is governed by some partial differential equation which does not have an explicit dependence on
Global modes are used in the stability analysis of hydrodynamical systems.
Philip Drazin introduced the concept of a global mode in his 1974 paper, and gave a technique for finding the normal modes of a linear PDE problem in which the coefficients or geometry vary slowly in
This technique is based on the WKBJ approximation, which is a special case of multiple-scale analysis.
[1] His method extends the Briggs–Bers technique, which gives a stability analysis for linear PDEs with constant coefficients.
[2] Since Drazin's 1974 paper, other authors have studied more realistic problems in fluid dynamics using a global mode analysis.
Such problems are often highly nonlinear, and attempts to analyse them have often relied on laboratory or numerical experiment.
[2] Examples of global modes in practice include the oscillatory wakes produced when fluid flows past an object, such as a vortex street.