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arXiv · 1501.06704

Stability analysis of shear flows in a Hele-Shaw cell

Alexander Chesnokov·Irina Stepanova
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Abstract

A mathematical model describing motion of an inhomogeneous incompressible fluid in a Hele-Shaw cell is considered. Linear stability analysis of shear flow class is provided. The role of inertia, linear friction and impermeable boundaries in Kelvin--Helmholtz instability development is studied. Hierarchy of simplified one-dimensional models of viscosity- and density-stratified flows is obtained in long-wave approximation. Interpretation of Saffman--Taylor instability development is given in the framework of these models.

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Alexander Chesnokov, Irina Stepanova. 2015-01-27. Stability analysis of shear flows in a Hele-Shaw cell. https://arxiv.org/abs/1501.06704

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