Acoustic resonances in gas-filled spherical bulb with parabolic temperature profile

Abstract

Acoustics is used to probe the temperature profile within a sulfur plasma lamp. A spherically symmetric temperature profile is assumed that drops with the square of the radius, consistent with a constant volumetric heating model. Acoustic resonance frequencies are calculated exactly in the case of an ideal gas. Experimental measurement of a few resonant frequencies allows determination of the temperature profile curvature. This technique can be viewed as an extension of ultrasonic resonant spectroscopy to systems that are highly non-uniform due to off-equilibrium energy flow.

Convective instability in a stratified ideal gas containing an acoustic field

“…The instability is therefore governed by the response of the system to perturbations from spherical symmetry. Figure 4( a ) is a photograph of the convection pattern, overlayed with a plot of the time-averaged acoustic field (the lowest-order spherically symmetric mode, see Koulakis, Pree & Putterman 2018 a ; Russell 2010) and arrows depicting the direction of flow in the plasma plumes. The gas is, on average over a spherical shell, hottest in the middle and coldest near the glass, and so the density gradient points mostly radially outward.…”

“…We can define an acoustic analogue with the transformation for acoustic wavenumber , root-mean-squared acoustic amplitude , ideal gas thermal expansion coefficient and characteristic length scale , We estimate Ra in the experiment of figures 2 and 4, calculated using , , , and estimated from data in Koulakis et al. (2018 a , c ). Note, however, that this Rayleigh number is not sustained in the experiment.…”

Compressible fluid modes in rigid ellipsoids: towards modal acoustic velocimetry

“…In acoustics, non-isentropic background states (as driven by thermal diffusion in experiments) modify the acoustic spectrum. A first step has been achieved by Koulakis, Pree & Putterman (2018). They found the analytical description of the spherical acoustic modes with a parabolic temperature profile.…”

Acoustic and inertial modes in planetary-like rotating ellipsoids

“…Consequently, the next theoretical step is to find a suitable mathematical description of the planetary compressible modes in the coreless ellipsoid. The compressible modes are indeed expected to be regular in the latter geometry, to agree with the anelastic (inertial) modes [34–36] or the non-rotating acoustic modes in thermally stratified spheres [37]. In the incompressible regime, Vantieghem [38] pioneered a groundbreaking method to compute the inertial modes in rigid ellipsoids, based on global polynomial elements in the Cartesian coordinates.…”