Kelvin waves on helical vortex tube in swirling flow

Vortex bursting near a free surface

“…The curved arrow in (e) marks the curl over at the tip of the Taylor tube. The abrupt reductions in diameter at the apex, marked in (g,i), indicate the presence of Kelvin mode m = 0 (Tsoy et al 2018). The root vortex cone (i-k) has just been relaxed after maximum stretching and the cone diameter shrinks; surface tension is reducing the surface area; see notes in (l).…”

“…Therefore, the vortex grows axially in an adverse pressure gradient ∂p/∂y > 0, the depth acting like a diffuser. The vortex bursting experiments by Sarpkaya (1995) and the Kelvin wave vortex experiments by Tsoy et al (2018) have been carried out in small angle diffusers. While pitching up or down in continuously pitching delta wings, the bursting occurs farther back or forward compared to the steady case, respectively.…”

“…Hence, from f = 1.0 Hz to 1.25 Hz, the kinetic energy rises by a factor of at least 2.44 since the vortex diameter δ 2 drops. If the vortex diameter drops abruptly by a factor of 2 as in Tsoy et al (2018) due to Kelvin mode m = 0, the kinetic energy stored increases by a total factor 10. Instead of any m = 0 mode, figure 6(d) shows that a vertical coiled vortex does exist connected to the slanted root vortex undergoing stretching (see left panel in figure SI-IA-6 for greater clarity).…”

“…We explore the successive stages of bursting in the aerated root vortex, in the air-jacketed foil boundary layer and in the rolled-up vorticity of the foil-tip flow. The bursting mechanisms are examined in the context of Saffman's (1990) modelling of vortex breaking and the cavitation visualization by Tsoy et al (2018) of the Kelvin modes in a long slender vortex tube in a swirling diffuser flow. We examine the relationship of stretching and sudden relaxation of aerated tubes to bubble formation.…”

“…The breaking time in the experiments is 0.2 s, and the modelled rejoining time is 0.4 s. These times will be compared with those in the present work. Tsoy et al (2018) have used cavitation bubbles as vortex markers in a diffuser to visualize the Kelvin modes formed in a vortex tube after reconnection. Kelvin wave modes m = 0, 1, 2 were observed to propagate along the axis.…”