Notion of stability
Classes of instability
Properties of instabilities

Notion of stability

    The notion of stability is very important in Fluids Mechanics for viscous fluids flows. This notion is based on the amplification or not of perturbations introduced in the flow.

    Effectively, if a perturbation is introduced in the viscous fluid flow we can have two cases :

        - the perturbation can grows less in time : the flow is said stable
        - the perturbation can develops in time : the flow is said unstable and instabilities can appear which can
lead to turbulence sometimes

Principle of stability/unstability


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Classes of instability

    We can inventory a lot of instabilities. We are going to explain you some of them most known in the next pages.

    Instabilities can de classified in two classes :

        - instabilities which occur inside fluid : Internal Instabilities
        - instabilities which occur on particular surfaces marking boundaries of different flows : Surface Instabilities

    For each class, we are going to explain several instabilities. Instabilities noticed in this work are most famous instabilities we can found in intrustry or Nature. Some instabilities can be linked, for example Stroual instability and instability in a jet are special cases of Kelvin-Helmholtz instability.

    All instabilities dealed with in this work are inventory in the following table :

Internal Instabilities
Surface Instabilities

Benard-Marangoni Instability

Taylor-Couette Instability


Stroual Instability

Instability in a Jet

Rayleigh-Taylor Instability

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Properties of instabilities

    Internal Instabilities present two common points. Firstly, there is in general a break of equilibrum between stabilizing forces and unstabilizing forces. Lastly, this break of equilibrum appears after a threshold of an adimensional parameter caracteristic of the flow.

    For Surface Instabilities, there is only one common point : in fact, there is in this case, no notion of treshold. The only presence of perturbations is sufficient to develop instabilities.

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