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Updated: Apr 16, 2026
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Experimental Methods for Investigation of Shape Memory Based Elastocaloric Cooling Processes and Model Validation
Published on: May 2, 2016
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Saffman-Taylor fingers with kinetic undercooling
Bennett P J Gardiner1, Scott W McCue1, Michael C Dallaston2
1Mathematical Sciences, Queensland University of Technology, Brisbane QLD 4001, Australia.
Summary
This study models Saffman-Taylor fingers with kinetic undercooling, revealing discrete finger shapes. The findings suggest a selection mechanism similar to surface tension, favoring a 1/2 channel width fraction.
Area of Science:
- Fluid dynamics
- Mathematical modeling
- Plasma physics
Background:
- Saffman-Taylor finger model in Hele-Shaw channels.
- Applications to 2D streamer discharges in periodic arrays.
- Kinetic undercooling as a regularization mechanism, penalizing high velocities.
Purpose of the Study:
- Numerically compute Saffman-Taylor fingers with kinetic undercooling.
- Investigate the subtle differences compared to surface tension regularization.
- Provide numerical evidence for the selection mechanism.
Main Methods:
- Asymptotic analysis of Hele-Shaw finger problem with kinetic undercooling.
- Numerical computation of finger shapes.
- Simulations combining kinetic undercooling and surface tension, taking the surface tension limit.
Main Results:
- Discrete set of possible finger shapes for a given kinetic undercooling parameter.
- Finger shapes can be corner-free but not analytic.
- Numerical evidence supports a selection mechanism favoring 1/2 channel width fraction in the limit.
Conclusions:
- Kinetic undercooling provides a regularization mechanism for streamer discharges.
- The selection of finger shapes by kinetic undercooling is qualitatively similar to surface tension.
- Numerical methods are crucial for understanding complex finger dynamics.
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