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We investigate the linear and non-linear properties of the Goldreich–Schubert–Fricke (GSF) instability in stellar radiative zones with arbitrary local (radial and latitudinal) differential rotation. This instability may lead to turbulence that contributes to the redistribution of angular momentum and chemical composition in stars. In our local Boussinesq model, we investigate varying the orientation of the shear with respect to the 'effective gravity', which we describe using the angle ϕ. We first perform an axisymmetric linear analysis to explore the effects of varying ϕ on the local stability of arbitrary differential rotations. We then explore the non-linear hydrodynamical evolution in three dimensions using a modified shearing box. The model exhibits both diffusive GSF instability and a non-diffusive instability that occurs when the Solberg-Høiland criteria are violated. We observe the non-linear development of strong zonal jets ('layering' in the angular momentum) with a preferred orientation in both cases, which can considerably enhance turbulent transport. By varying ϕ, we find instability with mixed radial and latitudinal shears transports angular momentum more efficiently (particularly if adiabatically unstable) than cases with purely radial shear (ϕ = 0). By exploring the dependence on box size, we find the transport properties of the GSF instability to be largely insensitive to this, implying we can meaningfully extrapolate our results to stars. However, there is no preferred length-scale for adiabatic instability, which therefore exhibits strong box-size dependence. These instabilities may contribute to the missing angular momentum transport required in red giant and subgiant stars and drive turbulence in the solar tachocline. [ABSTRACT FROM AUTHOR]

Taylor-Couette flow (TCF) is often used as a simplified model for complex rotating flows in the interior of stars and accretion discs. The flow dynamics in these objects is influenced by magnetic fields. For example, quasi-Keplerian flows in Taylor-Couette geometry become unstable to a travelling or standing wave in an external magnetic field if the fluid is conducting; there is an instability even when the flow is hydrodynamically stable. This magnetorotational instability leads to the development of chaotic states and, eventually, turbulence, when the cylinder rotation is sufficiently fast. The transition to turbulence in this flow can be complex, with the coexistence of parameter regions with spatio-temporal chaos and regions with quasi-periodic behaviour, involving one or two additional modulating frequencies. Although the unstable modes of a periodic flow can be identified with Floquet analysis, here we adopt a more flexible equation-free data-driven approach. We analyse the data from the transition to chaos in the magnetized TCF and identify the flow structures related to the modulating frequencies with dynamic mode decomposition; this method is based on approximating nonlinear dynamics with a linear infinite-dimensional Koopman operator. With the use of these structures, one can construct a nonlinear reduced model for the transition. [ABSTRACT FROM AUTHOR]

Flow in the body of gravity currents is typically assumed to be statistically two-dimensional, and cross-stream flow is often neglected (Simpson 1997; Meiburg et al. 2015). Here, we assess the validity of such assumptions using Shake-the-Box particle tracking velocimetry measurements of experimental gravity current flows. The resulting instantaneous, volumetric, whole-field velocity measurements indicate that cross-stream and vertical velocities (and velocity fluctuations) are equivalent in magnitude and thus are key to energy distribution and dissipation within the flow. Further, the presented data highlight the limitations of basing conclusions regarding body structure on a single cross-stream plane (particularly if that plane is central). Spectral analysis and dynamic mode decomposition of the fully three-dimensional, volumetric velocity data suggests internal waves within the current body that are associated with coherent three-dimensional motions in higher Reynolds number flows. Additionally, a potential critical layer at the height of the downstream velocity maximum is identified. [ABSTRACT FROM AUTHOR]

The Schmidt number, defined as the ratio of scalar to momentum diffusivity, varies by multiple orders of magnitude in real-world flows, with large differences in scalar diffusivity between temperature, solute, and sediment driven flows. This is especially crucial in gravity currents, where the flow dynamics may be driven by differences in temperature, solute, or sediment, and yet the effect of Schmidt number on the structure and dynamics of gravity currents is poorly understood. Existing numerical work has typically assumed a Schmidt number near unity, despite the impact of Schmidt number on the development of fine-scale flow structure. The few numerical investigations considering high Schmidt number gravity currents have relied heavily on two-dimensional simulations when discussing Schmidt number effects, leaving the effect of high Schmidt number on three-dimensional flow features unknown. In this paper, three-dimensional direct numerical simulations of constant-influx solute-based gravity currents with Reynolds numbers 100 ≤ R e ≤ 3000 and Schmidt number 1 are presented, with the effect of Schmidt number considered in cases with (R e , S c) = (100 , 10) , (100 , 100) , and (500, 10). These data are used to establish the effect of Schmidt number on different properties of gravity currents, such as density distribution and interface stability. It is shown that increasing Schmidt number from 1 leads to substantial structural changes not seen with increased Reynolds number in the range considered here. Recommendations are made regarding lower Schmidt number assumptions, usually made to reduce computational cost. [ABSTRACT FROM AUTHOR]

