An orthogonal decomposition for nonlinear modal analysis

An orthogonal modal decomposition for identifying triadic interactions in fluid flows is presented. The decomposition is based on spectral momentum transfer and extracts coherent structures that partake in three-wave interactions and are optimal in terms of the third-order space-time flow statistics. The method distinguishes between two quadratically interacting components, one acting as a catalyst and the other as a donor of momentum, that collectively contribute to a tertiary component, the recipient. The resulting modes maximize the covariance between the donor and recipient for each triad. The method can be understood as an extension of bispectral mode decomposition (BMD) by considering the exact form of the quadratic nonlinearity of the Navier-Stokes equations. Unlike BMD, and more similar to classical proper orthogonal decomposition (POD), it provides ranked bases for the donor and recipient that are jointly optimal and orthonormal in their respective inner products. Two applications are considered: numerical data of a canonical unsteady cylinder wake and experimental data of a turbulent wind turbine wake by Biswas and Buxton [1].