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Fig. 1. Sketches of three solutions to the Navier–Stokes and continuity
equations that lead to local flow separation patterns. These three types of
flow separation are commonly observed in experimental situations. (A) The open
negative bifurcation line consists of a negative bifurcation line from which a
separatrix emerges at the front of the separation. The negative bifurcation
always occurs in a pair with a positive bifurcation line. This kind of
separation is often found when a vortex approaches and impacts with a surface;
it is also involved in the separation over delta wings at moderate angle of
attack when two symmetric negative bifurcation lines form at the leading edges
and a single positive bifurcation line forms down the centreline of the delta.
The negative bifurcation contains no discrete critical points, but the
bifurcations – attachment and separation lines – are formed from a
critical point in a cross flow. (B) The Werlé–Legendre separation
has been studied since the 1960s, and occurs at the base of a dust-devil, or
over a delta wing at high angles of attack. The Werlé–Legendre
separation is a combination of a saddle point, from which a negative
bifurcation line emerges, and a focus. The separatrix arises from the saddle
point and negative bifurcation line. (C) The simple U-shaped separation occurs
in dynamic stall, or in the post-stall flow over a wing. It contains a
free-slip critical point (focus) above the line of symmetry, combined with a
node of attachment, and the separatrix emerges from a saddle-point and the
negative bifurcation (separation) lines that emerge from it at the front of
the separation.
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