  Hydrodynamics is the appropriate "effective theory" for describing any fluid
medium at sufficiently long length scales. This paper treats the vacuum as such
a medium and derives the corresponding hydrodynamic equations. Unlike a normal
medium the vacuum has no linear sound-wave regime; disturbances always
"propagate" nonlinearly. For an "empty vacuum" the hydrodynamic equations are
familiar ones (shallow water-wave equations) and they describe an
experimentally observed phenomenon -- the spreading of a clump of
zero-temperature atoms into empty space. The "Higgs vacuum" case is much
stranger; pressure and energy density, and hence time and space, exchange
roles. The speed of sound is formally infinite, rather than zero as in the
empty vacuum. Higher-derivative corrections to the vacuum hydrodynamic
equations are also considered. In the empty-vacuum case the corrections are of
quantum origin and the post-hydrodynamic description corresponds to the
Gross-Pitaevskii equation. I conjecture the form of the post-hydrodynamic
corrections in the Higgs case. In the 1+1-dimensional case the equations
possess remarkable `soliton' solutions and appear to constitute a new exactly
integrable system.
