Biphase as a diagnostic for scale interactions in wall-bounded turbulence

The phase of the bispectrum of a turbulent velocity signal is presented as a unified tool to relate the geometry and energetics of interactions between large- and small-scale motions in wall-bounded turbulence. The normalized bispectrum naturally describes nonlinear triadic interactions and thus is ideally suited for measuring the magnitude of coupling between the different scales of turbulence without the use of filtering procedures. In this study, the corresponding biphase is shown to represent the delay between large and small scales imposed by convective interactions and simultaneously to describe the direction of the turbulent streamwise energy cascade. The bispectrum and biphase are measured from a direct numerical simulation of a high-Reynolds-number channel flow and used to illustrate the relationship between the relative geometry of the interacting scales, the interaction delay, and the cascade of energy between them, offering an integrated perspective on scale interactions in turbulence through a single statistic.