Localized convection in a rotating system

We study two-dimensional spatially localized convection in a horizontal fluid layer rotating around the vertical and heated from below [1]. With stress-free boundary conditions stationary spatially localized convection is present [2]. These states are embedded in a background shear layer and lie on a pair of intertwined solution branches exhibiting ``slanted snaking'' [3]. Similar solutions with no-slip boundary conditions are no longer embedded in a background shear and exhibit standard snaking, i.e. snaking without a slant. These solutions may be stable [4]. 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. An explanation of the results is given.\\[4pt] [1] Veronis, J. Fluid Mech. 5, 401--435 (1959)\\[0pt] [2] Beaume et al., J. Fluid Mech. 717, 417--448 (2013)\\[0pt] [3] Dawes, SIAM J. Appl. Dyn. Syst. 7, 186--206 (2008)\\[0pt] [4] Beaume et al., submitted