Properties of the advective transport contribution to the inertial mean dynamics of rough-wall boundary layers

Measurements and scaling analyses are conducted to clarify the combined effects of roughness and Reynolds number on momentum transport in rough-wall turbulent boundary layers. Experiments employing a four element (``Foss style'') spanwise vorticity probe cover nearly a decade in Reynolds number, and nearly three decades in sand grain roughness, $k_s^+$. Here we leverage the expression that decomposes the Reynolds stress gradient into the difference of two velocity-vorticity correlations, i.e., $-\partial \overline{uv}/{\partial y} = \overline{v\omega_z}-\overline{w\omega_y}$. The present analyses focus on the first term on the left hand side, $v\omega_z$, in the logarithmic layer and outer regions, as it is known from smooth-wall studies that this advective transport mechanism is the largest contributor to $-\partial \overline{uv}/{\partial y}$ in the domain where the mean dynamics are inertially dominated. Streamwise correlation maps and length scales associated with the spectra and correlations of $v$ and $\omega_z$ are used to clarify the scaling behaviors of the motions underlying $-\partial \overline{uv}/{\partial y}$. The results are shown to further support the combined roughness Reynolds number description of Mehdi et al. 2013, \textit{J. Fluid Mech.} \textbf{731}, 682