Separation vortices and pattern formation

The hydraulic bump: The surface signature of a plunging jet

“…Figure 4b lends support to this scaling argument, and suggests a proportionality coefficient of c 2 = 2.5.As illustrated inFigure 1cand 1i, non-circular bumps may also arise downstream of polygonal hydraulic jumps. Similar nested jump-bump structures have been reported by Andersen et al11 and Bush et al14 . We note that the number of sides of the outer bump and inner jump polygons are not necessarily the same.Figure 1iillustrates a square jump within a pentagonal bump.…”

“…Yokoi et al 12 presented a numerical investigation of the link between this vortex dynamics and the underlying pressure distribution in the type II jumps and remarked upon the importance of surface tension in the transition from type I to II. The type II jumps are further classified 13 according to whether there is a substantial change in surface elevation downstream of the jump: if not, the jump is referred to as type IIa ( Remarkably, in certain parameter regimes, the circular hydraulic jump becomes unstable to polygons (Figure 1b), a phenomenon first reported by Ellegaard 15,16 , and subsequently examined by Bohr and coworkers 11,17 17 developed a theoretical model for the jump shape that yields polygons similar to those observed experimentally. When surface tension dominates, they demonstrate that the wavelength of the instability is consistent with that of Rayleigh-Plateau.…”

A mathematical model of 2P and 2C vortex wakes

“…We first consider the 2P wake shown in Fig. 1, which is from Andersen et al (2010). Note that the soap film flow is not a two-dimensional Newtonian flow, but there appears to be a close correspondence between the vortex dynamics in these two types of flows.…”

“…As a specific example of a 2P wake, consider the vortex street shown in Fig. 1, which is generated by a symmetric airfoil that is made to flap in a flowing soap film (Andersen et al, 2010;Schnipper et al, 2009). We examine this experimental wake in Section 3.…”

“…The image is from Fig. 4(a) in Andersen et al (2010), and experimental details are given in Schnipper et al (2009). (b) Approximate locations of the experimental vortex cores.…”