Article Dans Une Revue Journal of Fluid Mechanics Année : 2025

Baroclinic transition in acoustic streaming: beyond Rayleigh’s paradigm

Résumé

Standing acoustic waves in a channel generate time-mean Eulerian flows. In homogeneous fluids, these streaming flows have been shown by Rayleigh to result from viscous attenuation of the waves in oscillatory boundary (i.e. Stokes) layers. However, the strength and structure of the mean flow significantly depart from the predictions of Rayleigh when inhomogeneities in fluid compressibility or density are present. This change in mean flow behaviour is of particular interest in thermal management, as streaming flows can be used to enhance cooling. In this work, we consider standing acoustic wave oscillations of an ideal gas in a differentially heated channel with hot- and cold-wall temperatures respectively set to $T_* + \Delta \varTheta _*$ and $T_*$ . An asymptotic analysis for a normalised temperature differential $\Delta \varTheta _*/T_*$ comparable to the small acoustic Mach number is performed to capture the transition between the two documented regimes of Rayleigh streaming ( $\Delta \varTheta _*\,{=}\,0$ ) and baroclinic streaming ( $\Delta \varTheta _* =O(T_*)$ ). Our analytical solution accounts for existing experimental and numerical results and elucidates the separate contributions of viscous torques in Stokes layers and baroclinic forcing in the interior to driving the streaming flow. The analysis yields a scaling estimate for the temperature difference $\Delta \varTheta _{c_*}$ at which baroclinic driving is comparable to viscous forcing, signalling the smooth transition from Rayleigh to baroclinic acoustic streaming.

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Dates et versions

hal-05227424 , version 1 (28-08-2025)

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Remil Mushthaq, Guillaume Michel, Gregory P Chini. Baroclinic transition in acoustic streaming: beyond Rayleigh’s paradigm. Journal of Fluid Mechanics, 2025, 1017, pp.A32. ⟨10.1017/jfm.2025.10450⟩. ⟨hal-05227424⟩
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