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Publications and source records attributed to Jonathan M. Aurnou.
This paper is associated with a poster winner of a 2025 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, at https://doi.org/10.1103/APS.DFD.2025.GFM.P012
Magnetic field generation in giant planets and rapidly rotating stars produces a diverse range of field geometries, from large-scale dipole-dominated configurations to complex, small-scale multipolar structures. Earlier dynamo studies have suggested that multipolar solutions tend to arise when rotational effects become less dominant. We investigate the strength of non-dipolar magnetic fields generated in systems dominated by rotation. 40 three-dimensional, spherical-shell dynamo simulations were carried out using the MagIC code, primarily made up of bistable pairs - simulations with the same control parameters that can settle in both a dipolar and non-dipolar steady-state regime. We use this suite of models to test how their magnetic field strength scales with heat flux and velocity. Our dynamo simulations produce magnetic fields with morphologies that fall on the two distinct branches, dipolar or non-dipolar, yet have very similar convective velocities. The strength of the dipole component differs by an order of magnitude between the two regimes, when scaled as a function of driving power. However, their non-dipolar magnetic field strengths are very similar. We conclude that when attempting to predict the magnetic field strength of rapidly rotating planets and stars, one cannot assume that it will have a dipole-dominated geometry. In particular, the amplitude of the dipole component is expected to be an order of magnitude smaller in the non-dipolar regime.
Convection is ubiquitous in stellar and planetary interiors where it likely plays an integral role in the generation of magnetic fields. As the interiors of these objects remain hidden from direct observation, numerical models of convection are an important tool in the study of astrophysical dynamos. In such models, unrealistic large values of the viscous ($ν$) and thermal ($κ$) diffusivity are routinely used as an ad-hoc representation of the effects of subgrid scale turbulence which is otherwise too small-scale to resolve numerically. However, the functional forms of these diffusion coefficients can vary greatly between studies, complicating efforts to compare between results and against observations. We explore this issue by considering a series of non-rotating, non-magnetic, solar-like convection models with varying radial functions for the diffusivities and differing boundary conditions. We find that the bulk kinetic energy scales similarly regardless of the diffusivity parameterization. This scaling is consistent with a free-fall scaling, wherein viscosity plays a subdominant role in the force balance. We do not, however, observe such diffusion-free behavior in the convective heat transport. Our results also indicate that the functional form adopted for the diffusion coefficients can impact the distribution of turbulence within the convective shell. These results suggest that some care should be taken when comparing solar convection models directly against helioseismic observations.
Understanding planetary core convection dynamics requires the study of convective flows in which the Coriolis and Lorentz forces attain a leading-order, so-called magnetostrophic balance. Experimental investigations of rotating magnetoconvection (RMC) in the magnetostrophic regime are therefore essential to broadly characterize the properties of local-scale planetary core flow. Towards this end, we present here the first thermovelocimetric measurements of magnetostrophic, liquid metal convection, which are made using liquid gallium as the working fluid, at moderate rotation rates (Ekman numbers $10^{-4} \leq Ek\leq 10^{-5}$) and in the presence of dynamically strong magnetic fields (Elsasser number $Λ=1$). Complementary rotating convection (RC) experiments are performed at the same rotation rates to serve as reference cases. Our RMC velocity measurements adequately follow a geostrophic turbulent scaling for cases in which local-scale convective inertial forces exceed the Lorentz forces in the fluid bulk. In cases where Lorentz forces exceed local-scale inertia ($N_\ell \gtrsim 3$), the root-mean-square RMC velocities are magnetically damped, yielding values below the geostrophic turbulent RC scaling prediction. An enhancement in heat transfer is observed, which we attribute to the increased coherence of vertically aligned magnetostrophic convective flow. Extrapolating these laboratory results, we predict that convection-scale flows in Earth's core occur in the magnetically damped $N_\ell \gtrsim 3$ regime with Rayleigh number values between $10^{24}$ and $10^{26}$.
