The role of VLSMs in transferring energy across spatiotemporal scales and the wall-normal direction in a turbulent channel flow

Very-large-scale motions (VLSMs) in turbulent flows are well studied in the context of their energetic signature in the streamwise spectrum (e.g. Kim & Adrian 1999; Monty et al. 2009) and statistical significance through the amplitude modulation coefficient (e.g. Hutchins & Marusic 2007), however, their dynamical function is less understood. We investigate the role VLSMs in transferring energy across scales in the spectral domain and along the wall-normal direction in physical space for turbulent channel flow (Re_τ=550). The nonlinear term in the Navier-Stokes equation accounts for energy transfer across scales, which is not only globally conservative but also conservative on a triad-by-triad basis (Kraichnan 1957, Schmid & Henningson 2001). Intra-triad energy conservation is used to study the function of a representative VLSM mode in transferring energy across resonant triads. The flow is represented by spatio-temporal Fourier modes that are functions of the wall-normal coordinate and identified by their streamwise, spanwise, and frequency wavenumber components. This approach compactly represents the flow and retains information from all spatial dimensions and time. The frequency component defines a critical layer which fixes the mode's wall-normal location. As a result, every mode has an associated size, frequency, and wall-normal location. This representation is used to study how the VLSM links individual triads and routes energy across the inner and outer layers of the turbulent channel.