Study on Complex POD Analysis for the Estimation of Coherent Structures

Abstract

The estimation of the coherent structures existing in a random phenomenon is important for the study of fluctuating fields, such as the flow fields or the pressure fields around a structure. For the estimation of the coherent structures, Proper Orthogonal Decomposition (POD) is available, which is able to obtain the coherent structures as the principal components of the fluctuating fields. However the components calculated by the POD analysis are stationary modes in space, therefore it is impossible to express the advection phenomenon as a single principal component. In such a case, the complex POD analysis is available. In this paper, the procedure of the complex POD analysis is described. And also the interpretation of it by the use of the complex envelope is shown. The calculations of some model cases are carried out by the POD analysis and the complex POD analysis. By comparing the results, the effectiveness of the complex POD analysis is shown.