Density driven flows, also known as gravity currents, comprise a head, body, and tail. Yet whilst the body typically forms the largest part of such flows, its structure remains poorly understood. In this work, experimental data gathered using particle image velocimetry enables the instantaneous, whole-field dynamics of constant-influx solute-based gravity currents to be resolved. While averaged turbulent kinetic energy profiles are comparable to previous work, the instantaneous data sets reveal significant temporal variation, with velocity measurements indicating large-scale wave-like motions within the body. Spectral analysis and dynamic mode decomposition, of streamwise and vertical velocity, are used to identify the frequencies and structures of the dominant motions within the flow. By considering an idealised theoretical density profile, it is suggested that these structures may be internal gravity waves that form a critical layer within the flow located at the height of the maximum internal velocity. Irreversible internal wave breaking that has been postulated to occur at this critical layer suggests formation of internal eddy transport barriers, demonstrating that new dynamic models of turbulent mixing in gravity currents are needed. [ABSTRACT FROM AUTHOR]

A numerical investigation of convection-driven dynamos is carried out in the plane layer geometry. Dynamos with different magnetic Prandtl numbers Pm are simulated over a broad range of the Rayleigh number Ra. The heat transport, as characterized by the Nusselt number Nu, shows an initial departure from the heat transport scaling of non-magnetic Rayleigh-Bénard convection (RBC) as the magnetic field grows in magnitude; as Ra is increased further, the data suggest that Nu grows approximately as Ra2/7, but with a smaller prefactor in comparison with RBC. Viscous (u) and ohmic (B) dissipation contribute approximately equally to Nu at the highest Ra investigated; both ohmic and viscous dissipation approach a Reynolds-number-dependent scaling of the form Rea, where a ≈ 2.8. The ratio of magnetic to kinetic energy approaches a Pm-dependent constant as Ra is increased, with the constant value increasing with Pm. The ohmic dissipation length scale depends on Ra in such a way that it is always smaller, and decreases more rapidly with increasing Ra, than the viscous dissipation length scale for all investigated values of Pm. [ABSTRACT FROM AUTHOR]

Finite-amplitude hydromagnetic Rossby waves in the magnetostrophic regime are studied. We consider the slow mode, which travels in the opposite direction to the hydrodynamic or fast mode, in the presence of a toroidal magnetic field and zonal flow by means of quasi-geostrophic models for thick spherical shells. The weakly nonlinear long waves are derived asymptotically using a reductive perturbation method. The problem at the first order is found to obey a second-order ordinary differential equation, leading to a hypergeometric equation for a Malkus field and a confluent Heun equation for an electrical wire field, and is non-singular when the wave speed approaches the mean flow. Investigating its neutral non-singular eigensolutions for different basic states, we find the evolution is described by the Korteweg–de Vries equation. This implies that the nonlinear slow wave forms solitons and solitary waves. These may take the form of a coherent eddy, such as a single anticyclone. We speculate on the relation of the anticyclone to the asymmetric gyre seen in the Earth's fluid core, and in state-of-the-art dynamo direct numerical simulations. [ABSTRACT FROM AUTHOR]

