From 2D power to cumulative velocity variance

An idealized isotropic centroid field with P_2D(k) ∝ k^−β

Power slope β2.60

Beam FWHM0.45

Annular-mean P_2D(k)

Variance per logarithmic interval

Cumulative σ_v(<L)

intrinsicafter beamvariance bookkeeping

These are distinct quantities. P_2D(k) is an annular mean. In two dimensions the number of modes per logarithmic interval grows approximately as k², so dσ²/dln k ∝ k²P_2D(k). The cumulative curve sums those variance contributions from scales smaller than L.

From 2D power to cumulative velocity variance

Annular-mean P2D(k)

Variance per logarithmic interval

Cumulative σv(<L)

Annular-mean P_2D(k)

Cumulative σ_v(<L)