A numerical investigation of the Stokes boundary layer in the turbulent regime

The Stokes boundary layer in the turbulent regime is investigated by using large-eddy simulations (LES). The Reynolds number, based on the thickness of the Stokes boundary layer, is set equal to Reδ = 1790, which corresponds to test 8 of the experimental study of Jensen et al. (J. Fluid Mech. vol. 206, 1989, p. 265). Our results corroborate and extend the findings of relevant experimental studies: the alternating phases of acceleration and deceleration are correctly reproduced, as is the sharp transition to turbulence, observable at a phase angle between 30° and 45°, and its maximum between 90° and 105°. Overall, a very good agreement was found between our LES first- and second-order turbulent statistics and those of Jensen et al. (1989). Some discrepancies were observed when comparing turbulent intensities in the phases of the cycle characterized by a low level of turbulent activity. In the central part of the cycle, namely from the mid acceleration to the late deceleration phases, fully developed equilibrium turbulence is present in the flow field, and the boundary layer resembles that of a canonical, steady, wall-bounded flow. In those phases characterized by low turbulent activity, two separate regions can be detected in the flow field: a near-wall one, where the vertical turbulent kinetic energy varies much more rapidly than the other two components, thus giving rise to the formation of horizontal, pancake-like turbulence; and an outer region where both vertical and spanwise velocity fluctuations vary much faster than the streamwise ones, hence producing cigar-like turbulence. As a side result, the range of application of the plane-averaged dynamic mixed model was assessed based on the qualitative behaviour over the cycle of a significant parameter representing the ratio between a turbulent time scale and a free-stream time scale associated with the oscillatory motion.