Figure 7

The shear velocity associated with the reversing flow at the ground within the separation bubble scales linearly with the upwind shear velocity.

In the upper inset, we see the value of τ_x (cf. Eq. (3)) associated with the reversing flow within the separation bubble as a function of the downwind distance x − x_b, where x_b is the brink position. The minimum of τ_x, which gives the maximal magnitude of the shear stress associated with the reversing flow, is denoted by τ_rev and occurs at a horizontal distance l_rev downwind of the brink. The blue horizontal line indicates the impact threshold shear stress, . The black dot identifies the point {l_rev, τ_rev} associated with u_* = 1.0 m/s. We see in the lower inset that l_rev ≈ 55% of the reattachment length l and is nearly independent of u_*. Main plot: Magnitude of the maximal shear velocity at the ground, , as a function of the upwind shear velocity, u_*. The best fit using the equation u_*rev = ku_* (dashed line) gives k ≈ 0.55. The dashed area indicates the range of u_* for which no sustained transport occurs (u_*rev < u_t), while the regime of u_* where u_*rev is smaller than the threshold for direct entrainment (u_ft) is denoted by the green filled area.