One-dimensional turbulence: Application to incompressible spatially developing turbulent boundary layers

A map-based stochastic approach, One-Dimensional Turbulence (ODT), is applied to analyze the incompressible spatially developing turbulent boundary layer (SBL). In the present study, the SBL is formed by a plane moving wall and a free stream at rest. The flow variables are resolved on all scales along a 1-D domain. A deterministic process represents the molecular diffusion and a stochastic process is modeling the effect of turbulent advection and pressure fluctuations. Due to the reduced dimensions in the model, it achieves major cost reductions as compared to the full 3-D simulations and is, thus, able to explore large parameter regimes. The simulations are presented for momentum thickness Reynolds numbers, Re-theta, varied in the range Re-theta approximate to 1968 - 8000. We have investigated various features related to the SBL, such as mean, root mean square, Reynolds shear stress, skewness, flatness and pre-multiplied velocity profiles and skin friction coefficient and shape factor, all for two bulk velocities using ODT and compared our results to the available reference Direct Numerical Simulations (DNS) and large-eddy simulations (LES) results. We have further compared the results for spatial and temporal ODT formulations used to investigate the turbulent boundary layer with the reference data at matched Re-theta. The comparison presented suggests that ODT is a reasonably accurate approach for the simulations of the spatially developing turbulent boundary layers which can be further improved to yield accurate statistics at high Reynolds number by implementing Fourier transformation of the kernels which in the present formulation of the model is not implemented.