Numerical Study of Rough and Smooth Turbulent Boundary Layers at Zero Pressure Gradient.

The present study proposes an accurate numerical technique for determining the flow parameters of a rough turbulent boundary layer, based on the theory by George \& Castillo (GC-97). Moreover, an improvement in the Large Eddy Simulation (LES) of Bohr (2005) over a smooth flat plate, has been performed through a grid refinement and increase in the Reynolds number ($\delta^{+}$) range. This LES emphasizes a Rescaling-Recycling technique based on the Equilibrium Similarity Theory of GC-97, when it is implemented in the method originally proposed by Lund et al. (1998). The results, after comparing with the LES for smooth surfaces, and testing with experimental rough \& smooth data available, show that the ranges of the turbulent Reynolds number, $\delta^{+}$, and the blockage ratio, $k/\delta \ge 0.030$, at which similarity laws are expected to be valid are in consistency with the predictions by Jimenez (2005). The theoretical behavior of flow parameters such as $u_{\tau}$, $Re_{x}$, $Re_{\delta^{*}}$, $vs$ $Re_{\theta}$ indicate that for the rough surfaces tested, the GC-97 theory can be validated for hydraulically smooth, and transitionally rough surfaces until: $k^{+} \leq 35$. In addition, the analytical profiles of velocity ($U/U_{\infty}$), Reynolds shear stresses ($-\langle uv \rangle$), and Eddy viscosity ($\langle \nu_{T} \rangle$), are compared with the LES and experiments, showing good agreement (especially at high $\delta^{+}$'s values) in the inner and outer regions.