Effect of Modulated Taylor-Couette Flows on Crystal-Melt Interfaces: Theory and Initial Experiments

McFadden, Geoffrey B.; Murray, Bruce T.; Coriell, S. R.; Glicksman, M.E.; Selleck, M. E.

doi:10.1007/978-1-4613-9211-8_6

Cited by 1 publication

(4 citation statements)

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“…Figure Captions approaches the rigid-walled neutral curve displayed in [25]. The base state described in Section 3.1.1 is stable below the curves and unstable above them.…”

Section: Resultsmentioning

confidence: 99%

“…The instability has been observed only above the neutral curves given by either theory (see Figure 4 in [25]). The effect of the deformable crystal-melt interface is pronounced; both the theoretical and experimental results show that the two-phase system is significantly less stable than the rigid-walled system.…”

Section: Wide Gapmentioning

confidence: 99%

“…In the low frequency regime, on the other hand, the temporal behavior is complicated and cannot be described by a single mode in time [34]. The computation at the lowest frequencies is difficult for the pseudospectral approach with Floquet theory, and the computations are best performed there with the Fourier approach of [25].…”

Section: Wide Gapmentioning

confidence: 99%

“…The Taylor number may be related to the Reynolds number Re used in previous work [25] by 9n (15) Ta = -r--Re …”

Section: Wide Gapmentioning

confidence: 99%

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Asymptotic behavior of modulated Taylor-Couette flows with a crystalline inner cylinder

Murray¹,

Coriell²,

Glicksman³

et al. 1992

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We consider the linear stability of a modulated Taylor-Couette system when the inner cylindrical boundary consists of a crystalline solid-liquid interface. Both experimentally and in numerical calculations it is found that the two-phase system is significantly less stable than the analogous rigid-walled system for materials with moderately large Prandtl numbers. A numerical treatment based on Floquet theory is described, which gives results that are in good agreement with preliminary experimental findings. In addition, this instability is further examined by carrying out a formal asymptotic expansion of the solution in the limit of large Prandtl number. In this limit the Floquet analysis is considerably simplified, and the linear stability of the modulated system can be determined to leading order through a conventional stability analysis, without recourse to Floquet theory. The resulting simplified problem is then studied for both the narrow gap geometry and for the case of a finite gap. It is surprising that the determination of the linear stability of the two-phase system is considerably simpler than that of the rigid-walled system, despite the complications introduced by the presence of the crystal-melt interface.

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“…Figure Captions approaches the rigid-walled neutral curve displayed in [25]. The base state described in Section 3.1.1 is stable below the curves and unstable above them.…”

Section: Resultsmentioning

confidence: 99%

Section: Wide Gapmentioning

confidence: 99%