Analytic 1D power spectra: β-profile (red), Kolmogorov noise (blue), β-profile perturbed by the noise (black; ). The spectrum is normalized to the value at k₀ = 1/L = 0.01 (dimensionless units; 2π is dropped for clarity). The core radius is r_c = 20, i.e. L/5. The relative amplitude of the noise is ~10 percent. The noise clearly emerges beyond the core radius (k > 0.05), regardless of large-scale structures.