Spatially localized convection in a rotating layer

We study two-dimensional stationary convection in a horizontal fluid layer heated from below and rotating about the vertical. With stress-free boundary conditions at top and bottom, spatially localized states can be found that are embedded in a self-generated background shear zone and lie on a pair of intertwined solution branches exhibiting ``slanted snaking.'' States of this type are present even in the absence of bistability between conduction and periodic convection -- a consequence of the conservation of zonal momentum.\footnote{C. Beaume et al., J. Fluid Mech. 717, 417 (2013)} With no-slip boundary conditions this quantity is no longer conserved but localized states continue to exist. These are no longer embedded in a background shear zone and exhibit standard snaking. Homotopic continuation from free-slip to no-slip boundary conditions is used to track the changes in the properties of the solutions and the associated bifurcation diagrams.\footnote{C. Beaume et al., Phys. Fluids 25, 124105 (2013)}