Swift generator for 3D magnetohydrodynamic turbulence

Turbulent states of motion are almost unavoidable in fluids, gases, and plasmas. The ubiquitous presence of turbulence largely contributes to the central role that its study holds in many research fields. This work focuses on space and astrophysical plasmas, where magnetohydrodynamic turbulence is observed nearly everywhere. However, it builds on an issue that is shared by all turbulence-related field of studies: direct numerical simulations (DNS), required to verify turbulent states properties such as scaling law behaviors, require substantial computing resources.

The presentation will introduce the audience to BxC^[1], an analytic generator of realistic-looking turbulent magnetic fields, that computes 3D O(1000³ grid points) solenoidal vector fields in minutes to hours on desktops. The model is inspired by recent developments in 3D incompressible fluid turbulence theory: intermittent, multifractal random fields are generated through non-linear transformations of a Gaussian white noise vector, combined to specifically designed geometrical constructions. Furthermore, the model is implemented starting from a modified Biot-Savart law, which allows for a clear interpretation of the BxC parameters.

The turbulent magnetic field realized with BxC is then compared and validated against a much more computationally expensive DNS in terms of: (i) characteristic sheet-like structures of current density, (ii) volume-filling aspects across current intensity, (iii) power-spectral behaviour, (iv) probability distribution functions of increments for magnetic field and current density, structure functions, spectra of exponents, and (v) partial variance of increments.

 

[1] Durrive, J.-B., Changmai, M., Keppens, R., Lesaffre, P., Maci, D., and Momferatos, G. (2022). Swift generator for three-dimensional magnetohydrodynamic turbulence. Phys. Rev. E, 106:025307