Amplitude equations and thermoconvective rolls far from the threshold

Amplitude equations are used to show that third order harmonics of a basic roll convective pattern can appear in the highly nonlinear régime of Rayleigh-Bénard thermoconvection. The phenomenon is induced by the nonlinear interaction of the roll pattern with its second order harmonics, which were first generated by the quadratic nonlinearity due to the convective terms of the time derivatives in the field equations. Good qualitative agreement with experimental data is obtained with only 4 amplitude equations. More precise quantitative results are deduced by increasing the number of amplitude equations. Comparison with purely numerical calculations is also discussed.