The Finite Dean Problem: Nonlinear Theory

Kachoyan, B. J.

doi:10.1093/imamat/38.1.71

Cited by 2 publications

(5 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We note that the critical Taylor numbers T c found here are consistent with the results of Winters [38], who solved the full equations numerically. Winters also used bifurcation detection and continuation methods to follow the solution branches as the parameters were changed, and the results of Kachoyan [28] agree qualitatively with the numerical work of Winters. This and other aspects of the nonlinear problem are discussed in detail in Kachoyan [28].…”

Section: Oddsupporting

confidence: 53%

“…Winters also used bifurcation detection and continuation methods to follow the solution branches as the parameters were changed, and the results of Kachoyan [28] agree qualitatively with the numerical work of Winters. This and other aspects of the nonlinear problem are discussed in detail in Kachoyan [28]. [21] where On the finite Dean problem: linear theory p + j odd; p + j even, p + j odd; and all other quantities are as given by Kachoyan [29] with a = 0.…”

Section: Oddsupporting

confidence: 53%

“…The nonlinear analysis for the resultant vortex flow is presented elsewhere (Kachoyan [28]). We note that the critical Taylor numbers T c found here are consistent with the results of Winters [38], who solved the full equations numerically.…”

Section: Oddmentioning

confidence: 99%

“…Hence, any of the flow patterns described here are not necessarlty expected to eventuate, but are demonstrations of the variety of solutions made possible by a restriction of the domain. A weakly-nonlinear analysis will be given in a future paper (Kachoyan [28]) which will investigate the growth of steady solutions and which will include a comparison with the above previous work, especially that of Winters [38].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the finite Dean problem: linear theory

Kachoyan

Blennerhassett

1988

J. Aust. Math. Soc. Series B, Appl. Math

Self Cite

View full text Add to dashboard Cite

The Dean problem of pressure-driven flow between finite-length concentric cylinders is considered. The outer cylinder is at rest and the small-gap approximation is used. In a similar procedure to that of Blennerhassett and Hall [8] in the context of Taylor vortices, special end conditions are imposed in which the ends of the cylinder move with the mean flow, allowing the use of a perturbation analysis from a known basic flow. Difficulties specific to Dean flow (and more generally to nonTaylor-vortex flow) require the use of a parameter a which measures the relative strengths of the velocities due to rotation and the pressure gradient, to trace the solution from Taylor to Dean flow. Asymptotic expansions are derived for axial wavenumbers at a given Taylor number. The calculation of critical Taylor number for a given cylinder height is then carried out. Corresponding stream-function contours clearly show features not evident in infinite flow.

show abstract

Section: Oddsupporting

confidence: 53%

Section: Oddsupporting

confidence: 53%

Section: Oddmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the finite Dean problem: linear theory

Kachoyan

Blennerhassett

1988

J. Aust. Math. Soc. Series B, Appl. Math

Self Cite

View full text Add to dashboard Cite

show abstract

“…Kachoyan and Mckee [1] considered the problem of reflection of a twodimensional surface wave train by a sloping sea wall. Assuming the slope to be large they set up a perturbational scheme and calculated the velocity potential and the force on the wall approximately.…”

Section: Introductionmentioning

confidence: 99%