The instability of a membrane enclosed by two viscous fluids with a free surface
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916466302910464 |
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| author | Labarbe, Joris |
| author_facet | Labarbe, Joris |
| contents | This study examines the stability of a flexible material interface between two fluids of the same viscosity in interaction with a free surface. When the layers are motionless, we provide evidence for the onset of a novel instability by means of analytical and numerical solution of the associated boundary value problem in the region stable against Rayleigh--Taylor instability, i.e. when the acceleration due to gravity acts from the lighter to the heavier fluid. This destabilisation phenomenon is attributed to the non-conservative tangential forces acting at the interface and the fluid-structure interaction. Furthermore, we examine the scenario in which an external forcing mechanism induces a monotonic parallel shear flow within the upper layer. In addition to the long-established inflectional instability predicted in the inviscid limit, we demonstrate the existence of membrane flutter in the absence of density stratification. The latter is either due to an over-reflection process of surface gravity waves or to the growth of Tollmien--Schlichting waves, as outlined in the context of boundary-layer theory. This fluid-structure configuration represents a paradigmatic model for investigating the interplay between inflectional, radiation-induced and shear-induced instabilities. It also serves as a viscous counterpart to the classical Kelvin--Helmholtz instability when layers with distinct densities are assumed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01946 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The instability of a membrane enclosed by two viscous fluids with a free surface Labarbe, Joris Fluid Dynamics This study examines the stability of a flexible material interface between two fluids of the same viscosity in interaction with a free surface. When the layers are motionless, we provide evidence for the onset of a novel instability by means of analytical and numerical solution of the associated boundary value problem in the region stable against Rayleigh--Taylor instability, i.e. when the acceleration due to gravity acts from the lighter to the heavier fluid. This destabilisation phenomenon is attributed to the non-conservative tangential forces acting at the interface and the fluid-structure interaction. Furthermore, we examine the scenario in which an external forcing mechanism induces a monotonic parallel shear flow within the upper layer. In addition to the long-established inflectional instability predicted in the inviscid limit, we demonstrate the existence of membrane flutter in the absence of density stratification. The latter is either due to an over-reflection process of surface gravity waves or to the growth of Tollmien--Schlichting waves, as outlined in the context of boundary-layer theory. This fluid-structure configuration represents a paradigmatic model for investigating the interplay between inflectional, radiation-induced and shear-induced instabilities. It also serves as a viscous counterpart to the classical Kelvin--Helmholtz instability when layers with distinct densities are assumed. |
| title | The instability of a membrane enclosed by two viscous fluids with a free surface |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2411.01946 |