow is laminar, where the velocity vector of each fluid particle is parallel to the overall fluid flow. For 2000 < R < 4000 the flow slowly transitioned toward turbulence. For R > 4000 the flow is effectively turbulent, while it is possible for some parts of the fluid still remain laminar. Principle of mechanical similarity has experimentally scaled R as the dimensionless ratio of inertial force (normal?) over the viscous force (tangential?). But what is so magical about the lower bound value of 2000? This is approximately the dimensionless mass ratio of a proton to that of an electron (experiment: 1836.15267). Because of this near equality it can be said that the onset of quantum turbulence is just the excess mass ratio beyond this value. By no coincidence, both liquid helium isotopes He (boiling point 3.195°K) and He (bp 4.216°K) exhibit turbulence of superfluidity both with excess mass ratio greater than 1836. On the other hand, liquid hydrogen (bp 20.37°K) mass ratio exactly 1836 does not exhibit superfluidity even at the lambda point or triple point where solid, liquid, and gas coexist.