Scale-by-scale kinetic energy budget near the turbulent/nonturbulent interface

A scale-by-scale kinetic energy budget is analyzed near the turbulent/nonturbulent interfacial (TNTI) layer with direct numerical simulations (DNS s) of a local turbulent front evolving without mean shear (shear-free turbulence). A local volume average is used to decompose the flow variables into their large-scale and small-scale components near the TNTI layer. The kinetic energy and interscale energy flux from large to small scales of motion are shown to be severely depleted for small scales within the viscous superlayer. The forward interscale energy transfer from large to small scales near the TNTI layer is mostly caused by the velocity gradient in the interface normal direction while the velocity gradient in the tangential direction transfers, on average, the energy from small to large scales. The velocity gradients that cause the forward energy transfer near the TNTI layer are associated with a compressive motion in the interface normal direction and a shearing motion due to the velocity in the tangential direction. The pressure diffusion increases the kinetic energy near the interface except at small scales within the TNTI layer. The averaged pressure diffusion term at the small scales within the TNTI layer has negative values, which are consistent with the presence of small-scale vortices within the TNTI layer. The transports by turbulent diffusion and interaction between large and small scales are negatively correlated even near the TNTI layer, and their effects are locally canceled by each other as also observed in other turbulent flows.