Merchav Prize Seminar | A Nonlinear Diagnostic for Scale Interactions in Turbulent Flows

Turbulent flows are composed of a wide range of large- and small-scale coherent motions. These motions are responsible for practical engineering effects, like the generation of turbulent drag. Scale interactions between large- and small-scales in turbulent wall-bounded flows have historically been investigated by linear analysis which requires a filtering and envelope procedure. The phase delay between large and envelope of small scales was explained as a spatial delay in the flow. However, the linear analysis depends on the cutoff wavelength in the filtering process and the use of an artificial envelope of small scales that does not exist in real data. The Fourier transformed momentum equation shows that only the nonlinear advection term contributes to the interaction among different scales and thus all interactions occur in triads. A nonlinear diagnostic, the bispectrum, is introduced and applied to a numerical turbulent channel flow. The bispectrum shows that large-scale structure that is most strongly coupled, in a triadic sense, to small scales, is the very-large-scale-motion (VLSM). The phase of the bispectrum, the biphase, shows that there is an interaction delay in the triadic interaction. This will help to understand the scale interactions better and hopefully shed some light on the flow control in the turbulent boundary layers.