Identifying permitted triadic interactions and their effect on amplitude modulation in a turbulent channel flow*

We define criteria for quantifying permittable interactions between triadically compatible, spatio-temporal wavenumbers in a turbulent channel flow. Permitted interactions are determined based on the relative strength of the nonlinearly interacting modes and the strength of the interaction of the entire wavenumber triad, termed the interaction coefficient. The effect of these permitted interactions on the amplitude modulation statistic is studied in the framework of phase relationships; specifically, the relative phase between the large scales and the envelope of the small scales. A triad-by-triad approach is taken to explore the effects of individual triadic relationships on the amplitude modulation coefficient. We determine whether there are key interactions that persist across the channel height and look at how the number of permitted interactions change as a function of wall-normal distance. Ultimately, taking an individual triad approach to study the interactions between large- and small-scales lends itself well to low-order modeling applications as it may provide insight to key interactions that govern the flow and allow for a reduction in the number of scales required to describe the system.