We investigate turbulent Rayleigh-B & eacute;nard convection (RBC) in a convection cell with square cross section and aspect ratio Gamma = width/height = 25 filled with the liquid metal alloy GaInSn at Prandtl number Pr approximate to 0.03. A dense array of thermocouples and ultrasonic Doppler velocimetry is employed to measure the temperature distributions at the top of the convection cell and horizontal velocity profiles, respectively, in the Rayleigh number range 3.27 & times; 10(4) less than or similar to Ra less than or similar to 2.17 & times; 10(5). Conspicuous thermal structures manifest themselves in the two-dimensional temperature fields and closely resemble the turbulent superstructures predicted in numerical simulations. The velocity data reveal flow features that indicate the presence of "jump rope vortices" (JRV). This can be seen in characteristic oscillations that permeate the entire 3D flow structure. The measured frequencies, f0 correspond very well with the empirical scaling f(0) proportional to Ra-0.419.The results thus provide experimental evidence that the jump-rope vortex, which has previously been identified as the striking dynamical feature of large-scale convection (LSC) in geometries with moderate aspect ratios (1.4 <= Gamma <= 5), also persists as a robust, three-dimensional mode embedded within turbulent convective superstructures at very large aspect ratios.

We present measurements of temperature fields and flow structures in a liquid metal Rayleigh–Bénard convection at a low Prandtl number, which were carried out for the first time using embedded fiber Bragg grating sensors (FBG) in combination with ultrasonic Doppler velocimetry (UDV). The FBG sensors enable minimally invasive, spatially resolved temperature measurements in optically opaque and electrically conductive liquids, thereby overcoming significant limitations of conventional thermocouples and optical techniques. This approach was applied in a cuboid Rayleigh–Bénard cell with an aspect ratio $$\Gamma = 5$$ Γ = 5 filled with GaInSn. In this paper, we present measurements at two Rayleigh numbers, $$\textrm{Ra} = 6.8 \times 10^4$$ Ra = 6.8 × 10 4 and $$2.1 \times 10^5$$ 2.1 × 10 5 . At the lower Rayleigh number, a coherent three-roll structure is observed with low-frequency modulation of thermal fluctuations. At the higher Rayleigh number, a cellular convection regime emerges, featuring checkerboard-like temperature patterns in the mid-plane and periodic plume emissions. Spectral analysis reveals a dominant oscillation frequency near $$f = 0.029$$ f = 0.029 Hz, while autocorrelation and extremum tracking highlight strong temporal coherence near the center and more volatile plume behavior near the sidewalls. The results of the temperature measurements and the UDV velocity measurements are consistent, thus confirming the capability of FBG sensors as a robust tool for investigating the spatio-temporal dynamics in convective systems.

The effect of a horizontal magnetic field on heat transport and flow structures in vertical liquid metal convection (Prandtl number $Pr \approx 0.03$ ) is investigated experimentally. The experiments are carried out for Rayleigh numbers in the range of $1.48 \times 10<^>6 \leqslant Ra \leqslant 3.54 \times 10<^>{7}$ and Chandrasekhar numbers in the range of $2 \times 10<^>2 \leqslant Q \leqslant 1.86 \times 10<^>6$ , as well as for the non-magnetic case ( $Q=0$ ). Measurements of the heat transport show a rise in the Nusselt number at low and moderate magnetic field strengths up to an optimum value of $Q$ , before a further increase in the magnetic field leads to a decrease in the transport properties. By applying simultaneous velocity and temperature measurements, we are able to identify three different oscillatory flow regimes for $10<^>{-5}\lt Q/Ra \lt 0.5$ and assign them to the respective heat transfer characteristics. In the range $10<^>{-5}\gt Q/Ra\gt 10<^>{-3}$ , first evidence of a transition to anisotropic flow structures caused by the magnetic field is visible. Two strongly oscillatory regimes are identified, where the energy is either distributed around a dominant frequency ( $10<^>{-3}\gt Q/Ra\gt 10<^>{-2}$ ), or strongly concentrated on a single frequency ( $10<^>{-2}\gt Q/Ra\gt 0.5$ ). The dominating frequency increases with the Rayleigh number according to $Ra<^>{0.71\pm 0.02}$ . This flow structure based regime separation correspond to changes of both the heat transfer through the Nusselt number and mass transfer through the Reynolds number.

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.

In Rayleigh–Bénard convection, the size of a flow domain and its aspect ratio $\varGamma$ (a ratio between the spatial length and height of the domain) affect the shape of the large-scale circulation. For some aspect ratios, the flow dynamics includes a three-dimensional oscillatory mode known as a jump rope vortex (JRV); however, the effects of varying aspect ratios on this mode are not well investigated. In this paper, we study these aspect ratio effects in liquid metals, for a low Prandtl number ${{Pr}}=0.03$ . Direct numerical simulations and experiments are carried out for a Rayleigh number range $2.9 \times 10^4 \leq {{Ra}} \leq 1.6 \times 10^6$ and square cuboid domains with $\varGamma =2$ , $2.5$ , $3$ and $5$ . Our study demonstrates that a repeating pattern of a JRV encountered at aspect ratio $\varGamma \approx 2.5$ is the basic structural unit that builds up to a lattice of interlaced JRVs at the largest aspect ratio. The size of the domain determines how many structural units are self-organised within the domain; the number of the realised units is expected to scale as $\varGamma ^2$ with sufficiently large and growing $\varGamma$ . We find the oscillatory modes for all investigated $\varGamma$ ; however, they are more pronounced for $\varGamma =2.5$ and $5$ . Future studies for large-aspect-ratio domains of different shapes would enhance our understanding of how the JRVs adjust and reorganise at such scaled-up geometries, and answer the question of whether they are indeed the smallest superstructure units.

