In this talk, we will discuss the temperature patch problem for incompressible Boussinesq equation for 2-D and 3-D cases. This striated type problem was first considered for the 2-D incompressible Euler system, namely vortex patch problem solved by V.I.Yudovich and J.-Y.Chemin in 1963 and 1990s respectively. Later P.Gaublin and X. Saint-Raymond studied the vortex patch problem for 3-D inviscid flow and R. Danchin considered viscous vortex problem for Navier-Stokes system amd some related limit problems, which are fundamental to our talk.