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We present three results on stability of rolls in Boussinesq convection in aplane horizontal layer with rigid boundaries that is rotating about an inclinedaxis with the angular velocity $\Omega=(\Omega_1,\Omega_2,\Omega_3)$. i. Wecall the full problem the set of equations governing the temporal behaviour ofthe flow and temperature for an arbitrary $\Omega$, and by the reduced problemthe set of equations for the angular velocity $(\Omega_1,0,\Omega_3)$. Here$x,y$ are horizontal Cartesian coordinates in the layer and $z$ is the verticalone. We prove that a $y$-independent solution to one of the two problems isalso a solution to the second one. ii. We calculate the critical Rayleighnumber for the monotonic onset of convection. The instability mode in the formof rolls (a flow independent of a horizontal direction) is assumed. Let $\beta$be the angle between the horizontal projection of $\Omega$ and the rolls axes.We show that $\beta=0$ for the least stable mode. Taking i into account, weconclude that the critical Rayleigh number for the onset of convection isindependent of $\Omega_1$ and $\Omega_2$ and the emerging flow are rolls withaxis aligned with the horizontal component of the rotation vector. iii. Westudy the behaviour of convective flows by integrating numerically thethree-dimensional equations of convection for $\Omega=(0,\Omega_2,\Omega_3)$and a range of the Rayleigh numbers, other parameters of the problem beingfixed. We assume square horizontal periodicity cells, whose sides are equal tothe period of the most unstable mode. The computations indicate that, ingeneral, in the nonlinear regime convective rolls become more stable as$\Omega_2$ increases. Namely, on increasing $\Omega_2$, the interval of theRayleigh numbers for which convective rolls are stable increases.

Stability of convective rolls in a horizontal layer rotating about an inclined axis