Kolmogorov Turbulence: The −5/3 Power Law Hidden in Chaos

ε (dissipation rate): 1.0 Shifts the −5/3 line up/down
η (Kolmogorov scale): 0.01 Moves the dissipation cutoff

Key fact

At k = 2k₀:

E drops by 25/3 ≈ 3.17×

Not 2×, not 4× — exactly 25/3. The exponent is precisely −5/3 across 4 orders of magnitude.

Reference lines

White noise (slope 0)
Brownian (slope −2)
Kolmogorov −5/3

Slope ruler

Drag the ruler on the chart to measure rise/run in the inertial subrange. Lock onto the red curve to verify slope = −5/3 ≈ −1.667.