Near wall patch representation of wall bounded turbulence

Wall bounded turbulent flows at high Re are characterized by the separation of scales between the near-wall eddies and the larger structures farther away from the wall. It is well known that there is a near-wall autonomous cycle of self-sustaining mechanisms whose existence does not depend on the outer layer (Jimenez et al., JFM Vol. 389). In addition, there is evidence that the large scale structures in the outer layer modulate the inner layer turbulence (Marusic et al., Science Vol. 329). Lastly, recent work by Lee et al. (JFM Vol. 774) suggests that the small-scale dynamics of the near-wall region are Re independent. With these works in mind, we formulate numerical simulations of near-wall turbulence in a small domain localized to the boundary, whose size scales in viscous units. The primary goal is to accurately capture the small scales in the near-wall region, which we assess by comparing our statistics to those of a posteriori filtered DNS. To mimic the environment in which the small-scale near-wall turbulence evolves, our formulation accounts for the flux of mean momentum and turbulent kinetic energy through the upper boundary of the domain. We discuss the degree to which our formulation successfully describes near-wall dynamics, and its utility in a wall-modeled LES.