Direct statistical simulation (DSS) solves the equations of motion for the statistics of turbulent flows in place of the traditional route of accumulating statistics by direct numerical simulation (DNS). That low-order statistics usually evolve slowly compared with instantaneous dynamics is one important advantage of DSS. Depending on the symmetry of the problem and the choice of averaging operation, however, DSS is usually more expensive computationally than DNS because even low-order statistics typically have higher dimension than the underlying fields. Here we show that it is in some cases possible to go much further by using a form of unsupervised learning, proper orthogonal decomposition, to address the 'curse of dimensionality'. We apply proper orthogonal decomposition directly to DSS in the form of expansions in equal-time cumulants to second order. We explore two averaging operations (zonal and ensemble) and test the approach on two idealized barotropic models of fluid on a rotating sphere (a jet that relaxes deterministically towards an unstable profile and a stochastically driven flow that spontaneously organizes into jets). We show that the method offers the possibility of parameter continuation, in the reduced basis, for the lower-order statistics of the flow. Order-of-magnitude savings in computational cost are sometimes obtained in the reduced basis, potentially enabling access to parameter regimes beyond the reach of DNS. [ABSTRACT FROM AUTHOR]

The relationship between nonlinear large-scale dynamo action and the generation and transport of magnetic helicity is investigated at moderate values of the magnetic Reynolds number ($Rm$). The model consists of a helically forced, sheared flow in a Cartesian domain. The boundary conditions are periodic in the horizontal and impenetrable for the vertical. The magnetic field is required to be vertical at the upper and lower boundaries. There are two consequences of this choice; one is that the magnetic helicity is not gauge invariant, the second is that fluxes of magnetic helicity are allowed in and out of the domain. We select the winding gauge, define all the contributions to the evolution of the helicity in this gauge and measure these contributions for various solutions of the dynamo equations. We vary $Rm$ and the shear strength, and find a rich landscape of dynamo solutions including travelling waves, pulsating waves and non-wave-like solutions. We find that, at the $Rm$ considered, the main contribution to the growth of magnetic helicity comes from processes throughout the volume of the fluid and that boundary terms respond by limiting the growth. We find that, in this magnetic Reynolds number regime, helicity conservation is not a strong constraint on large-scale dynamo action. We speculate on what may happen at higher $Rm$. [ABSTRACT FROM AUTHOR]

We continue our investigation into the non-linear evolution of the Goldreich–Schubert–Fricke (GSF) instability in differentially rotating radiation zones. This instability may be a key player in transporting angular momentum in stars and giant planets, but its non-linear evolution remains mostly unexplored. In a previous paper we considered the equatorial instability, whereas here we simulate the instability at a general latitude for the first time. We adopt a local Cartesian Boussinesq model in a modified shearing box for most of our simulations, but we also perform some simulations with stress-free, impenetrable, radial boundaries. We first revisit the linear instability and derive some new results, before studying its non-linear evolution. The instability is found to behave very differently compared with its behaviour at the equator. In particular, here we observe the development of strong zonal jets ('layering' in the angular momentum), which can considerably enhance angular momentum transport, particularly in axisymmetric simulations. The jets are, in general, tilted with respect to the local gravity by an angle that corresponds initially with that of the linear modes, but which evolves with time and depends on the strength of the flow. The instability transports angular momentum much more efficiently (by several orders of magnitude) than it does at the equator, and we estimate that the GSF instability could contribute to the missing angular momentum transport required in both red giant and subgiant stars. It could also play a role in the long-term evolution of the solar tachocline and the atmospheric dynamics of hot Jupiters. [ABSTRACT FROM AUTHOR]

Bottom-heated convection in rotating spherical shells provides a simple analogue for many astrophysical and geophysical fluid systems. We construct a database of 74 three-dimensional numerical convection models to investigate the scaling behaviour of seven diagnostics over a range of Ekman $(10^{-6}\leqslant E\leqslant 10^{-3})$ and Rayleigh $(15\leqslant \widetilde{Ra}\leqslant 18\,000)$ numbers while using a Prandtl number of unity. Our configuration is chosen to model Earth's core as defined by the fixed flux thermal boundary conditions, radius ratio $r_{i}/r_{o}$ of $0.35$ and a gravity profile that varies linearly with radius. The quantities of interest are the viscous and thermal boundary layer thickness, mean temperature gradient, mean interior temperature, Nusselt number, horizontal flow length scale, and Reynolds number. We find four parameter regimes characterised by different scaling behaviour. For $E\leqslant 10^{-4}$ and low $Ra$ the weakly nonlinear regime is characterised by a balance between viscous, Archimedean and Coriolis forces and the heat transfer is described by weakly nonlinear theory. At low $E$ and moderate $Ra$ , the rapidly rotating regime sees inertia take over from viscosity in the global force balance. In this regime the heat transfer scaling has increasing exponent with decreasing Ekman number and shows no saturation to the diffusion free $Ra^{3/2}E^{2}$ scaling. At high $Ra$ and all $E$ the importance of the Coriolis force gradually decreases and all diagnostics continually change in the transitional regime before approaching the scaling behaviour of non-rotating convection. [ABSTRACT FROM AUTHOR]