The capabilities of Fiber Bragg Grating (FBG) sensors to measure temperature variations in the bulk of liquid flows were considered. In the first step of our research project, reported in this paper, we investigated to what extent the use of thin glass fibers without encapsulation, which only minimally disturb a flow, can fulfill the requirements for robustness and measurement accuracy. Experimental tests were performed in a benchmark setup containing 24 FBG measuring positions, which were instrumented in parallel with thermocouples for validation. We suggest a special assembly procedure in which the fiber is placed under a defined tension to improve its stiffness and immobility for certain flow conditions. This approach uses a single FBG sensor as a reference that measures the strain effect in real time, allowing accurate relative temperature measurements to be made at the other FBG sensor points, taking into account an appropriate correction term. Absolute temperature readings can be obtained by installing another well-calibrated, strain-independent thermometer on the reference FBG. We demonstrated this method in two test cases: (i) a temperature gradient with stable density stratification in the liquid metal GaInSn and (ii) the heating of a water column using a local heat source. In these measurements, we succeeded in recording both spatial and temporal changes in the linear temperature distribution along the fiber. We present the corresponding results from the tests and, against this background, we discuss the capabilities and limitations of this measurement technique with respect to the detection of temperature fields in liquid flows.

The acoustic spectrum of a gas-filled resonating cavity can be used to indirectly probe its internal velocity field. This unconventional velocimetry method is particularly interesting for opaque fluid or rapidly rotating flows, which cannot be imaged with standard methods. This requires to (i) identify a large enough number of acoustic modes, (ii) accurately measure their frequencies, and (iii) compare with theoretical synthetic spectra. Relying on a dedicated experiment, an air-filled rotating spheroid of moderate ellipticity, our study addresses these three challenges. To do so, we use a comprehensive theoretical framework, together with finite-element calculations, and consider symmetry arguments. We show that the effects of the Coriolis force can be successfully retrieved through our acoustic measurements, providing the first experimental measurements of the rotational splitting (or Ledoux) coefficients for a large collection of modes. Our results pave the way for the modal acoustic velocimetry to be a robust, versatile, and non-intrusive method for mapping large-scale flows. Pages: 1-14

Motivated by planetary-driven applications and experiments in non-spherical geometries, we study compressible fluid modes in rotating rigid ellipsoids. Such modes are also required for modal acoustic velocimetry (MAV), a promising non-invasive method to track the velocity field components in laboratory experiments. To calculate them, we develop a general spectral method in rigid triaxial ellipsoids. The description is based on an expansion onto global polynomial vector elements, satisfying the non-penetration condition on the boundary. Then, we investigate the diffusionless compressible modes in rotating (and magnetised) rigid ellipsoids. The spectral description is successfully benchmarked against three-dimensional finite-element computations and analytical predictions. A spectral convergence is obtained. Our results have direct implications for MAV in experiments, for instance in the ZoRo experiment (gas-filled rigid spheroid). So far, deformation and rotational effects have been theoretically considered separately, as small perturbations of the solutions in non-rotating spheres. We carefully compare the perturbation approach, in this illustrative geometry, to the polynomial solutions. We show that second-order ellipticity effects are often present, even in weakly deformed ellipsoids. Moreover, high-order effects due to rotation and/or ellipticity should be observed for some acoustic modes in experimental conditions. Thus, perturbation theory should be used with care in MAV. Instead, the spectral polynomial method paves the way for future MAV applications in fluid experiments with rigid ellipsoids.

Les modes acoustiques sont couramment utilises pour determiner les proprietes physiques de l'interieur des planetes et des etoiles. La methode d'imagerie par velocimetrie acoustique a ete recemment introduite en mecanique des fluides, en complement des methodes d'imagerie existantes. Elle consiste a reconstruire l'ecoulement a partir de la levee de degenerescence des modes acoustiques, observee experimentalement (par exemple) en presence d'un profil de rotation. Ainsi, des algorithmes d'inversion sont necessaires pour reconstruire indirectement l'ecoulement en rotation dans des experiences en geometrie quasi-spherique. Cependant, les objets celestes et les experiences ne sont pas rigoureusement spheriques, mais plutot ellipsoidaux (au premier ordre). Les effets topographiques et la rotation doivent alors etre pris en compte correctement dans le modele physique. Les methodes analytiques et numeriques existantes (en geometrie deformee) ne peuvent plus alors etre couplees facilement et efficacement aux algorithmes d'inversion. Pour remedier a ce probleme, nous avons developpe une nouvelle methode de Galerkin semi-analytique en ellipsoides tri-axes. Elle repose sur une decomposition polynomiale explicite, en coordonnees cartesiennes, des ecoulements potentiels en ellipsoides. Nous illustrons la methode en considerant les modes acoustiques d'un fluide compressible, uniforme et homentropique, avec une condition de Dirichlet homogene a la paroi (condition isobare). Nous validons nos resultats avec des simulations numeriques realisees avec le logiciel comsol. Nous etendrons cette methode novatrice afin de prendre en compte des effets physiques supplementaires, afin de decrire plus precisement les conditions experimentales.