Current structure models of Jupiter and Saturn suggest that helium becomes immiscible in hydrogen in the outer part of the planets' electrically conducting regions. This likely leads to a layer in which overturning convection is inhibited due to a stabilizing compositional gradient. The presence of such a stably stratified layer impacts the location and mechanism of convectively-driven dynamo action. Juno's measurements of Jupiter's magnetic field enabled an estimate of its dynamo radius based on the magnetic Lowes spectrum. A depth of ~0.8R_J is obtained, where 1R_J is Jupiter's radius. This is rather deep, considering that the electrical conductivity inside Jupiter is expected to reach significant values at ~0.9R_J. Here we use 3-dimensional numerical dynamo simulations to explore the effects of the existence and location of a stably stratified helium rain layer on both the inferred Lowes radius and location of the radial extent of dynamo action. We focus on a Jupiter-like internal structure and electrical conductivity profile. We find that for shallower stable layers, there is no magnetic field generation occurring above the stable layer and the effective dynamo radius and the inferred Lowes radius is at the base of the layer. For deeper stable layers, Lowes radii of ~0.87R_J are inferred as a shallow secondary dynamo operates above the stable layer. Our results strongly suggest the existence of a stable layer extending from ~0.8R_J up to at least ~0.9R_J inside Jupiter. The physical origin of this extended stable layer and its connection to helium rain remain to be elucidated.
Convection in planets and stars is predicted to occur in the "ultimate regime'' of diffusivity-free, rapidly rotating turbulence, in which flows are characteristically unaffected by viscous and thermal diffusion. Boundary layer diffusion, however, has historically hindered experimental study of this regime. Here, we utilize the boundary-independent oscillatory thermal-inertial mode of rotating convection to realize the diffusivity-free scaling in liquid metal laboratory experiments. This oscillatory style of convection arises in rotating liquid metals (low Prandtl number fluids) and is driven by the temperature gradient in the fluid bulk, thus remaining independent of diffusive boundary dynamics. We triply verify the existence of the diffusivity-free regime via measurements of heat transfer efficiency $Nu$, dimensionless flow velocities $Re$, and internal temperature anomalies $θ$, all of which are in quantitative agreement with planar asymptotically-reduced models. Achieving the theoretical diffusivity-free scalings in desktop-sized laboratory experiments provides the validation necessary to extrapolate and predict the convective flows in remote geophysical and astrophysical systems.
We investigate how the strength of the Lorentz force alters stellar convection zone dynamics in a suite of buoyancy-dominated, three-dimensional, spherical shell convective dynamo models. This is done by varying only the magnetic Prandtl number, $Pm$, the non-dimensional form of the fluid's electrical conductivity $σ$. Because the strength of the dynamo magnetic field and the Lorentz force scale with $Pm$, it is found that the fluid motions, the pattern of convective heat transfer, and the mode of dynamo generation all differ across the $0.25 \leq Pm \leq 10$ range investigated here. For example, we show that strong magnetohydrodynamic effects cause a fundamental change in the surface zonal flows: differential rotation switches from solar-like (prograde equatorial zonal flow) for larger electrical conductivities to an anti-solar differential rotation (retrograde equatorial zonal flow) at lower electrical conductivities. This study shows that the value of the bulk electrical conductivity is important not only for sustaining dynamo action, but can also drive first-order changes in the characteristics of the magnetic, velocity, and temperature fields. It is also associated with the relative strength of the Lorentz force in the system as measured by the local magnetic Rossby number, $Ro_\ell^M$, which we show is crucial in setting the characteristics of the large-scale convection regime that generates those dynamo fields.
In this study, we analyse "magneto-Stokes" flow, a fundamental magnetohydrodynamic (MHD) flow that shares the cylindrical-annular geometry of the Taylor-Couette cell, but uses applied electromagnetic forces to circulate a free-surface layer of electrolyte at low Reynolds numbers. The first complete, analytical solution for time-dependent magneto-Stokes flow is presented and validated with coupled laboratory and numerical experiments. Three regimes are distinguished (shallow-layer, transitional, and deep-layer flow regimes), and their influence on the efficiency of microscale mixing is clarified. The solution in the shallow-layer limit belongs to a newly-identified class of MHD potential flows, and thus induces mixing without the aid of axial vorticity. We show that these shallow-layer magneto-Stokes flows can still augment mixing in distinct Taylor dispersion and advection-dominated mixing regimes. The existence of enhanced mixing across all three distinguished flow regimes is predicted by asymptotic scaling laws and supported by three-dimensional numerical simulations. Mixing enhancement is initiated with the least electromagnetic forcing in channels with order-unity depth-to-gap-width ratios. If the strength of the electromagnetic forcing is not a constraint, then shallow-layer flows can still yield the shortest mixing times in the advection-dominated limit. Our robust description of momentum evolution and mixing of passive tracers makes the annular magneto-Stokes system fit for use as an MHD reference flow.