We present an investigation into the non-linear evolution of the Goldreich–Schubert–Fricke (GSF) instability using axisymmetric and 3D simulations near the equator of a differentially rotating radiation zone. This instability may provide an important contribution to angular momentum transport in stars and planets. We adopt a local Boussinesq Cartesian shearing box model, which represents a small patch of a differentially rotating stellar radiation zone. Complementary simulations are also performed with stress-free, impenetrable boundaries in the local radial direction. The linear and non-linear evolution of the equatorial axisymmetric instability is formally equivalent to the salt fingering instability. This is no longer the case in 3D, but we find that the instability behaves non-linearly in a similar way to salt fingering. Axisymmetric simulations – and those in 3D with short dimensions along the local azimuthal direction – quickly develop strong jets along the rotation axis, which inhibit the instability and lead to predator-prey-like temporal dynamics. In 3D, the instability initially produces homogeneous turbulence and enhanced momentum transport, though in some cases jets form on a much longer time-scale. We propose and validate numerically a simple theory for non-linear saturation of the GSF instability and its resulting angular momentum transport. This theory is straightforward to implement in stellar evolution codes incorporating rotation. We estimate that the GSF instability could contribute towards explaining the missing angular momentum transport required in red giant stars, and play a role in the long-term evolution of the solar tachocline. [ABSTRACT FROM AUTHOR]

It is widely accepted that astrophysical magnetic fields are generated by dynamo action. In many cases, these fields exhibit organisation on a scale larger than that of the underlying turbulent flow (e.g. the 11-year solar cycle). The mechanism for the generation of so-called large-scale fields remains an open problem. In cases where the magnetic Reynolds number (Rm) is small, dynamo-generated fields are coherent but at (the astrophysically relevant) high Rm, the fields are overwhelmed by small-scale fluctuating field. Recently Tobias and Cattaneo have shown that an imposed large-scale shear flow can suppress the small-scale fluctuations and allow the large-scale temporal behaviour to emerge. Shear is also believed to modify the electromotive force by introducing correlations between the flow and the field. However, in previous models at high Rm the shear is often artificially imposed or driven by an arbitrary body force. Here we consider a simple kinematic model of a convective dynamo in which shear is self-consistently driven by the presence of a horizontal temperature gradient (resulting in a thermal wind) and a rotation vector that is oblique to gravity. By considering a -dimensional system, we are able to reach high Rm so that the dynamo approaches the asymptotic regime where the growth rate becomes approximately independent of Rm. We find the flows studied here to be excellent small-scale dynamos, but with very little systematic behaviour evident at large Rm. We attribute this to being unable to self-consistently generate flows with both large (net) helicity and strong shear in this setup. [ABSTRACT FROM AUTHOR]

Turbulence and waves in Earth's iron-rich liquid outer core are believed to be responsible for the generation of the geomagnetic field via dynamo action. When waves break upon the mantle they cause a shift in the rotation rate of Earth's solid exterior and contribute to variations in the length-of-day on a ∼6-yr timescale. Though the outer core cannot be probed by direct observation, such torsional waves are believed to propagate along Earth's radial magnetic field, but as yet no self-consistent mechanism for their generation has been determined. Here we provide evidence of a realistic physical excitation mechanism for torsional waves observed in numerical simulations. We find that inefficient convection above and below the solid inner core traps buoyant fluid forming a density gradient between pole and equator, similar to that observed in Earth's atmosphere. Consequently, a shearing jet stream—a 'thermal wind'—is formed near the inner core; evidence of such a jet has recently been found. Owing to the sharp density gradient and influence of magnetic field, convection at this location is able to operate with the turnover frequency required to generate waves. Amplified by the jet it then triggers a train of oscillations. Our results demonstrate a plausible mechanism for generating torsional waves under Earth-like conditions and thus further cement their importance for Earth's core dynamics. [ABSTRACT FROM AUTHOR]