We present a numerical study of axisymmetric flow in a rotating annulus in which local thermal forcing, via a heated annular ring on the outside of the base and a cooled circular disk in the centre of the top surface, drives convection. This new configuration is a variant of the classical thermally-driven annulus, where uniform heating and cooling are applied through the outer and inner sidewalls respectively. The annulus provides an analogue to a planetary circulation and the new configuration, with its more relaxed vertical thermal boundary conditions, is expected to better emulate vigorous convection in the tropics and polar regions as well as baroclinic instability in the mid-latitude baroclinic zone. Using the Met Office/Oxford Rotating Annulus Laboratory (MORALS) code, we have investigated a series of equilibrated, two dimensional axisymmetric flows across a large region of parameter space. These are characterized in terms of their velocity and temperature fields. When rotation is applied several distinct flow regimes may be identified for different rotation rates and strengths of differential heating. These regimes are defined as a function of the ratio of the horizontal Ekman layer thickness to the non-rotating thermal boundary layer thickness and are found to be similar to those identified in previous annulus experiments. Convection without rotation is also considered and the scaling of the heat transport with Rayleigh number is calculated. This is then compared with existing work on the classical annulus as well as horizontal and Rayleigh-Bénard convection. As with previous studies on both rotating and non-rotating convection the system’s behaviour is found to be aspect ratio dependent. This dependence is seen in the scaling of the non-rotating Nusselt number and in transitions between regimes in the rotating case although further investigation is required to fully explain these observations.

Vélocimétrie acoustique modale dans un sphéroïde gazeux en rotation Les vents zonaux sont une famille d’écoulement jouant un rôle majeur dans la transmission de la chaleur dans les systèmes géophysiques tels que le noyau de la Terre ou l’atmosphère de Jupiter. Cependant ces systèmes présentent des régimes turbulents dominés par la rotation, ce qui rend l’étude des vents zonaux diÿcile. De ce fait les méchanismes de leur formation et de leur dynamique sont encore mal compris. Les études expérimen-tales permettent une approche complémentaire où toutes les tailles de structures peuvent facilement coexister. Pour des raisons pratiques, la plupart des expériences existantes présentent des régimes di˙érents de ceux des systèmes planétaires.Nous présentons une nouvelle expérience de laboratoire appelée ZoRo pour étudier les vents zonaux. L’originalité de ce nouveau montage est qu’il se rapproche autant que possible des conditions présentes dans les systèmes planétaires. Pour ce faire, nous avons choisi de construire un sphéroïde (sphère aplatie) rempli d’air en rotation rapide.Pour mesurer la vitesse des éoulements nous avons développé une nouvelle technique de mesure qui s’appuie sur les modes acoustiques de la cavité fluide. Cette technique est non-intrusive et particulièrement adaptée à la mesure d’écoulement azimuthaux de grande échelle. Nous avons testé cette méthode sur des cas synthétiques puis des écoulements réels mesurés dans ZoRo. Grâce à la résolution d’un problème inverse, il est possible de remonter au champ de vitesse à partir des fréquences des modes acoustiques.Les vents zonaux sont une famille d’écoulement jouant un rôle majeur dans la transmission de la chaleur dans les systèmes géophysiques tels que le noyau de la Terre ou l’atmosphère de Jupiter. Cependant ces systèmes présentent des régimes turbulents dominés par la rotation, ce qui rend l’étude des vents zonaux diÿcile. De ce fait les méchanismes de leur formation et de leur dynamique sont encore mal compris. Les études expérimen-tales permettent une approche complémentaire où toutes les tailles de structures peuvent facilement coexister. Pour des raisons pratiques, la plupart des expériences existantes présentent des régimes di˙érents de ceux des systèmes planétaires.Nous présentons une nouvelle expérience de laboratoire appelée ZoRo pour étudier les vents zonaux. L’originalité de ce nouveau montage est qu’il se rapproche autant que possible des conditions présentes dans les systèmes planétaires. Pour ce faire, nous avons choisi de construire un sphéroïde (sphère aplatie) rempli d’air en rotation rapide.Pour mesurer la vitesse des éoulements nous avons développé une nouvelle technique de mesure qui s’appuie sur les modes acoustiques de la cavité fluide. Cette technique est non-intrusive et particulièrement adaptée à la mesure d’écoulement azimuthaux de grande échelle. Nous avons testé cette méthode sur des cas synthétiques puis des écoulements réels mesurés dans ZoRo. Grâce à la résolution d’un problème inverse, il est possible de remonter au champ de vitesse à partir des fréquences des modes acoustiques.