Buoyancy Instability Research Articles

On the Lorentz Force and Torque of Solar Photospheric Emerging Magnetic Fields

Abstract Magnetic flux generated and intensified by the solar dynamo emerges into the solar atmosphere, forming active regions (ARs) including sunspots. Existing theories of flux emergence suggest that the magnetic flux can rise buoyantly through the convection zone but is trapped at the photosphere, while its further rising into the atmosphere resorts to the Parker buoyancy instability. To trigger such an instability, the Lorentz force in the photosphere needs to be as large as the gas pressure gradient to hold up an extra amount of mass against gravity. This naturally results in a strongly non-force-free photosphere, which is indeed shown in typical idealized numerical simulations of flux tube buoyancy from below the photosphere into the corona. Here we conduct a statistical study of the extents of normalized Lorentz forces and torques in the emerging photospheric magnetic field with a substantially large sample of Solar Dynamics Observatory/Helioseismic and Magnetic Imager vector magnetograms. We found that the photospheric field has a rather small Lorentz force and torque on average, and thus is very close to a force-free state, which is not consistent with theories as well as idealized simulations of flux emergence. Furthermore, the small extents of forces and torques seem not to be influenced by the emerging AR’s size, the emergence rate, or the nonpotentiality of the field. This result puts an important constraint on future development of theories and simulations of flux emergence.

Buoyant flow and instability in a vertical cylindrical porous slab with permeable boundaries

The basic stationary buoyant flow in a vertical annular porous passage induced by a boundary temperature difference is investigated. The vertical cylindrical boundaries are considered both isothermal and permeable to external fluid reservoirs. There exists a stationary parallel velocity field with a zero flow rate and pure conduction heat transfer. Its linear stability is analysed with normal mode perturbations of the pressure and temperature fields. The transition to convective instability is caused by the basic horizontal temperature gradient. Hence, its nature differs from that of the usual Rayleigh–Bénard instability. The linear dynamics of the perturbed flow is formulated as an eigenvalue problem, solved numerically. Its solution provides the neutral stability curve at each fixed aspect ratio between the external radius and the internal radius. The critical Rayleigh number triggering the instability is evaluated for different aspect ratios. It is shown that the system becomes more an more unstable as the aspect ratio increases, with the critical Rayleigh number dropping to zero when the aspect ratio tends to infinity.

Continuously-fed gravity currents propagating over a finite porous substrate

We present the results of laboratory investigations of continuously-fed density currents that propagate first over a smooth horizontal bed and then over a porous substrate of limited length. Inflow discharge, initial excess density, and substrate porosities are varied. Density measurements, acquired through an image analysis technique, are performed above the porous layer simultaneously with quasi-instantaneous vertical velocity profiles. After a first phase in which the current sinks into the substrate, freshwater entrainment from the bed begins and, gradually, a mixing layer forms at the interface between the surface flow and the porous bed. Shear-driven and Rayleigh-Taylor instabilities rule the dynamics of this mixing layer. The porous boundary effects are observed in the vertical distributions of both density and velocity, especially in the near-bed region. Here, larger flow velocities are recorded over porous substrates. We argue that these are due to the presence of a longitudinal pressure gradient, which in turn is a consequence of the current mass loss. Its presence over the porous substrate is proved by the current interface longitudinal slope. However, other effects of the presence of the porous substrate, such as the relaxation of the no-slip boundary condition and the bed-normal momentum exchange, also affect the velocity field. The turbulent structure changes significantly over the porous substrate: while streamwise turbulence decreases, shear and bed-normal Reynolds stresses increase in large part of the current depth. Buoyancy instabilities further enhance the bed-normal momentum flux and, in the near-bed region, contribute to turbulent kinetic energy generation together with shear.

Buoyancy driven convection instability and related pulsing of continuous optical discharges

Optical discharges find now ever expanding applications in science, engineering and medicine. In present study authors discuss the phenomenon of periodic pulsing of a continuous optical discharge (COD) on the base of original experimental results. In the literature there is no general agreement regarding the origin of the considered instability. Authors have obtained the dependence of oscillation frequency on the gas pressure and proposed semi-empirical relations to estimate pulse frequency pressure dependence observed. Regular self-sustained oscillations of COD plasma were explained by the pulsations of heated gas bubble surrounding COD followed by buoyancy driven vortex formation that was detected on schlieren images of convection zone. This kind of buoyant convection instability was determined to obey the same similarity law as cycling frequency of puffing or flickering in diffusion and premixed flames. The instability discussed can affect the performance of COD in some important applications such as high brightness broadband light sources, for instance.

