Asymptotic Laws of Thermovibrational Convecton in a Horizontal Fluid Layer

作者：Smorodin B L^*; Myznikova B I; Keller I O

来源：Microgravity Science and Technology, 2017, 29(1-2): 19-28.

DOI：10.1007/s12217-016-9522-9

• Thermovibrational convection
• Instability
• Asymptotic behaviour

Theoretical study of convective instability is applied to a horizontal layer of incompressible single-component fluid subjected to the uniform steady gravity, longitudinal vibrations of arbitrary frequency and initial temperature difference. The mathematical model of thermovibrational convection has the form of initial boundary value problem for the Oberbeck-Boussinesq system of equations. The problems are solved using different simulation strategies, like the method of averaging, method of multiple scales, Galerkin approach, Wentzel-Kramers-Brillouin method and Floquet technique. The numerical analysis has shown that the effect of vibrations on the stability threshold is complex: vibrations can either stabilize or destabilize the basic state depending on values of the parameters. The influence of the Prandtl number on the instability thresholds is investigated. The asymptotic behaviour of critical values of the parameters is studied in two limiting cases: (i) small amplitude and (ii) low frequency of vibration. In case (i), the instability is due to the influence of thermovibrational mechanism on the classical Rayleigh-Benard convective instability. In case (ii), the nature of the instability is related to the instability of oscillating counter-streams with a cubic profile.

• 出版日期2017-2