  In strictly speaking, all the natural phenomena on the earth should be
treated under rotating coordinate. The existence of baroclinic nonequivalent
barotropic laminar solution for rotating fluids is still open though the
laminar solutions for the irrotational fluid had been well studied. In this
letter, all the possible equivalent barotropic (EB) laminar solution are
firstly explored and all the possible baroclinic non-EB elliptic circulations
and hyperbolic laminar modes are discovered. The baroclinic EB circulations
(including the vortex streets and hurricane like vortices) possess rich
structures because either the arbitrary solutions of arbitrary nonlinear Poison
equations can be used or an arbitrary two-dimensional stream function is
revealed. The discovery of the baroclinic non-EB modes disproves a known
conjecture. The results may be broadly applied in atmospheric and oceanic
dynamics, plasma physics, astrophysics and so on.
