Amplitude equations for three dimensional roll-type double-diffusive convection with an arbitrary cell width in the neighborhood of Hopf bifurcation points

Three dimensional roll-type double-diffusive convection in a horizontally infinite layer of an uncompressible liquid is considered in the neighborhood of Hopf bifurcation points. An A$\Psi$-system of amplitude equations for the variations of convective rolls amplitude is derived by multiple-scaled method. The cell width can be arbitrary, which is important for large Rayleigh numbers. It is noted that in 3D case an interaction of convection and horizontal vorticity field plays an essential role and can hardly be neglected. Different cases of the derived equations are discussed.