In this paper we examine the role of weak magnetic fields in breaking Kelvin's circulation theorem and in vortex breakup in two-dimensional magnetohydrodynamics for the physically important case of a fluid with low magnetic Prandtl number (low Pm).We consider three canonical inviscid solutions for the purely hydrodynamical problem, namely a Gaussian vortex, a circular vortex patch and an elliptical vortex patch. We examine how magnetic fields lead to an initial loss of circulation Γ and attempt to derive scaling laws for the loss of circulation as a function of field strength and diffusion as measured by two non-dimensional parameters. We show that for all cases the loss of circulation depends on the integrated effects of the Lorentz force, with the patch cases leading to significantly greater circulation loss. For the case of the elliptical vortex, the loss of circulation depends on the total area swept out by the rotating vortex, and so this leads to more efficient circulation loss than for a circular vortex. [ABSTRACT FROM AUTHOR]

In this paper, we examine the interaction of convection, rotation and mean flows in a thermal annulus. In this system, mean flows are driven by correlations induced by rotation leading to nontrivial Reynolds stresses. The mean flows act back on the convective turbulence acting as a barrier to transport. For this system, we demonstrate that the generalized quasilinear approximation (Marston et al. 2016 Phys. Rev. Lett. 116, 214501. (doi:10.1103/PhysRevLett.116.214501)) may provide a much better approximation to the complicated full nonlinear dynamics than the widely used quasilinear approximation. This result will enable the construction of more accurate statistical theories for the description of geophysical and astrophysical flows. [ABSTRACT FROM AUTHOR]

We utilize reconstructions based on cosmogenic radionuclides as well as direct observations of solar magnetic activity, to argue that the solar dynamo has operated similarly to the present day for at least the past 10 000 yr. The persistence of the 87-yr Gleissberg cycle throughout supermodulation events suggests that the Hale and Schwabe cycles continue independently of the modulational mechanism for activity. We further analyse behaviour of solar activity during the Spörer and Maunder Minima. Such grand minima recur with the characteristic de Vries period of approximately 208 yr but their incidence is modulated by the Hallstatt cycle with a characteristic period of around 2300 yr.We ascribe the latter to supermodulation, caused by breaking the symmetry of the dynamo pattern. Finally, we emphasize the need for further calculations in order to determine the effects of changes in solar field morphology and symmetry on the solar wind and on cosmic ray deflection. [ABSTRACT FROM AUTHOR]

In this paper, we perform direct statistical simulations of a model of two-dimensional flow that exhibits a transition from jets to vortices. The model employs two-scale Kolmogorov forcing, with energy injected directly into the zonal mean of the flow. We compare these results with those from direct numerical simulations. For square domains, the solution takes the form of jets, but as the aspect ratio is increased, a transition to isolated coherent vortices is found. We find that a truncation at second order in the equal-time but nonlocal cumulants that employ zonal averaging (zonal CE2) is capable of capturing the form of the jets for a range of Reynolds numbers as well as the transition to the vortex state but, unsurprisingly, is unable to reproduce the correlations found for the fully nonlinear (non-zonally symmetric) vortex state. This result continues the program of promising advances in statistical theories of turbulence championed by Kraichnan. [ABSTRACT FROM AUTHOR]

Waves in a thin layer on a rotating sphere are studied. The effect of a toroidal magnetic field is considered, using the shallow water ideal MHD equations. The work is motivated by suggestions that there is a stably stratified layer below the Earth’s core mantle boundary, and the existence of stable layers in stellar tachoclines. With an azimuthal background field known as the Malkus field,,being the co-latitude, a non-diffusive instability is found with azimuthal wavenumber. A necessary condition for instability is that the Alfvén speed exceedswhereis the rotation rate andthe sphere radius. Magneto-inertial gravity waves propagating westward and eastward occur, and become equatorially trapped when the field is strong. Magneto-Kelvin waves propagate eastward at low field strength, but a new westward propagating Kelvin wave is found when the field is strong. Fast magnetic Rossby waves travel westward, whilst the slow magnetic Rossby waves generally travel eastward, except for somemodes at large field strength. An exceptional very slow westwardmagnetic Rossby wave mode occurs at all field strengths. The current-driven instability occurs forwhen the slow and fast magnetic Rossby waves interact. With strong field the magnetic Rossby waves become trapped at the pole. An asymptotic analysis giving the wave speed and wave form in terms of elementary functions is possible both in polar trapped and equatorially trapped cases. [ABSTRACT FROM PUBLISHER]

