Abstract The onset of natural convection in a fluid-saturated anisotropic porous layer, which rotates about the vertical axis, under hypothesis local thermal non-equilibrium, is analysed. Since porosity medium assumed to be high, more suitable Darcy-Brinkman model adopted. Linear instability analysis conduction solution carried out. Nonlinear stability with respect $$L^2$$ <mml:math xmlns:mml="...