  A noncommutative extension of an ideal (Hamiltonian) fluid model in
$3+1$-dimensions is proposed. The model enjoys several interesting features: it
allows a multi-parameter central extension in Galilean boost algebra (which is
significant being contrary to existing belief that similar feature can appear
only in $2+1$-dim.); noncommutativity generates vorticity in a canonically
irrotational fluid; it induces a non-barotropic pressure leading to a
non-isentropic system. (Barotropic fluids are entropy preserving as pressure
depends only on matter density.)
  Our fluid model is termed "Exotic" since it has close resemblance with the
extensively studied planar (2+1-dim.) Exotic models and Exotic (noncommutative)
field theories.
