Editing Squeeze mapping (section)

===Corner flow===
In [[fluid dynamics]] one of the fundamental motions of an [[incompressible flow]] involves [[Bifurcation theory|bifurcation]] of a flow running up against an immovable wall.
Representing the wall by the axis ''y'' = 0 and taking the parameter ''r'' = exp(''t'') where ''t'' is time, then the squeeze mapping with parameter ''r'' applied to an initial fluid state produces a flow with bifurcation left and right of the axis ''x'' = 0. The same [[mathematical model|model]] gives '''fluid convergence''' when time is run backward. Indeed, the [[area]] of any [[hyperbolic sector]] is [[invariant (mathematics)|invariant]] under squeezing.

For another approach to a flow with hyperbolic [[streamlines, streaklines and pathlines|streamlines]], see {{section link|Potential flow|Power laws with n {{=}} 2}}.

In 1989 Ottino<ref>J. M. Ottino (1989) ''The Kinematics of Mixing: stretching, chaos, transport'', page 29, [[Cambridge University Press]]</ref> described the "linear isochoric two-dimensional flow" as
:<math>v_1 = G x_2 \quad v_2 = K G x_1</math>
where K lies in the interval [&minus;1, 1]. The streamlines follow the curves
:<math>x_2^2 - K x_1^2 = \mathrm{constant}</math>
so negative ''K'' corresponds to an [[ellipse]] and positive ''K'' to a hyperbola, with the rectangular case of the squeeze mapping corresponding to ''K'' = 1.

Stocker and Hosoi<ref>Roman Stocker & [[Anette Hosoi|A.E. Hosoi]] (2004) "Corner flow in free liquid films", ''Journal of Engineering Mathematics'' 50:267&ndash;88</ref> described their approach to corner flow as follows:
:we suggest an alternative formulation to account for the corner-like geometry, based on the use of hyperbolic coordinates, which allows substantial analytical progress towards determination of the flow in a Plateau border and attached liquid threads. We consider a region of flow forming an angle of ''π''/2 and delimited on the left and bottom by symmetry planes.
Stocker and Hosoi then recall Moffatt's<ref>H.K. Moffatt (1964) "Viscous and resistive eddies near a sharp corner", [[Journal of Fluid Mechanics]] 18:1&ndash;18</ref> consideration of "flow in a corner between rigid boundaries, induced by an arbitrary disturbance at a large distance." According to Stocker and Hosoi,
:For a free fluid in a square corner, Moffatt's (antisymmetric) stream function ... [indicates] that hyperbolic coordinates are indeed the natural choice to describe these flows.