In the stability theory of shear layers, the term `local stability' refers to the stability properties of a particular velocity profile at a given position in the flow. When the basic flow develops the streamwise direction, e.g. in a growing boundary layer, the changing local stability properties can be mapped out downstream. If there are regions of local absolute instability then there is the possibility of a `global instability' of the entire flow. When the basic flow varies slowly in the downstream direction the global stability can be determined from the local stability.  »»» 

Abstrakt:
Large deformations of a solid are investigated. We use a polar decomposition of gradient matrix F = RW (R is rotation matrix, W is stretch matrix). Large deformations of solids involve local spacial interactions either in an extension or in a rotation. Because local interactions are well described by spacial gradient, matrix W intervene for extensions and matrix gradR intervene for rotations. Thus the free energy depends on W and on gradR. Moreover, free energy takes into account the local impenetrability condition. Reactions to this impenetrability condition are important in constitutive laws.  »»» 

Turbulence will be introduced as the typical state of real flowing viscous fluids (historical overview). Attributes of turbulence will be presented (diffusivity, deterministic chaos, fractal structure…). A mathematical model will be introduced and its basic properties will be shown including the Kolmogorov theory. Then a few phenomenological aspects will demonstrate the typical features of the phenomenon (stability, complexity…).