Gravity Modes in ZZ Ceti Stars. III. Effects of Turbulent Dissipation

Abstract

We investigate dynamical interactions between turbulent convection and g-mode pulsations in ZZ Ceti variables. Since our understanding of turbulence is rudimentary, we are compelled to settle for order-of-magnitude results. A key feature of these interactions is that convective response times are much shorter than pulsation periods. Thus the dynamical interactions enforce near uniform horizontal velocity inside the convection zone. They also give rise to a narrow shear layer in the region of convective overshoot at the top of the radiative interior. Turbulent damping inside the convection zone is negligible for all modes, but that in the region of convective overshoot may be significant for a few long-period modes near the red edge of the instability strip. These conclusions are in accord with those reached earlier by Brickhill. Our major new result concerns nonlinear damping arising from the Kelvin-Helmholtz instability of the aforementioned shear layer. Amplitudes of overstable modes saturate where dissipation due to this instability balances excitation by convective driving. This mechanism of amplitude saturation is most effective for long-period modes, and it may play an important role in defining the red edge of the instability strip.