All the possible equivalent barotropic (EB) laminar solutions are firstly explored,and all the possible non-EB elliptic circulations and hyperbolic laminar modes of rotating stratified fluids are discovered in this paper.The EB circulations (including the vortex streets and hurricane like vortices) possess rich structures,because either the arbitrary solutions of arbitrary nonlinear Poisson equations can be used or an arbitrary two-dimensional stream function is revealed which may be broadly applied in atmospheric and oceanic dynamics,plasma physics,astrophysics and so on.The discovery of the non-EB modes disproves a known conjecture.
Chinese ancient sage Laozi said that everything comes from'nothing'.Einstein believes the principle of nature is simple.Quantum physics proves that the world is discrete.And computer science takes continuous systems as discrete ones.This report is devoted to deriving a number of discrete models,including well-known integrable systems such as the KdV,KP,Toda,BKP,CKP,and special Viallet equations,from'nothing'via simple principles.It is conjectured that the discrete models generated from nothing may be integrable because they are identities of simple algebra,model-independent nonlinear superpositions of a trivial integrable system(Riccati equation),index homogeneous decompositions of the simplest geometric theorem(the angle bisector theorem),as well as the Möbious transformation invariants.
