A barotropic fluid is defined as that state of a fluid
for which 
is a function of only the pressure. The
condition of barotropy of a fluid represents another rather
idealized state. However, in this case the situation is
closer to reality since compressibility is allowed for.
The term ``barotropic'' infers ``turning with (or in the
same manner as) the isobars'', referring to the isopycnals.
The name is a lucid one since it is obvious that if
depends only on p then the isopycnal surfaces must
always be parallel to the isobaric surfaces, hence any change
in inclination of the latter brings about an identical
change in orientation of the isopycnal surfaces.
The spacing of the isobaric surfaces with respect to 
under quasistatic conditions depends only on p for a
barotropic fluid. Furthermore, since is increased
with increasing pressure for a compressible fluid it is
apparent that the spacing of isobaric surfaces (for equal
increments of p) relative to will decrease with
increasing p. The condition of barotropy is illustrated
in Fig. 3.08-1(b).
A fluid under conditions of perfect hydrostatic balance would asume a barotropic state for which the pressure gradient can be represented as a function of p alone. However, this is a very special case of barotropy where the isobaric surfaces are level.