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The two-dimensional (or Lagrange) stream function, introduced by Joseph Louis Lagrange in 1781, [1] is defined for incompressible (divergence-free), two-dimensional flows. The Stokes stream function, named after George Gabriel Stokes, [2] is defined for incompressible, three-dimensional flows with axisymmetry.
When we consider 2-D flows on the perpendicular plane, a line source appears as a point source. By symmetry, we can assume that the fluid flows radially outward from the source. The strength of a source can be given by the volume flow rate Q {\displaystyle Q} that it generates.
In fluid dynamics, a stagnation point flow refers to a fluid flow in the neighbourhood of a stagnation point (in two-dimensional flows) or a stagnation line (in three-dimensional flows) with which the stagnation point/line refers to a point/line where the velocity is zero in the inviscid approximation. The flow specifically considers a class of ...
Two solutions of the three-dimensional Euler equations with cylindrical symmetry have been presented by Gibbon, Moore and Stuart in 2003. [29] These two solutions have infinite energy; they blow up everywhere in space in finite time.
Shock waves at the pointed leading edge of two-dimensional wedge or three-dimensional cone (Taylor–Maccoll flow) has constant intensity. 2) For weak shock waves, the entropy jump across the shock wave is a third-order quantity in terms of shock wave strength and therefore can be neglected. Shock waves in slender bodies lies nearly parallel to ...
The resulting flow is two-dimensional if the plates are infinitely long in the axial direction, or the plates are longer but finite, if one were neglect edge effects and for the same reason the flow can be assumed to be entirely radial i.e., = (,), =, =.
The 3-D particle tracking velocimetry (PTV) belongs to the class of whole-field velocimetry techniques used in the study of turbulent flows, allowing the determination of instantaneous velocity and vorticity distributions over two or three spatial dimensions. 3-D PTV yields a time series of instantaneous 3-component velocity vectors in the form of fluid element trajectories.
In the larger context of the Navier-Stokes equations (and especially in the context of potential theory), elementary flows are basic flows that can be combined, using various techniques, to construct more complex flows. In this article the term "flow" is used interchangeably with the term "solution" due to historical reasons.
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