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

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.