Stability of buoyant convection in a layer submitted to acoustic streaming
Résumé
The linear stability of the flows induced in a fluid layer by buoyant convection (due to an applied horizontal temperature gradient) and by acoustic streaming (due to an applied horizontal ultrasound beam) is studied. The vertical profiles of the basic flows are determined analytically, and the eigenvalue problem resulting from the temporal stability analysis is solved by a spectral Tau Chebyshev method. Pure acoustic streaming flows are found to be sensitive to a shear instability developing in the plane of the flow (two-dimensional instability), and the thresholds for this oscillatory instability depend on the normalized width Hb of the ultrasound beam with a minimum for Hb=0.32. Acoustic streaming also affects the stability of the buoyant convection. For a centered beam, effects of stabilization are obtained at small Prandtl number Pr for large beam widths Hb (two-dimensional shear instability) and for moderate Pr (three-dimensional oscillatory instability), but destabilization is also effective at small Pr for small beam widths Hb and at large Pr with a spectacular decrease of the thresholds of the three-dimensional steady instability. An adequate decentring of the ultrasound beam can enhance the stabilization. Insight into the stabilizing and destabilizing mechanisms is gained from the analysis of the fluctuating energy budget associated with the disturbances at threshold. The modifications affecting the two-dimensional shear instability thresholds are strongly connected to modifications of the velocity fluctuations when acoustic streaming is applied. Concerning the three-dimensional steady instability, the spectacular decrease of the thresholds is explained by the extension of the zone with inverse stratification in the lower half of the layer.
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