Role of pressure in Reynolds shear stress transport in high Re wall-bounded turbulence*

We investigate the role of pressure in the transport equation of the Reynolds shear stress (RSS), ⟨u'v'⟩, in high Re wall-bounded turbulent channel flows. The spectral analysis technique from Lee & Moser (J. Fluid Mech., vol 860, 886-938) is applied to channel flow DNS data at Re_τ = 5200. The spectral density of the RSS is highly concentrated in streamwise-elongated modes with a negligible contribution from spanwise-elongated modes. However, there is a non-negligible production of RSS in the spanwise elongated modes, and the inter-scale transfer mechanism moves RSS from streamwise elongated  to spanwise elongated modes. The pressure-strain correlation is the only term in the transport equation that is a sink of RSS in spanwise elongated modes. Decomposing the pressure into rapid, slow, and Stokes contributions shows that the rapid pressure-strain is responsible for removing about half of the RSS produced in the spanwise elongated modes. The slow pressure-strain removes the remainder, plus the RSS deposited in spanwise elongated modes via scale transfer. These observations can be interpreted as the consequence of the kinematic continuity constraint on the production and scale transfer processes.