Internal waves in xenon near the critical point

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Abstract
Just above the liquid-vapor critical point, a fluid’s large compressibility causes a stable stratification in which the density varies by as much as 10% in 1 cm. This stratification supports internal gravity waves which we observed with an oscillator immersed in a near-critical xenon sample. We found the number and frequencies of the observable modes depended on the sample cell’s orientation, with only two modes seen in the horizontal cell. The frequencies of the two modes had different temperature dependences: with decreasing temperature, the higher frequency increased monotonically from 0.7 to 2.8 Hz, but the lower frequency varied nonmonotonically, with a maximum of 1.0 Hz at 20 mK above the critical temperature. These temperature dependences continued to 20 mK below the critical temperature, where the xenon was separated into liquid and vapor phases. We calculated these two frequencies by solving the eigenvalue problem of internal waves in a box containing a stratified fluid. The fluid’s density profile was obtained from xenon’s equation of state. The calculated and measured frequencies agree to within 15%. Analytical calculations based on simple approximations of the density profile provide insight into the observed temperature dependences.