Spatially localized patterns in 2D and 3D doubly diffusive convection

Doubly diffusive convection, that is, convection driven by a combination of concentration and temperature gradients, is known to display a wealth of dynamical behavior whose properties depend on the gradients. In the present work, we first investigate spatially localized states in two-dimensional horizontal thermosolutal convection with no-slip boundary conditions at top and bottom and vertical gradients of temperature and concentration. Numerical continuation demonstrates the formation of stationary convectons in the form of 1-pulse and 2-pulse states of both odd and even parity while time integration reveals the presence of stable time dependent spatially localized states. We next turn to large scale three-dimensional vertical enclosures placed in horizontal thermal and solutal gradients. Different types of spatially localized states are computed and the results related to the presence of homoclinic snaking.