Nonlinear beat Cepheid models

The numerical hydrodynamic modeling of beat Cepheid behavior has been a lon g-standing quest in which purely radiative models have failed miserably. We find that beat pulsations occur naturally when turbulent convection is acc ounted for in our hydrodynamics codes. The development of a relaxation code and of a Floquet stability analysis greatly facilitates the search for and analysis of beat Cepheid models. The conditions for the occurrence of beat behavior can be understood easily and at a fundamental level with the help of amplitude equations. Here a discriminant D arises whose sign decides wh ether single-mode or double-mode pulsations can occur in a model, and this D depends only on the values of the nonlinear coupling coefficients between the fundamental and the first overtone modes. For radiative models D is al ways found to be negative, but with sufficiently strong turbulent convectio n its sign reverses.