Basis Dispersionlet Bispectral Analysis in 3D systems*

Ritz-type bispectral analysis¹ is a class of techniques that use statistical correlations in turbulence fluctuation data to infer the underlying model equations.  This offers a novel approach to theory-experiment comparisons, and more recent techniques can also infer spatial information such as profile functions and topological boundaries from fluctuation data.  The most recent addition to this class of techniques is basis dispersionlet bispectral analysis, which uses wavelet-like operators, or dispersionlets, to represent the underlying model equations. 

One issue encountered with this method is the analysis of three-dimensional systems.  Ritz-type bispectral analysis typically assumes a 2D model equation, relying on the anisotropy of the magnetized plasma to create a quasi-2D system.  However, significant parallel variation can still exist, presenting challenges for this type of algorithm.

The present work will explore the limitations of this method and possible solutions to these problems.  These will be demonstrated through analysis of turbulence data from the STORM module of BOUT++.² 

 

References:

1.  Ch. P. Ritz and E. J. Powers, Physica D 20, 320 (1986).

2.  F. Riva, F. Mililtello, S. Elmore, J. Omotani, B. Dudson, N. R. Walkden, Plasma Phys. Controlled Fusion 61, 095013 (2019).