  The definitions of temporal instability and of spatial instability in a flow
system are comparatively surveyed. The simple model of one-dimensional Burgers'
flow is taken as the scenario where such different conceptions of instability
are described. The temporal analysis of instability stems from Lyapunov's
theory, while the spatial analysis of instability interchanges time and space
in defining the evolution variable. Thus, the growth rate parameter for
temporally unstable perturbations of a basic flow state is to be replaced by a
spatial growth rate when a coordinate assumes the role of evolution variable.
Finally, the idea of spatial instability is applied to a Rayleigh-B\'enard
system given by a fluid-saturated horizontal porous layer with an anisotropic
permeability and impermeable boundaries kept at different uniform temperatures.
