Streaming flows due to g-jitter-induced natural convection

Abstract

We investigate streaming in a square cavity where a lateral temperature gradient interacts with a constant gravity field modulated by small harmonic oscillations of order ε. The Boussinesq equations are expanded by regular perturbation in powers of ε, and the O(ε2) equations contain Reynolds-stress-type terms that cause streaming. The resulting hierarchy of equations is solved by finite differences to investigate the O(ε1) and O(ε2) fields and their parametric dependence on the Rayleigh number Ra, Prandtl number Pr, and forcing frequency ω. It has been found that the streaming flow is quite small at small values of Ra, but becomes appreciable at high Ra and starts to influence such flow properties as the strength of the circulation and the overall heat transfer. Under suitable parametric conditions of finite frequency and moderate Pr the periodic forcing motion interacts with the instabilities associated with the O(εo) base flow leading to resonances that become stronger as Ra increases. It is argued that these resonances will have their greatest effect on streaming for Pr ≈ 1. At low frequencies the streaming flow shows marked structural changes as Ra is increased leading to an interesting change in the sign of the O(ε2) contribution to the Nusselt number. Also, as the frequency is changed the O(ε2) Nusselt number again changes sign at approximately the resonant frequency.