Rotating convective turbulence is ubiquitously found across geophysical settings, such as surface and subsurface oceans, planetary atmospheres, molten metal planetary cores, magma chambers, and magma oceans. Depending on the thermal and material properties of the system, buoyant convection can be driven thermally or compositionally, where a Prandtl number ($Pr = ν/ κ_i$) defines the characteristic diffusion properties of the system, with $κ_i = κ_T$ representing thermal diffusion and $κ_i = κ_C$ representing chemical diffusion. These numbers vary widely for geophysical systems; for example, the liquid iron undergoing thermal-compositional convection in Earth's core is defined by $Pr_T \approx 0.1$ and $Pr_C \approx 100$, while a thermally-driven liquid silicate magma ocean is defined by $Pr_T \approx 100$. Currently, most numerical and laboratory data for rotating convective flows exists at $Pr = O(1)$; high $Pr$ rotating convection relevant to compositionally-driven core flow and other systems is less commonly studied. Here, we address this deficit by carrying out a broad suite of rotating convection experiments made over a range of $Pr$ values, employing water and three different silicone oils as our working fluids ($Pr = $ 6, 41, 206, and 993). Using measurements of flow velocities (Reynolds, $Re$) and heat transfer efficiency (Nusselt, $Nu$), a baroclinic torque balance is found to describe the turbulence regardless of Prandtl number so long as $Re$ is sufficiently large ($Re \gtrsim 10$). Estimated turbulent scales are found to remain close to onset scales in all experiments, a result that may extrapolate to planetary settings. Lastly, we use our data to build $Pr$-dependent predictive nondimensional and dimensional scaling relations for rotating convective velocities that can be applied across a broad range of geophysical fluid dynamical settings.
The operation of the solar dynamo, with all of its remarkable spatio-temporal ordering, remains an outstanding problem of modern solar physics. A number of mechanisms that might plausibly contribute to its operation have been proposed, but the relative role played by each remains unclear. This uncertainty stems from continuing questions concerning the speed and structure of deep-seated convective flows. Those flows are in-turn thought to sustain both the Sun's turbulent EMF and the large-scale flows of differential rotation and meridional circulation suspected of influencing the dynamo's organization and timing. Continued progress in this area is complicated by (i) inconsistencies between helioseismic measurements of convective and meridional flow made with different techniques and instruments, and (ii) a lack of high-latitude data for convection, differential rotation, and meridional flow. We suggest that the path forward to resolving these difficulties is twofold. First, the acquisition of long-term helioseismic and emissivity measurements obtained from a polar vantage point is vital to complete our picture of the Sun's outer convection zone. Second, sustained and expanded investment in theory-oriented and combined theory/observational research initiatives will be crucial to fully exploit these new observations and to resolve inconsistencies between existing measurements.
Coupled laboratory-numerical experiments of Rayleigh-Bénard convection (RBC) in liquid gallium subject to a vertical magnetic field are presented. The experiments are carried out in two cylindrical containers with diameter-to-height aspect ratio $Γ= 1.0$ and $2.0$ at varying thermal forcing (Rayleigh numbers $10^5 \lesssim Ra \lesssim 10^8$) and magnetic field strength (Chandrasekhar numbers $0\lesssim Ch \lesssim 3\times 10^5$). Laboratory measurements and numerical simulations confirm that magnetoconvection in our finite cylindrical tanks onsets via non-drifting wall-attached modes, in good agreement with asymptotic predictions for a semi-infinite domain. With increasing supercriticality, the experimental and numerical thermal measurements and the numerical velocity data reveal transitions between wall mode states with different azimuthal mode numbers and between wall-dominated convection to wall and interior multimodality. These transitions are also reflected in the heat transfer data, which combined with previous studies, connect onset to supercritical turbulent behaviors in liquid metal magnetoconvection over a large parameter space. The gross heat transfer behaviors between magnetoconvection and rotating convection in liquid metals are compared and discussed.
