1972
DOI: 10.1017/s0022112072002046
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Dissipation and breakdown of a wing-tip vortex

Abstract: The solutions of the incompressible quasi-cylindrical momentum-integral equations describing the flow in the viscous core of a wing-tip vortex are obtained in a closed form and are shown to have two distinct branches. The discontinuities of these solutions have infinite axial gradients and therefore, following Hall, are assumed to signal the inception of the vortex breakdown. Benjamin's finite transition, with its excess flow force dissipated, is shown to give results equivalent to a sudden cross-over, upstrea… Show more

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Cited by 48 publications
(19 citation statements)
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“…Reynolds numbers large enough for comparison, it was not possible to conclusively demonstrate that the failure of the quasi-cylindrical approximation, which occurs in the analysis of Mager (1972) for e1 greater than a particular value e 1 independent of…”
Section: Comparisons With Experiments and Theorymentioning
confidence: 96%
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“…Reynolds numbers large enough for comparison, it was not possible to conclusively demonstrate that the failure of the quasi-cylindrical approximation, which occurs in the analysis of Mager (1972) for e1 greater than a particular value e 1 independent of…”
Section: Comparisons With Experiments and Theorymentioning
confidence: 96%
“…He thus identified with vortex breakdown both the failure of the quasicylindrical approximation and the appearance of the critical state. Mager (1972), following the work of Gartshore (1963) and Bossel (1967Bossel ( ,1971, showed that the solutions of the quasi-cylindrical momentum-integral equations have two distinct branches and, with the appropriate upstream conditions, discontinuities which represent the appearance of infinite axial gradients and are assumed to signal the inception of vortex breakdown. He then demonstrated that Benjamin's finite transition could be explained as a sudden cross-over, upstream of the discontinuity, from one branch of the solution to the other, and suggested that the physical manifestation of the discontinuity might be the spiral breakdown while the cross-over, if it occurred, might appear as the axisymmetric bubble upstream.…”
Section: Theoretical Explanationsmentioning
confidence: 99%
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“…(i) vortex breakdown is similar to the separation of a two-dimensional boundary layer (Hall [2,3], Mager [4]);…”
Section: Introductionmentioning
confidence: 99%
“…An extensive and comparative analysis has been carried out by Hall (1972) and Leibovitch (1978). In the first theory, due to Gartshore (1963), Hall (1972), andMager (1972), vortex breakdown is interpreted as corresponding to the failure of the quasi-cylindrical _approximation~of_the~Na"Rier-=Stokes_equations_._l'he_theor-y-is~ana-logous-t;o'-----------boundary layer theory. In the second theory, due to Ludwig (1970), vortex breakdown is explained as a consequence of an instability of the flow to helical disturbances.…”
mentioning
confidence: 99%