Lecture

Viscous Jet Instabilities

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In course

ME-466: Instability

This course focuses on the physical mechanisms at the origin of the transition of a flow from laminar to turbulent using the hydrodynamic instability theory. ...

Description

This lecture covers the destabilization of a jet, dispersion relation, viscosity-dominated flows, surface tension effects, eigenmodes of viscous jets, and fundamental solutions for boundary conditions. It discusses the global and local stability of flows, emphasizing the importance of absolute instability. The presentation includes equations from Eggers and Dupont (1994) and Rayleigh (1892), as well as the non-dimensionalization of the governing equations. The instructor explains the implications of surface tension on jet stability and the conditions for global instability. The lecture concludes with a detailed analysis of eigenmodes and absolute frequencies in viscous jet flows.

Instructor

François Gallaire

google scholar https://scholar.google.ch/citations?hl=fr&user=T3OooAcAAAAJ François Gallaire earned his engineering degree from Ecole Polytechnique in 1998 and a master's in Liquids Physics from Université Pierre et Marie Curie in 1999. He completed his PhD in 2002 at LadHyX on swirling flow instabilities and vortex breakdown. After six years at the Mathematics department of Université de Nice, he joined EPFL in 2009, founding the Fluid Mechanics and Instabilities Lab (LFMI). He became an associate professo

Official source

Related concepts (32)

Surface tension

Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to float on a water surface without becoming even partly submerged. At liquid–air interfaces, surface tension results from the greater attraction of liquid molecules to each other (due to cohesion) than to the molecules in the air (due to adhesion). There are two primary mechanisms in play.

Surface energy

In surface science, surface free energy (also interfacial free energy or surface energy) quantifies the disruption of intermolecular bonds that occurs when a surface is created. In solid-state physics, surfaces must be intrinsically less energetically favorable than the bulk of the material (the atoms on the surface have more energy compared with the atoms in the bulk), otherwise there would be a driving force for surfaces to be created, removing the bulk of the material (see sublimation).

Tension (physics)

In physics, tension is described as the pulling force transmitted axially by the means of a string, a rope, chain, or similar object, or by each end of a rod, truss member, or similar three-dimensional object; tension might also be described as the action-reaction pair of forces acting at each end of said elements. Tension could be the opposite of compression. At the atomic level, when atoms or molecules are pulled apart from each other and gain potential energy with a restoring force still existing, the restoring force might create what is also called tension.

Mixed boundary condition

In mathematics, a mixed boundary condition for a partial differential equation defines a boundary value problem in which the solution of the given equation is required to satisfy different boundary conditions on disjoint parts of the boundary of the domain where the condition is stated. Precisely, in a mixed boundary value problem, the solution is required to satisfy a Dirichlet or a Neumann boundary condition in a mutually exclusive way on disjoint parts of the boundary.

Robin boundary condition

In mathematics, the Robin boundary condition (ˈrɒbɪn; properly ʁɔbɛ̃), or third type boundary condition, is a type of boundary condition, named after Victor Gustave Robin (1855–1897). When imposed on an ordinary or a partial differential equation, it is a specification of a linear combination of the values of a function and the values of its derivative on the boundary of the domain. Other equivalent names in use are Fourier-type condition and radiation condition.

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