Convergence study of multi-field singular value decomposition for turbulence fields

TL;DR

This paper investigates the convergence properties of multi-field singular value decomposition (MFSVD) in turbulence analysis, demonstrating its efficiency in capturing nonlinear correlations and converging faster than single-field methods.

Contribution

The study provides a detailed convergence analysis of MFSVD applied to turbulence fields, highlighting its improved efficiency over traditional single-field approaches.

Findings

MFSVD reproduces power-law-like singular value spectra in artificial multi-scale structures.

In turbulence data, MFSVD converges faster for nonlinear quantities than single-field SVD.

Relative errors decrease significantly with fewer modes in multi-field analysis.

Abstract

Convergence of a matrix decomposition technique, the multi-field singular value decomposition (MFSVD) which efficiently analyzes nonlinear correlations by simultaneously decomposing multiple fields, is investigated. Toward applications in turbulence studies, we demonstrate that SVD for an artificial matrix with multi-scale structures reproduces the power-law-like distribution in the singular value spectrum with several orthogonal modes. Then, MFSVD is applied to practical turbulence field data produced by numerical simulations. It is clarified that relative errors in the reproduction of quadratic nonlinear quantities in multi-field turbulence converge remarkably faster than the single-field case, which requires thousands of modes to converge.