StructureFunctions.jl

Structure functions of turbulent and spatially varying fields, on point lists, multi-fields, grids and the sphere, with the spectra, fluxes and fits derived from them.

Features

• Operators of any order: the longitudinal, transverse and full increments, signed transverse components with a stated convention, scalar and mixed velocity–scalar moments, cross-field advective moments, the whole increment moment tensor.
• Point lists (D, N) on the serial, threaded, distributed, MPI and GPU backends, with cell culling, pair weights, joint (distance × value) and (distance × angle) histograms, the six isotropic invariants and the Helmholtz split in one pass, and batches over auxiliary axes.
• Grids through FlowGeometries: uniform, stretched and lat-lon grids, masks at any order, and an exact transform engine that computes each polynomial operator at every lag at once, on the CPU or a device. A direct lag sweep computes the same quantity by a different route.
• The sphere: parallel-transported pair frames, SphericalDistance(R), the zonal transform, and a harmonic route with Legendre and Wigner-d kernels.
• One-dimensional lists in O(N log N), and scattered points by non-uniform FFT, which soft bins and is not exact.
• Spectra from structure functions in one, two and three dimensions and on the sphere, exact on grids through the lag space; the Helmholtz E/B split; fluxes from third-order functions with their boundary terms; regularised fits of spectra and fluxes with posterior covariances.
• Exact laws: four-fifths, four-thirds and Yaglom inversions.

Quick start

using StructureFunctions: Calculations as SFC, StructureFunctionTypes as SFT, LogBinEdges
using ComputationalBackends: ComputationalBackends as CB

x = rand(2, 2048) .* 1.0e4          # (D, N) coordinates
u = randn(2, 2048)                  # (D, N) velocity components
bins = LogBinEdges(collect(exp10.(range(log10(50.0), log10(5.0e3); length = 41))))

sf = SFC.calculate_structure_function(SFT.L2SFType(), x, u, bins; backend = CB.AutoBackend())
sf.distance, sf.values              # the bin edges and the averaged ⟨δu_L²⟩ per bin

res = SFC.calculate_structure_functions_single_pass(x, u, bins)
res.L2, res.T2, res.helmholtz       # all six invariants and the Helmholtz split in one pass

Where to next

• Theory — the definitions, conventions and relations the code implements.
• Walkthrough — one analysis end to end, on fields whose answers are known.
• Architecture — operator × schedule × backend, and how a call becomes a kernel.
• Backends and GPU acceleration — where each calculation runs.
• Extensions — what each optional package adds.
• Exact laws, Validation, API reference.

Installation

using Pkg
Pkg.add("StructureFunctions")

The package depends on ComputationalBackends for the backend types; bring the trigger packages of the extensions you need (OhMyThreads, KernelAbstractions + CUDA, FFTW, FlowGeometries, Bessels, NUFSHT, NonuniformFFTs or FINUFFT, LsqFit). The algorithm tags come from SpectralBackends, a dependency.