Andres Larraza Anthony A. Atchley
Phys. Dept., Code PH/La, Naval Postgraduate School, Monterey, CA 93943
Nonlinear effects that lead to amplitude saturation in a thermoacoustic prime mover, are described. The evolution of the acoustic amplitude is described by a homogeneous Ginzburg equation of the form dA/dt=(alpha)A-(beta)A[sup 2]. The linear term represents the contribution from the power output due to the temperature gradient and viscous and thermal losses. The coefficient (alpha) is positive above onset. The cubic term is a consequence of the nonlinear induced vorticity at the boundary layer that originates from irreversible terms. In the approximation considered, the coefficient (beta) is positive and a steady state results from the balance between the linear growth and the nonlinear saturation. The steady-state amplitudes are in qualitative agreement with observations made by Wheatley [Frontiers in Physical Acoustics, Varena (1986)] and Hofler et al. [see abstract in this session]. Observations made by Swift [J. Acoust. Soc. Am. 92, 1551 (1992)] on the dependence of acoustic pressure versus heater power are also in qualitative agreement with the theory. [Work supported by ONR and NPS Direct-Funding Program.]