Lecture

Rayleigh Taylor: Normal Mode Expansion

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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 normal mode expansion in the context of Rayleigh Taylor instability, focusing on the Fourier transform in space and time, the solution to Laplace equation, and the dispersion relation analysis. It also delves into the lubrication approximation and the flattened kinematic boundary conditions. The instructor discusses the eigenvalue problem arising from the boundary conditions and the stability analysis based on the dispersion relation. The lecture concludes with a detailed exploration of the dispersion relation and the implications of different wave behaviors. Additionally, the scaling of the Stokes equations for a thin liquid film and the simplified and dimensionless forms of the governing equations are presented.

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

Ontological neighbourhood

Mathematics

Discrete mathematics: Discrete exterior calculus

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Neumann boundary condition

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Cauchy boundary condition

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