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.
Highlights
The detection of acoustic modes in the Sun led to one of the great breakthroughs in stellar physics, as it allowed the determination of the internal differential rotation in the convective zone and in the upper radiative zone [1]
Based on a variational principle established by Chandrasekhar [2] and later generalized by Lynden-Bell and Ostriker [3], it is possible to show that the eigenfrequency of an adiabatic pmode depends on the amount of global rotation, and on the internal differential rotation of the stellar medium [4]
We present here the first study involving acoustic modes to obtain a global measurement of a fluids differential rotation in a spherically symmetric cavity, validated through direct measurement of the differential rotation using conventional hot film anemometry
Summary
The detection of acoustic modes in the Sun led to one of the great breakthroughs in stellar physics, as it allowed the determination of the internal differential rotation in the convective zone and in the upper radiative zone [1]. Based on a variational principle established by Chandrasekhar [2] and later generalized by Lynden-Bell and Ostriker [3], it is possible to show that the eigenfrequency of an adiabatic pmode depends on the amount of global rotation, and on the internal differential rotation of the stellar medium [4]. This is in contrast to the rotationally-induced splitting of the Earths free oscillations, which, though routinely observed, can be successfully modeled by global rotation alone [5]. We conclude by discussing the potential of the technique as a general diagnostic tool for rotating fluids in axisymmetric cavities
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