Turbulent kinetic energy balance of an oscillatory boundary layer in the transition to the fully turbulent regime

The sinusoidal oscillation of a fluid in the vicinity of a rigid smooth wall is studied using the results of direct numerical simulation of the Navier-Stokes equations. Simulations are performed at a wave Reynolds number Re_w = U_maxA/ν = 1.41 × 10⁶ in the turbulent regime. The computed statistics are compared with great success with the available experimental results reported in the literature for U_max = 1.02 m/s the maximum orbital velocity, A = 1.58 m the amplitude of the water excursion, and ν = 1.14 × 10⁶ m²/s the kinematic viscosity of the fluid (Re_w = U_maxA/ν = 1.41 × 10⁶). The simulation results allow to identify the development of an unsteady shear layer and regions of zero and negative turbulent kinetic energy (TKE) production. The TKE balance is studied in detail, analyzing the role of each of the terms in the balance equation and the relative relevance of different TKE transport mechanisms. It is found that the local derivative of the TKE is particularly important in the shear layer region. The present results provide an accurate and detailed dataset that could be used for validation of both analytical and numerical models of oscillatory boundary layer flows.