We examine the effectiveness of the generalised quasilinear (GQL) approximation introduced by Marston et al. (Phys. Rev. Lett., vol. 116 (21), 2016, 214501). This approximation splits the variables into large and small scales in directions where there is a translational symmetry and removes nonlinear interactions involving only small scales. We utilise as a paradigm problem three-dimensional, turbulent, rotating Couette flow. We compare the results obtained from direct numerical solution of the equations with those from quasilinear (QL) and GQL calculations. In this three-dimensional setting, there is a choice of cutoff wavenumber for the GQL approximation both in the streamwise and in the spanwise directions. We demonstrate that the GQL approximation significantly improves the accuracy of mean flows, spectra and two-point correlation functions over models that are quasilinear in any of the translationally invariant directions, even if only a few streamwise and spanwise modes are included. We argue that this provides significant support for a programme of direct statistical simulation utilising the GQL approximation. [ABSTRACT FROM AUTHOR]

We consider kinematic dynamo action in a sheared helical flow at moderate to high values of the magnetic Reynolds number (Rm). We find exponentially growing solutions which, for large enough shear, take the form of a coherent part embedded in incoherent fluctuations. We argue that at large Rm large-scale dynamo action should be identified by the presence of structures coherent in time, rather than those at large spatial scales. We further argue that although the growth rate is determined by small-scale processes, the period of the coherent structures is set by mean-field considerations. [ABSTRACT FROM AUTHOR]

In this paper, we argue that the solar activity record, as revealed by telescopic observations and proxy data from the abundances of cosmogenic isotopes, is consistent with the action of a deterministic non-linear chaotic dynamo. In particular, we claim that the long time-scale 'supermodulation' apparent in the isotopic record can be ascribed to switching of the dynamo between two different modulational patterns. The first (which is currently in operation) involves deep grand minima and occasional changes in symmetry triggered by these minima. The second, which exhibits only weak modulation and no grand minima, arises as a consequence of symmetry breaking. These processes are demonstrated for highly idealized simple models of the non-linear dynamo equations. [ABSTRACT FROM AUTHOR]

The predominant force balance in rapidly rotating planetary cores is between Coriolis, pressure, buoyancy and Lorentz forces. This magnetostrophic balance leads to a Taylor state where the spatially averaged azimuthal Lorentz force is compelled to vanish on cylinders aligned with the rotation axis. Any deviation from this state leads to a torsional oscillation, signatures of which have been observed in the Earth's secular variation and are thought to influence length of day variations via angular momentum conservation. In order to investigate the dynamics of torsional oscillations (TOs), we perform several 3-D dynamo simulations in a spherical shell. We find TOs, identified by their propagation at the correct Alfvén speed, in many of our simulations. We find that the frequency, location and direction of propagation of the waves are influenced by the choice of parameters. Torsional waves are observed within the tangent cylinder and also have the ability to pass through it. Several of our simulations display waves with core traveltimes of 4–6 yr. We calculate the driving terms for these waves and find that both the Reynolds force and ageostrophic convection acting through the Lorentz force are important in driving TOs. [ABSTRACT FROM PUBLISHER]

In this article we present direct numerical simulations of stratified flow at resolutions of up to $204{8}^{2} \times 513$, to explore scalings for the dynamics of stably stratified turbulence. Recent work suggests that for strong enough stratification, the vertical integral scale of the turbulence adjusts to yield a vertical Froude number, ${F}_{v} $, of order unity at high enough Reynolds number, whilst the horizontal Froude number, ${F}_{h} $, decreases as stratification is increased. Our numerical simulations are consistent with predictions by Lindborg (J. Fluid Mech., vol. 550, 2006, pp, 207–242), and with numerical simulations at lower resolution, in that the horizontal kinetic energy spectrum follows a Kolmogorov spectrum (after replacing the wavenumber with the horizontal wavenumber) and that the horizontal potential energy spectrum similarly follows the Corrsin–Obukhov spectrum for a passive scalar. Most importantly, we build upon these previous results by thoroughly exploring the dependence of the horizontal spectrum of horizontal kinetic energy on both the stratification and the relative size of the vertical dissipation terms, as quantified by the buoyancy Reynolds number. Our most important result is that variations in the power-law exponent scale entirely with the buoyancy Reynolds number and not with the stratification itself, lending considerable support to the Lindborg (2006) hypothesis that horizontal spectra are independent of stratification at large Reynolds numbers. We further demonstrate that even at the large numerical resolution of this study, the spectrum and hence the dynamics are affected by the buoyancy Reynolds number unless it is larger than $O(10)$, indicating that extreme care must be taken when assessing claims made from previous numerical simulations of stratified flow at low or moderate resolution and extrapolating the results to geophysical or astrophysical Reynolds numbers. [ABSTRACT FROM PUBLISHER]

