By Vladimir Shtern

Counterflows play very important roles in nature and expertise. A ordinary instance is the Gulf move and the other stream within the ocean depths. Technological purposes comprise hydrocyclones, vortex tubes, and vortex combustors. those elongated counterflows are wildly turbulent yet live on severe blending, a seeming paradox. neighborhood counterflows, whose spatial volume is small in comparison with that of surrounding flows, happen at the back of bluff our bodies and in swirling streams. The latter are frequently known as vortex breakdown bubbles, which happen in tornadoes and above delta wings. such a lot scale counterflows are cosmic bipolar jets. such a lot miniature counterflows take place in capillary menisci of electrosprays and gas atomizers. This publication discusses the actual mechanisms that force counterflows, analyzing how they emerge, enhance, develop into double and a number of counterflows, and contain either worldwide and native circulations.

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**Sample text**

As the forcing further increases, the circulation region expands in the radial direction and inward of the needle. The flow-through reaches high speed, moves within a narrow annular region near the needle wall, then near the liquid-gas interface. As the forcing passes another threshold, time-periodic dripping is established. 4. 1. Observations of Spontaneous Swirl Appearance The appearance of rotation in a swirl-free flow due to instability or bifurcation with no visible swirl forcing seems to be a more striking and intriguing manifestation of symmetry breaking than the convection cell onset or even the hydromagnetic dynamo.

The local heating induces a counterflow; there is an ascending round jet (plume) near the axis and a descending flow near the sidewall. This meridional circulation is typically swirl-free, but the plume starts to rotate around the axis as the strength of the local heat source exceeds a threshold. An interesting effect related to swirl appearance is observed in a glass of water oscillating in a horizontal direction; at some values of the oscillation amplitude and frequency, the surface wave begins to rotate around the vessel axis (Funakoshi & Inoue 1988).

The velocity at the axis of symmetry, Rva/ν = −ψ0 (1), becomes unbounded as Re → Recr. It is striking that the singularity develops at a finite value of the Reynolds number and not as Re → ∞, the latter of which is typical of boundary layers. From a mathematical point of view, the solution regularity loss is clear. 3. Super-Collimated Jet 17 d ψ c b Figure 15. 6727 (d). a x zero. For Re < Recr, the xp value is larger than 1; xp decreases as Re increases; and xp becomes less than 1 for Re > Recr.