New hyperbolic tangent formula for mixing layer in vegetated flow

Hydrodynamic pressure and effective mixing length in vegetated free-flow region

“…The flow resistance changes suddenly at canopy top (z = h v ) in the VSL but maintains vertically constant in the PML. Therefore, (1) the inflection point locates at middle position of the PML, but it lies at canopy top (z = h v ) in the VSL [1]; and (2) an anti-symmetric U profile is observed in the PML rather than in the VSL [12]. Zhao et al [10] divides the VSL into the free-flow region and the canopy region (Figure 1), and the thickness of the former one (i.e., h o -h v ) is significantly larger than thickness of the latter (i.e., h v -h p ).…”

“…Zhao et al [10] divides the VSL into the free-flow region and the canopy region (Figure 1), and the thickness of the former one (i.e., h o -h v ) is significantly larger than thickness of the latter (i.e., h v -h p ). On the base of the VSL subdivision, the U distribution law for each region has been separately proposed through turbulence theory analyses [12].…”

“…Each case is labeled as "letter -H/ h v -U m ", where letters A, B, C, D, E, and F represent different S x and S y conditions. For specific information about the experiments, please refer to [10][11][12].…”

“…The L value is a function of both the length scales of the free shear turbulence and boundary shear turbulence [15]. The former scale equals to (h o -h v ), which remains constant vertically [12], whereas the latter scale is (z -h v ) and varies linearly along the z direction [13]. Experiment results indicate that L/ (h o -h v ) remains relatively stable in the lower zone of the vegetated free-flow region, and it increases linearly upwards for z > 0.5(h v + h o ).…”