Effect of gravitational acceleration on temperature wave propagation in a critical fluid

Temperature propagation near the critical point of a classical fluid is investigated theoretically. The governing equations of thermal energy transfer near the critical point are introduced and a linear analysis is carried out. The dispersion relation between the angular frequency and the wave number is obtained and the wave characteristics are discussed. The effect of gravitational acceleration on the temperature wave propagation is made clear. Through this analysis, the following results were obtained; (1) The propagation speed of temperature waves is γ/(ρ0κT),where γ, ρ0, and κT are, respectively, the ratio of specific heats, the density, and the isothermal compressibility, with or without gravity if the wavelength is larger than 10−3.(2) The amplitude of wave increases with time in the antigravitational direction and decreases in the gravitational direction but the decay time is long if the wave number is small. (3) Waves decay quickly if the wave number is larger than 104.