Stability analysis of shear flows in a Hele-Shaw cell
Alexander Chesnokov, Irina Stepanova
TL;DR
This paper presents a mathematical stability analysis of shear flows in a Hele-Shaw cell, exploring the effects of inertia, friction, and boundaries on instabilities, and deriving simplified models for stratified flows.
Contribution
It provides a linear stability analysis of shear flows in a Hele-Shaw cell and introduces simplified models for stratified flows in the long-wave approximation.
Findings
Inertia, friction, and boundaries influence Kelvin--Helmholtz instability.
Hierarchy of simplified models for stratified flows is developed.
Interpretation of Saffman--Taylor instability within these models.
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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Taxonomy
TopicsLattice Boltzmann Simulation Studies · Fluid Dynamics and Turbulent Flows · Theoretical and Computational Physics