It seems doubtful whether we can expect to understand fully the
instability of fluid flow without obtaining a mathematical representa-
tion of the motion of a fluid in some particular case in which
instability can actually be ob- served, so that a detailed comparison
can be made between the results of analysis and those of experiment. -
G.l. Taylor (1923) Though the equations of fluid dynamics are quite
complicated, there are configurations which allow simple flow patterns
as stationary solutions (e.g. flows between parallel plates or between
rotating cylinders). These flow patterns can be obtained only in certain
parameter regimes. For parameter values not in these regimes they cannot
be obtained, mainly for two different reasons: - The mathematical
existence of the solutions is parameter dependent; or - the solutions
exist mathematically, but they are not stable. For finding stable steady
states, two steps are required: the steady states have to be found and
their stability has to be determined.