Identification of interscale dynamics and triadic interactions of coherent structures in turbulent wakes

Turbulent wakes are often characterized by dominant coherent structures over disparate scales. Coherent structure formation, evolution, and breakdown can be attributed to kinetic energy transport and transfer between spatio-temporal scales. Energy transfer is governed by triadic interactions, which are non-linear, non-local, and manifest as a triplet of wavenumbers or frequencies. The spatial and spectral qualities of a broad range coherent structure frequency scales are identified through Koopman mode decomposition and triple decomposition of the velocity in the wake of a square cylinder at Re=3900. The formulation results in a system of evolution of coherent kinetic energy equations based on specific identified scales coupled by interscale energy transfer terms. The frequency sum-zero condition of triadic interactions is implicitly enforced, and coherent kinetic energy based on interaction of two scales and energy budget of a single scale are explicitly quantified. Spectra reveal organization for both forward and reverse energy cascade. While turbulence production is concentrated in lower frequency scales related to vortex shedding, the transfer between scales is significant over a wide range.