Modal acoustic velocimetry in libration-driven flows

Abstract

Flows in rapidly spinning bodies, such as the iconic libration-induced flow, are key ingredients of the dynamics of stars and planetary interiors. Laboratory experiments of such flows experience a strong centrifugal acceleration, which hinders the use of classical velocimetry methods relying on particle tracking. Modal acoustic velocimetry was introduced by Triana et al. (New J Phys 16(11):113005, 2014) as a new particle-free method, inspired from helioseismology, to alleviate this problem. In this method, acoustic modes are excited in the fluid and recorded in the spinning container. Rotation and fluid flow modify the characteristics of these modes, lifting the degeneracy of non-axisymmetric modes. To date, this method has only been applied to stationary or statistically stationary flows, by measuring frequency splittings in the spectral domain. Here, we analyze time-varying libration-induced flows. We propose and test two data acquisition strategies. The first strategy operates in the frequency domain and relies on the periodicity of the flow, while the second strategy involves a high-resolution algorithm applied in the time domain. The retrieved mode frequency splittings are compared to those computed for a classical linear libration-induced flow model as reported (Greenspan The theory of rotating fluids, Cambridge University Press, Cambridge, 1968). A very good agreement is obtained, but we observe an unexpected time delay, which we attribute to the buildup time of acoustic modes. We retrieve more than 50 splitting measurements at 10 successive libration phases. Inverting these data with the SOLA method, often used in helioseismology, we derive profiles (1D inversion) and maps (2D inversion) of the azimuthally averaged fluid rotation rate. The inversions recover the main characteristics of this time-dependent flow. The 2D inversion confirms the invariance of the flow along the rotation axis. Resolution kernels show that flow can be mapped on patches that spread over approximately \(5 \%\) of a meridian quarter-plane. Our study paves the way to the investigation of more exotic regimes of precession- or libration-induced flows.