Baroclinic equivalent and nonequivalent barotropic modes for rotating stratified flows

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.