We present laboratory measurements of the interaction between thermoelectric currents and turbulent magnetoconvection. In a cylindrical volume of liquid gallium heated from below and cooled from above and subject to a vertical magnetic field, it is found that the large scale circulation (LSC) can undergo a slow axial precession. Our experiments demonstrate that this LSC precession occurs only when electrically conducting boundary conditions are employed, and that the precession direction reverses when the axial magnetic field direction is flipped. A thermoelectric magnetoconvection (TEMC) model is developed that successfully predicts the zeroth-order magnetoprecession dynamics. Our TEMC magnetoprecession model hinges on thermoelectric current loops at the top and bottom boundaries, which create Lorentz forces that generate horizontal torques on the overturning large-scale circulatory flow. The thermoelectric torques in our model act to drive a precessional motion of the LSC. This model yields precession frequency predictions that are in good agreement with the experimental observations. We postulate that thermoelectric effects in convective flows, long argued to be relevant in liquid metal heat transfer and mixing processes, may also have applications in planetary interior magnetohydrodynamics.
Coriolis-centrifugal convection (C$^3$) in a cylindrical domain constitutes an idealised model of tornadic storms, where the rotating cylinder represents the mesocyclone of a supercell thunderstorm. We present a suite of C$^3$ direct numerical simulations, analysing the influence of centrifugal buoyancy on the formation of tornado-like vortices (TLVs). TLVs are self-consistently generated provided the flow is within the quasi-cyclostrophic (QC) regime. This requires the Froude number to be greater than the radius-to-height aspect ratio, $Fr \gtrsim γ$. We show that the TLVs share many features with realistic tornadoes, such as azimuthal velocity profiles, intensification of the vortex strength, and helicity characteristics. Further, we analyse the influence of the mechanical bottom boundary conditions on the formation of TLVs, finding that a rotating fluid column above a stationary surface does not generate TLVs if centrifugal buoyancy is absent. In contrast, TLVs are generated in the QC regime with any bottom boundary conditions when centrifugal buoyancy is present. Our simulations bring forth insights into natural supercell thunderstorm systems by identifying properties that determine whether a mesocyclone becomes tornadic or remains non-tornadic. Our $Fr \gtrsim γ$ predictions dimensionally imply a critical mesocyclone angular rotation rate of $\widetildeΩ_{mc} \gtrsim \sqrt{g/H_{mc}}$. Taking a typical mesocyclone height of $H_{mc}\approx 12$ km, this translates to $\widetildeΩ_{mc}\gtrsim 3~\times~10^{-2}$s$^{-1}$ for centrifugal buoyancy-dominated, quasi-cyclostrophic tornadogenesis. The formation of the simulated TLVs happens at all heights on the centrifugal buoyancy time scale $τ_{cb}$. This implies a roughly 1 minute, height-invariant formation for natural tornadoes, consistent with recent observational estimates.
We present the first detailed thermal and velocity field characterization of convection in a rotating cylindrical tank of liquid gallium, which has thermophysical properties similar to those of planetary core fluids. Our laboratory experiments, and a closely associated direct numerical simulation, are all carried out in the regime prior to the onset of steady convective modes. This allows us to study the oscillatory convective modes, sidewall modes and broadband turbulent flow that develop in liquid metals before the advent of steady columnar modes. Our thermo-velocimetric measurements show that strongly inertial, thermal wind flows develop, with velocities reaching those of comparable non-rotating cases. Oscillatory bulk convection and wall modes coexist across a wide range of our experiments, along with strong zonal flows that peak in the Stewartson layer, but that extend deep into the fluid bulk in the higher supercriticality cases. The flows contain significant time-mean helicity that is anti-symmetric across the midplane, demonstrating that oscillatory liquid metal convection contains the kinematic components to sustain system-scale dynamo generation.
