Kelvin-Helmholtz wavepackets in Actuator disk wake with turbulent co-flow*

The interaction of a dragging, fixed thrust coefficient actuator disk with decaying homogeneous isotropic turbulence (HIT) of varying spatial integral length scales and dissipation rates is studied using Large Eddy Simulation performed at high resolution. The shear layer entrainment (and hence wake recovery) is shown to be strongly sensitive to the integral length scale of the upstream HIT (as opposed to its intensity) and this observation is reconciled using a space-time modal decomposition of the flow field to identify the dominant Kelvin-Helmholtz wavepackets that dictate the shear layer growth rate. This spectral proper orthogonal decomposition (SPOD) further suggests that due to the turbulent co-flow and core, the overall fluctuation fields lack any tonal behavior, and hence a low-rank projection-based representation is not possible. However, a truncated representation of the turbulent wake based on these SPOD modes can be enriched to its full spectral bandwidth using spectrally and spatially localized Gabor wavepackets, previously used to enrich LES of boundary layer turbulence (Ghate & Lele, J. Fluid Mech., 2017).