{
  "id": "2411.01946",
  "version": "v1",
  "published": "2024-11-04T10:15:40.000Z",
  "updated": "2024-11-04T10:15:40.000Z",
  "title": "The instability of a membrane enclosed by two viscous fluids with a free surface",
  "authors": [
    "Joris Labarbe"
  ],
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-04T10:15:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free surface",
      "viscous fluids",
      "monotonic parallel shear flow",
      "external forcing mechanism induces",
      "fluid-structure configuration represents"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}