Helioseismology in a bottle: modal acoustic velocimetry

Abstract

Measurement of the differential rotation of the Sunʼs interior is one of the great achievements of helioseismology, providing important constraints for stellar physics. The technique relies on observing and analyzing rotationally-induced splittings of p-modes in the star. Here, we demonstrate the first use of the technique in a laboratory setting. We apply it in a spherical cavity with a spinning central core (spherical-Couette flow) to determine the mean azimuthal velocity of the air filling the cavity. We excite a number of acoustic resonances (analogous to p-modes in the Sun) using a speaker and record the response with an array of small microphones on the outer sphere. Many observed acoustic modes show rotationally-induced splittings, which allow us to perform an inversion to determine the airʼs azimuthal velocity as a function of both radius and latitude. We validate the method by comparing the velocity field obtained through inversion against the velocity profile measured with a calibrated hot film anemometer. This modal acoustic velocimetry technique has great potential for laboratory setups involving rotating fluids in axisymmetric cavities. It will be useful especially in liquid metals where direct optical methods are unsuitable and ultrasonic techniques very challenging at best.

Acoustic spectra of a gas-filled rotating spheroid

“…We aim to use this modal acoustic velocimetry method to image flow fields in our ZoRo apparatus. Having identified modes up to l = 10 and n = 3, we can expect a spatial resolution of 1/5 of the cavity radius 8 . This modal acoustic velocimetry is thus a robust, versatile and non-intrusive velocimetry method.…”

“…invariant along the axis of rotation of the fluid, forming concentric cylindrical shells 18,19 . Such flows are expected to have significant influence on acoustic global modes 7,8 .…”

The Internal Rotation Profile of the B-Type Star Kic 10526294 From Frequency Inversion of Its Dipole Gravity Modes

“…Helioseismology provided a very detailed view of the internal rotation profile q W r, ( ) of the Sun for the radial range Î   r R R 0.2 , 1.0 [ ] (  R denotes the solar radius) and for all co-latitudes θ, through frequency inversion of the rotational splittings of its hundreds of detected acoustic modes (e.g., Christensen-Dalsgaard 2002; Thompson et al 2003), a technique that has even found its way to laboratory experiments (Triana et al 2014). Given that acoustic modes do not have sufficient probing power in the innermost regions, and that the Sun does not reveal gravity modes, it is not possible to deduce the rotational profile for   r R 0.2 .…”

“…Despite their frequent occurrence in, e.g., geophysics, counter-rotating solutions were considered inappropriate for stars. Independent of that restriction, the Kepler results for W r ( ) have so far delivered an important calibration for the improvement of evolutionary models for single and binary lowmass stars, given that the theoretical predictions of angular momentum transport result in core rotation rates that are higher by at least an order of magnitude than observed (see, e.g., Eggenberger et al 2012;van Saders & Pinsonneault 2013;Cantiello et al 2014, for the input physics in question). The redistribution and loss of angular momentum during evolution is also required based on the internal rotation properties of white dwarfs derived from both forward modeling and the inversion of their rotationally split g mode oscillation frequencies (Charpinet et al 2009;Córsico et al 2012).…”

Low-cost Solutions for Velocimetry in Rotating and Opaque Fluid Experiments using Ultrasonic Time of Flight

“…However, it comes with the drawback, that ToF only provides an integrated value of the velocity over the length of the ultrasonic path and there is no spatial resolution of the flow velocity. Recent studies have also introduced the concept of modal acoustic tomography, that relies on the rotational splitting of acoustic normal modes, to extract flows in the absence of tracer particles [9][10][11]. This method has successfully been implemented using gas as a fluid medium and bears potential for measurements in other opaque fluids such as liquid metals.…”