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Lecture

Hydrodynamic Instabilities: Part 2

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 physical mechanisms behind Kelvin-Helmholtz instability, including the dispersion relation and kinematic boundary conditions. It delves into 2D parallel flow concepts, linearized equations, and perturbed kinematic boundary conditions. The lecture also explores normal mode expansion, the solution to Laplace equation, and perturbed and linearized Euler equations. Furthermore, it discusses the dispersion relation, the influence of stratification and surface tension, and the joint influence of both. The lecture concludes with applications of Kelvin-Helmholtz instability in geophysics and the formation of toroidal vortices and vortex rings.

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Instructor

François Gallaire

Né le 26 février 1975, François Gallaire obtient, en 1998, le diplôme dingénieur de lEcole Polytechnique à Paris et, en 1999, un master en « Physique des liquides » à lUniversité Pierre et Marie Curie, toujours à Paris. Il rejoint ensuite le Laboratoire dhydrodynamique (LadHyX) à lEcole polytechnique où il soutient, en 2003, une thèse sur le thème des instabilités des jets tournants et sur le contrôle de léclatement tourbillonnaire sous la direction de Jean-Marrc Chomaz. En 2003, il est nommé chargé de recherche au CNRS au Laboratoire J.A. Dieudonné de lUniversité de Nice Sophia-Antipolis.En 2009, il rejoint l'EPFL pour y fonder le laboratoire des mécanique des fluides et instabilités (LFMI). Ses recherches se concentrent sur létude des propriétés fondamentales de stabilité des écoulements de fluides et sont guidées par les applications réelles, en particulier le contrôle des écoulements. Récemment, il a réalisé dimportantes contributions dans les domaines de la micro-fluidique (lanalyse de la manipulation par laser dune goutte dans un micro-canal) et la dynamique des bio-fluides (le descriptif mécanique de lanévrisme de laorte abdominale).

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Related concepts (25)

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In fluid dynamics, a vortex (: vortices or vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in the wake of a boat, and the winds surrounding a tropical cyclone, tornado or dust devil. Vortices are a major component of turbulent flow. The distribution of velocity, vorticity (the curl of the flow velocity), as well as the concept of circulation are used to characterise vortices.

Viscosity

The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity is defined scientifically as a force multiplied by a time divided by an area. Thus its SI units are newton-seconds per square metre, or pascal-seconds. Viscosity quantifies the internal frictional force between adjacent layers of fluid that are in relative motion.

Potential flow

In fluid dynamics, potential flow (or ideal flow) describes the velocity field as the gradient of a scalar function: the velocity potential. As a result, a potential flow is characterized by an irrotational velocity field, which is a valid approximation for several applications. The irrotationality of a potential flow is due to the curl of the gradient of a scalar always being equal to zero. In the case of an incompressible flow the velocity potential satisfies Laplace's equation, and potential theory is applicable.

Boundary layer

In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary condition (zero velocity at the wall). The flow velocity then monotonically increases above the surface until it returns to the bulk flow velocity. The thin layer consisting of fluid whose velocity has not yet returned to the bulk flow velocity is called the velocity boundary layer.

Boundary layer thickness

This page describes some of the parameters used to characterize the thickness and shape of boundary layers formed by fluid flowing along a solid surface. The defining characteristic of boundary layer flow is that at the solid walls, the fluid's velocity is reduced to zero. The boundary layer refers to the thin transition layer between the wall and the bulk fluid flow. The boundary layer concept was originally developed by Ludwig Prandtl and is broadly classified into two types, bounded and unbounded.

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