  We present a formalism to describe the motion of a fluid that is fully
covariant with respect to arbitrary observers. To achieve full covariance, we
write prognostic equations for quantities that belong to the graded exterior
algebra of the cotangent bundle of the manifold occupied by the fluid. With the
new formalism, we consider problems of stability, and we derive a
generalization of the Orr-Sommerfeld equation that describes the evolution of
perturbations relative to an arbitrary observer. The latter is applied to cases
where the observer is the Lagrangian observer comoving with the background
flow.