Buoyancy-driven convection is likely the dominant driver of turbulent motions in the universe, and thus, is widely studied by physicists, engineers, geophysicists and astrophysicists. Maybe unsurprisingly, these different communities discuss the gross convective behaviors in different ways, often without significant cross-talk existing between them. Here, we seek to draw connections between these communities. We do so by carrying out a set of basic scale estimations for how heat and fluid momentum transport should behave in non-rotating, slowly rotating and rapidly rotating buoyancy-driven convective environments. We find that slowly and rapidly rotating scalings can be inter-related via one parameter, the so-called convective Rossby number $\RoC$, a dissipation-free parameter measuring the importance of buoyancy driving relative to rotation. Further, we map between non-flux-based and the flux-based, buoyancy-driven scalings used by different groups. In doing so, these scalings show that there are clean connections between the different communities' approaches and that a number of the seemingly different scalings are actually synonymous with one another.
Understanding large scale circulations (LSCs) in turbulent convective systems is important for the study of stars, planets and in many industrial applications. The canonical model of the LSC is quasi-planar with additional horizontal sloshing and torsional modes [Brown E, Ahlers G (2009) J. Fluid Mech. 638:383--400; Funfschilling D, Ahlers G (2004) Phys. Rev. Lett. 92(19):194502; Xi HD et al. (2009) Phys. Rev. Lett. 102(4):044503; Zhou Q et al. (2009) J. Fluid Mech. 630:367--390]. Using liquid gallium as the working fluid, we show via coupled laboratory-numerical experiments that the LSC in a tank with aspect ratios greater than unity takes instead the form of a "jump rope vortex", a strongly three-dimensional mode that periodically orbits around the tank following a motion much like a jump rope on a playground. Further experiments show that this jump rope flow also exists in more viscous fluids such as water, albeit with a far smaller signal. Thus, this new jump rope mode is an essential component of the turbulent convection that underlies our observations of natural systems.
The onset of dynamo action is investigated within the context of a newly developed low Rossby, low magnetic Prandtl number, convection-driven dynamo model. This multiscale model represents an asymptotically exact form of an $α^2$ mean field dynamo model in which the small-scale convection is represented explicitly by finite amplitude, single mode solutions. Both steady and oscillatory convection are considered for a variety of horizontal planforms. The kinetic helicity is observed to be a monotonically increasing function of the Rayleigh number. As a result, very small magnetic Prandtl number dynamos can be found for sufficiently large Rayleigh numbers. All dynamos are found to be oscillatory with an oscillation frequency that increases as the strength of the convection is increased and the magnetic Prandtl number is reduced. Kinematic dynamo action is strongly controlled by the profile of the helicity; single mode solutions which exhibit boundary layer behavior in the helicity show a decrease in the efficiency of dynamo action due to the enhancement of magnetic diffusion in the boundary layer regions. For a given value of the Rayleigh number, lower magnetic Prandtl number dynamos are excited for the case of oscillatory convection in comparison to steady convection. With regards to planetary dynamos, these results suggest that the low magnetic Prandtl number dynamos typical of liquid metals are more easily driven by thermal convection than by compositional convection.
It is a well established result of linear theory that the influence of differing mechanical boundary conditions, i.e., stress-free or no-slip, on the primary instability in rotating convection becomes asymptotically small in the limit of rapid rotation. This is accounted for by the diminishing impact of the viscous stresses exerted within Ekman boundary layers and the associated vertical momentum transport by Ekman pumping. By contrast, in the nonlinear regime recent experiments and supporting simulations are now providing evidence that the efficiency of heat transport remains strongly influenced by Ekman pumping in the rapidly rotating limit. In this paper, a reduced model is developed for the case of low Rossby number convection in a plane layer geometry with no-slip upper and lower boundaries held at fixed temperatures. A complete description of the dynamics requires the existence of three distinct regions within the fluid layer: a geostrophically balanced interior where fluid motions are predominately aligned with the axis of rotation, Ekman boundary layers immediately adjacent to the bounding plates, and thermal wind layers driven by Ekman pumping in between. The reduced model uses a classical Ekman pumping parameterization to alleviate the need for spatially resolving the Ekman boundary layers. Results are presented for both linear stability theory and a special class of nonlinear solutions described by a single horizontal spatial wavenumber. It is shown that Ekman pumping allows for significant enhancement in the heat transport relative to that observed in simulations with stress-free boundaries. Without the intermediate thermal wind layer the nonlinear feedback from Ekman pumping would be able to generate a heat transport that diverges to infinity. This layer arrests this blowup resulting in finite heat transport at a significantly enhanced value.