astronomix.analysis_helpers.energy_spectrum

`astronomix.analysis_helpers.energy_spectrum`#

Shell-averaged energy, cross and helicity spectra of 3D vector fields.

Provides the FFT-based spectral diagnostics used by the snapshot machinery: generic vector-field energy and cross spectra, plus the MHD physics wrappers (density-weighted kinetic energy, magnetic energy, cross helicity, magnetic helicity). All spectra share a single shell-binning of the wavenumber grid so their bins line up.

Module Contents#

Functions#

`vector_field_energy_spectrum`	Energy spectrum E(k) of a vector field (fx, fy, fz).
`vector_field_cross_spectrum`	Cross spectrum C(k) between two vector fields f1 and f2.
`get_kinetic_energy_spectrum`	Kinetic energy spectrum with density weighting.
`get_magnetic_energy_spectrum`	Magnetic energy spectrum.
`get_cross_helicity_spectrum`	Cross-helicity spectrum H_c(k).
`get_magnetic_helicity_spectrum`	Magnetic helicity spectrum H_m(k).

Data#

`LOG_BINNING`
`INTEGER_BINNING`
`PHYSICAL_BINNING`

API#

astronomix.analysis_helpers.energy_spectrum.LOG_BINNING = 0#

astronomix.analysis_helpers.energy_spectrum.INTEGER_BINNING = 1#

astronomix.analysis_helpers.energy_spectrum.PHYSICAL_BINNING = 2#

astronomix.analysis_helpers.energy_spectrum.vector_field_energy_spectrum(fx, fy, fz, energy_coeff=1.0, binning=PHYSICAL_BINNING)[source]#

Energy spectrum E(k) of a vector field (fx, fy, fz).

Satisfies: sum(E(k)) == mean(c * |f|^2) over the domain (shell-summed convention).

Args:: fx, fy, fz: Field components, each shaped (Nx, Ny, Nz). energy_coeff: Scalar multiplier c (default 1.0). binning: LOG_BINNING, INTEGER_BINNING, or PHYSICAL_BINNING.
Returns:: wavenumber_centers: Physical wavenumber bin centers. Ek: Energy spectrum per bin.

Based on: https://qiauil.github.io/blog/2026/tke_spectrum/

astronomix.analysis_helpers.energy_spectrum.vector_field_cross_spectrum(f1x, f1y, f1z, f2x, f2y, f2z, coeff=1.0, binning=PHYSICAL_BINNING)[source]#

Cross spectrum C(k) between two vector fields f1 and f2.

Satisfies: sum(C(k)) == mean(c * f1 . f2) over the domain.

The spectrum is the shell-summed co-spectrum (real part of the conjugate dot product in Fourier space). Unlike energy spectra, cross spectra are not positive-definite.

Args:: f1x, f1y, f1z: First field components, each (Nx, Ny, Nz). f2x, f2y, f2z: Second field components, each (Nx, Ny, Nz). coeff: Scalar multiplier (default 1.0). binning: LOG_BINNING, INTEGER_BINNING, or PHYSICAL_BINNING.
Returns:: wavenumber_centers: Physical wavenumber bin centers. Ck: Cross spectrum per bin.

astronomix.analysis_helpers.energy_spectrum.get_kinetic_energy_spectrum(vx, vy, vz, rho, binning=PHYSICAL_BINNING)[source]#

Kinetic energy spectrum with density weighting.

Uses w = sqrt(rho) * u so that sum(E_k) == mean(0.5 * rho * |u|^2).

Args:: vx, vy, vz: Velocity components, each (Nx, Ny, Nz). rho: Density field, (Nx, Ny, Nz). binning: LOG_BINNING, INTEGER_BINNING, or PHYSICAL_BINNING.
Returns:: wavenumber_centers, Ek: Wavenumber bin centers and kinetic energy spectrum.

astronomix.analysis_helpers.energy_spectrum.get_magnetic_energy_spectrum(Bx, By, Bz, mu0=1.0, binning=PHYSICAL_BINNING)[source]#

Magnetic energy spectrum.

sum(E_m) == mean(|B|^2 / (2 * mu0)).

Args:: Bx, By, Bz: Magnetic field components, each (Nx, Ny, Nz). mu0: Magnetic permeability (default 1.0 for Alfvénic units). binning: LOG_BINNING, INTEGER_BINNING, or PHYSICAL_BINNING.
Returns:: wavenumber_centers, Em: Wavenumber bin centers and magnetic energy spectrum.

astronomix.analysis_helpers.energy_spectrum.get_cross_helicity_spectrum(vx, vy, vz, Bx, By, Bz, binning=PHYSICAL_BINNING)[source]#

Cross-helicity spectrum H_c(k).

Cross helicity: H_c = integral(u . B) dV. Spectrum satisfies: sum(H_c(k)) == mean(u . B).

Args:: vx, vy, vz: Velocity components, each (Nx, Ny, Nz). Bx, By, Bz: Magnetic field components, each (Nx, Ny, Nz). binning: LOG_BINNING, INTEGER_BINNING, or PHYSICAL_BINNING.
Returns:: wavenumber_centers, Hc: Wavenumber bin centers and cross-helicity spectrum.

astronomix.analysis_helpers.energy_spectrum.get_magnetic_helicity_spectrum(Bx, By, Bz, binning=PHYSICAL_BINNING)[source]#

Magnetic helicity spectrum H_m(k).

Magnetic helicity: H_m = integral(A . B) dV, where B = curl(A). In a periodic domain with Coulomb gauge, the vector potential is recovered in Fourier space as: A_hat(k) = +i k x B_hat(k) / |k|^2.

Spectrum satisfies: sum(H_m(k)) == mean(A . B).

Args:: Bx, By, Bz: Magnetic field components, each (Nx, Ny, Nz). binning: LOG_BINNING, INTEGER_BINNING, or PHYSICAL_BINNING.
Returns:: wavenumber_centers, Hm: Wavenumber bin centers and magnetic helicity spectrum.