The response of a near-critical fluid to low-frequency vibrations is investigated by means of numerical simulations. Its characteristics are first established by one-dimensional analysis. It is shown that the strong thermo-mechanical coupling occurring in the boundary layers tends to make the fluid oscillate homogeneously at low frequencies, and with a larger amplitude than in a normal gas. The numerical results obtained in this first part are found to confirm earlier predictions made in

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... ing theoretical work. Then, the study is extended to a two-dimensional configuration. In a square cavity, the wall shear stresses developing along the longitudinal boundaries do not affect the one-dimensional regime, since the viscous layer present in these areas behaves like the Stokes boundary layer. By contrast, thermostatting these boundaries, like the others, generates local curvature of the stream lines. The fluid response to the homogeneous acceleration field then takes some more pronounced two-dimensional patterns, but remains driven by the strong alternating expansions and retractions of the fluid in the thermal boundary layers, which are specific to near-critical fluids.