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- W2086379126 abstract "The complicated nature of singularities associated with topological transition in the plane Taylor-bubble problem is briefly discussed in the context of estimating the speed of the fastest smooth Taylor-bubble in the absence of surface tension. Previous numerical studies were able to show the presence of a stagnation point at the tip of the bubbles for dimensionless speed F<0.357 but were incomplete in characterizing the topology of these bubbles at the tip for values of F>0.29 due to difficulties in obtaining numerical solutions with well-rounded profiles at the apex. These difficulties raise the question whether the bubbles rising at a speed F∈(0.29,0.357) are smooth, pointed or spurious. This issue has led us to carefully scrutinize certain asymptotic behavior of the Fourier spectrums of the numerical solutions for a wide range of values of F and to extend these results in an appropriate limiting sense. Our findings indicate that these plane bubbles with F<0.35784 (accurate up to four decimal places) have well-rounded profiles at the apex. The purpose of this paper is to describe our approach and its use in arriving at the above conclusion." @default.
- W2086379126 created "2016-06-24" @default.
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- W2086379126 date "2000-08-01" @default.
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- W2086379126 title "The fastest smooth Taylor bubble" @default.
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- W2086379126 doi "https://doi.org/10.1016/s0168-9274(99)00037-9" @default.
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