A uniform momentum zone-vortical fissure model of the turbulent boundary layer

Recent studies show evidence that the turbulent boundary layer (TBL) structure at high Reynolds number ($Re_{\tau}$) can be considered like a binary arrangement of large-scale zones of nearly uniform streamwise momentum (UMZ) being segregated by narrow fissures of concentrated vorticity. A simple model to reproduce the statistical dynamics of TBL and channel flow using these two elements is presented. In brief, the UMZs are created by following the edge velocity of the adjacent fissures, while the sharp change in momentum across the fissures scale with the friction velocity $\mathcal{O}$$(u_{\tau})$. The length and velocity scalings of the fissures are informed by the theory. Furthermore, a momentum exchange mechanism is enforced throughout the boundary layer. Then, an ensemble of statistically independent instantaneous velocity profiles is created by allowing the fissures move randomly in the wall normal direction while they exchange momentum with the surrounding fluid. The numerical results shows that the model is able to reproduce the main statistical moments of the streamwise velocity from low to high-moderate $Re_{\tau}$ (e.g. $Re_{\tau}=1000,5000,10000$). Additionally, a dynamical wake mechanism is investigated for accurately modeling the entire domain of the given flow.