In this article we examine the range of applicability of the anelastic approximation, which is often used in describing the dynamics of geophysical and astrophysical flows. Specifically, we consider two linear problems: magnetoconvection and magnetic buoyancy, and compare the fully compressible solutions with those determined by solving the anelastic problem. We further compare a subsequent simplification introduced by Lantz [Dynamical behavior of magnetic fields in a stratified, convecting fluid layer. Ph.D. Thesis, Cornell University: Ithaca, U.S.A., 1992] with the anelastic formulation. We find that for the magnetoconvection problem the anelastic approximation works well if the departure from adiabaticity is small (as expected) and determine where the approximation breaks down. The results for magnetic buoyancy are less straightforward, with the accuracy of the approximation being determined by the growth rate of the instability. We argue that these results make it difficult to assess a priori whether the anelastic approximation will provide an accurate approximation to the fully compressible system for stably stratified problems. Thus, unlike the magnetoconvection problem, for magnetic buoyancy it is difficult to provide general rules as to when the anelastic approximation can be used. [ABSTRACT FROM AUTHOR]

In an earlier paper [P. W. Livermore, D. W. Hughes, and S. M. Tobias, “The role of helicity and stretching in forced kinematic dynamos in a spherical shell,” Phys. Fluids 19, 057101 (2007)], we considered the kinematic dynamo action resulting from a forced helical flow in a spherical shell. Although mean field electrodynamics suggests that the resulting magnetic field should have a significant mean (axisymmetric) component, we found no evidence for this; the dynamo action was distinctly small scale. Here we extend our investigation into the nonlinear regime in which the magnetic field reacts back on the velocity via the Lorentz force. Our main result is somewhat surprising, namely, that nonlinear effects lead to a considerable change in the structure of the magnetic field, its final state having a significant mean component. By investigating the dominant flow-field interactions, we isolate the dynamo mechanism and show schematically how the generation process differs between the kinematic and nonlinear regimes. In addition, we are able to calculate some components of the transport coefficient α and thus discuss our results within the context of mean field electrodynamics. [ABSTRACT FROM AUTHOR]

The operation of an interface dynamo (as has been suggested for the Sun and other stars with convective envelopes) relies crucially upon the effective transport of magnetic flux between two spatially disjoint generation regions. In the simplest models communication between the two regions is achieved solely by diffusion. Here we incorporate a highly simplified anisotropic transport mechanism in order to model the net effect of flux conveyance by magnetic pumping and by magnetic buoyancy. We investigate the influence of this mechanism on the efficiency of kinematic dynamo action. It is found that the effect of flux transport on the efficiency of the dynamo is dependent upon the spatial profile of the transport. Typically, transport hinders the onset of dynamo action and increases the frequency of the dynamo waves. However, in certain cases, there exists a preferred magnitude of transport for which dynamo action is most efficient. Furthermore, we demonstrate the importance of the imposition of boundary conditions in drawing conclusions on the role of transport. [ABSTRACT FROM AUTHOR]

Considerations of mean-field theory suggest that small-scale helical flows are an effective means of generating large-scale (mean) magnetic fields, whereas fast dynamo considerations reveal the importance of Lagrangian chaos in the flow for generating small-scale magnetic fields in the limit of high magnetic Reynolds number. We explore these ideas further by considering the kinematic magnetic fields generated by three forced steady flows in a spherical shell that differ both in their helicity and in their stretching properties. The full magnetic induction equation is solved numerically, with no a priori assumptions about the nature of the generated magnetic field. There are two surprising aspects to our results. One is that the most significant mean field is generated by a flow with zero net helicity; the other is that the flow with the “best” stretching properties turns out to be the most inefficient dynamo. Our results, therefore, suggest that it may not be possible to determine the nature of a kinematic-dynamo generated magnetic field simply from the knowledge of certain flow properties. [ABSTRACT FROM AUTHOR]

