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Turbulence — the Energy Cascade
Stir energy in at one big scale and it does not stay there. Big swirls spin off medium swirls, medium spin off small, small off smaller — until the eddies are tiny enough for friction to burn the energy off as heat. The dye gets stretched and folded across every scale at once.
The journey: Richardson’s rhyme (1922) — “big whirls have little whirls” — became Kolmogorov’s 1941 law: in the range between stirring and friction the energy spectrum must fall as k⁻⁵⃗³. The plot bottom-right is this field’s spectrum against that slope.