Stellar magnetic activity – which has been observed in a diverse set of stars including the Sun – originates via a magnetohydrodynamic dynamo mechanism working in stellar interiors. The full set of magnetohydrodynamic equations governing stellar dynamos is highly complex, and so direct numerical simulation is currently out of reach computationally. An understanding of the bifurcation structure, likely to be found in the partial differential equations governing such dynamos, is vital if we are to understand the activity of solar-like stars and its evolution with varying stellar parameters such as rotation rate. Low-order models are an important aid to this understanding, and can be derived either as approximations of the governing equations themselves or by using bifurcation theory to obtain systems with the desired structure. We use normal-form theory to derive a third-order model with robust behaviour. The model is able to reproduce many of the basic types of behaviour found in observations of solar-type stars. In the appropriate parameter regime, a chaotic modulation of the basic cycle is present, together with varying periods of low activity such as that observed during the solar Maunder minima. [ABSTRACT FROM AUTHOR]

We investigate the kinematic dynamo properties of interacting vortex tubes. These flows are of great importance in geophysical and astrophysical fluid dynamics: for a large range of systems, turbulence is dominated by such coherent structures. We obtain a dynamically consistent 2 1/2-dimensional velocity field of the form (u(x,y,t),v(x,y,t),w(x,y,t)) by solving the z-independent Navier-Stokes equations in the presence of helical forcing. This system naturally forms vortex tubes via an inverse cascade. It has chaotic Lagrangian properties and is therefore a candidate for fast dynamo action. The kinematic dynamo properties of the flow are calculated by determining the growth rate of a small-scale seed field. The growth rate is found to have a complicated dependence on Reynolds number Rey and magnetic Reynolds number Rem, but the flow continues to act as a dynamo for large Rey and Rem. Moreover the dynamo is still efficient even in the limit Rey gg Rem, providing Rem is large enough, because of the formation of coherent structures. [ABSTRACT FROM AUTHOR]

Examines the effect of solar variability on climate. Introduction of solar forcing into the Lorentz equation as a model of the climate; Exhibition of resonant behavior for the symmetric system subject forcing from the solar dynamo model; Quantitative measures of the role of forcing.

Astrophysical magnetic fields often display remarkable organization, despite being generated by dynamo action driven by turbulent flows at high conductivity. An example is the eleven-year solar cycle, which shows spatial coherence over the entire solar surface. The difficulty in understanding the emergence of this large-scale organization is that whereas at low conductivity (measured by the magnetic Reynolds number, Rm) dynamo fields are well organized, at high Rm their structure is dominated by rapidly varying small-scale fluctuations. This arises because the smallest scales have the highest rate of strain, and can amplify magnetic field most efficiently. Therefore most of the effort to find flows whose large-scale dynamo properties persist at high Rm has been frustrated. Here we report high-resolution simulations of a dynamo that can generate organized fields at high Rm; indeed, the generation mechanism, which involves the interaction between helical flows and shear, only becomes effective at large Rm. The shear does not enhance generation at large scales, as is commonly thought; instead it reduces generation at small scales. The solution consists of propagating dynamo waves, whose existence was postulated more than 60 years ago and which have since been used to model the solar cycle. [ABSTRACT FROM AUTHOR]

We consider the generation of magnetic activity—dynamo waves—in the astrophysical limit of very large magnetic Reynolds number. We consider kinematic dynamo action for a system consisting of helical flow and large-scale shear. We demonstrate that large-scale dynamo waves persist at high Rm if the helical flow is characterized by a narrow band of spatial scales and the shear is large enough. However, for a wide band of scales the dynamo becomes small scale with a further increase of Rm, with dynamo waves re-emerging only if the shear is then increased. We show that at high Rm, the key effect of the shear is to suppress small-scale dynamo action, allowing large-scale dynamo action to be observed. We conjecture that this supports a general “suppression principle”—large-scale dynamo action can only be observed if there is a mechanism that suppresses the small-scale fluctuations. [ABSTRACT FROM AUTHOR]