Loss of buoyancy control in the copepod Calanus finmarchicus.

A mechanism is demonstrated that could explain large-scale aggregations of lipid-rich copepods in the surface waters of marine environments. Laboratory experiments establish that changes in salinity and temperature induce lipid-mediated buoyancy instability that entrains copepods in surface waters. Reduced hydrostatic pressure associated with forced ascent of copepods at fjordic sills, shelf breaks and seamounts would also reduce the density of the lipid reserves, forcing copepods and particularly those in diapause to the surface. We propose that salinity, temperature and hydrodynamics of the physical environment, in conjunction with the biophysical properties of lipids, explain periodic high abundances of lipid-rich copepods in surface waters.

Water tank modelling of variations in inversion breakup over a circular city

Air pollution and extreme heat waves are among the major environmental challenges faced by modern cities. Stable stratification and temperature inversion help to trap urban airborne pollutants and produce a strong urban heat island intensity. Such adverse effects can disappear when the buoyancy flows introduced by the city heat is sufficiently strong to break up the inversion. This paper investigates the possible mechanisms of the inversion breakup process and their effects. A lack of time-saving and cost-effective techniques with high temporal and spatial resolution in the field study has been the main limiting factor to a systematic investigation of the physical process of inversion breakup. In this study, water tank experiments were conducted to study the characteristics of the mean and turbulent flow structures of the inversion breakup process. Four cases with different background density profiles are simulated. Three stages of inversion breakup were identified, the two-dome stage, the wing-shrinking stage and the perforative-plume stage. During the two-dome stage, shear instability and buoyancy instability (Fig. 3d) are both important for heat and mass transfer between the lower-level dome in the stable layer near the surface and the upper-level dome in the neutral residual layer aloft. The vertical dimension of the lower-level dome begins to grow, whilst the horizontal extent shrinks at the wing-shrinking stage. Finally, in the perforative-plume stage, the stable layer is destroyed, and the plume extends from the surface to the top of the residual layer. The pollutants and heat dispersion are both enhanced significantly during this stage.

On Magnetic Inhibition Theory in Non-resistive Magnetohydrodynamic Fluids

We investigate why the non-slip boundary condition for the velocity, imposed in the direction of impressed magnetic fields, can contribute to the magnetic inhibition effect based on the nonhomogeneous magnetic Rayleigh--Taylor (abbr. NMRT) problem in non-resistive magnetohydrodynamic (abbr. MHD) fluids. Exploiting an infinitesimal method in Lagrangian coordinates, the idea of (equivalent) magnetic tension, and the differential version of magnetic flux conservation, we give an explanation of physical mechanism for the magnetic inhibition phenomenon in a non-resistive MHD fluid. Moreover, we find that the magnetic energy in the non-resistive MHD fluid depends on the displacement of fluid particles, and thus can be regarded as elastic potential energy. Motivated by this observation, we further use the well-known minimum potential energy principle to explain the physical meaning of the stability/instability criteria in the NMRT problem. As a result of the analysis, we further extend the results on the NMRT problem to the stratified MHD fluid case. We point out that our magnetic inhibition theory can be used to explain the inhibition phenomenon of other instabilities, such as thermal instability, magnetic buoyancy instability, and so on, by impressed magnetic fields in non-resistive MHD fluids.

Combustion instability effect on sound generation by jet diffusion flame

This paper presented a numerical study of flow instability effects on the sound generation by jet diffusion flames. Numerical simulation coupled with the acoustic analogy based on Lilley’s equation was employed to predict the sound radiation. A parametric study by varying the Froude number was carried out, and simulations were performed with different levels of external forcing to shed light on the competing acoustic responses of the buoyant and jet preferred instabilities. The detailed sound source structure was provided by the flow details. It is shown that the increase of buoyancy is responsible for the development of the acoustic source in the downstream flame region. When the Froude number is larger than unity, only low-frequency noise will be affected, and when the Froude number is less than unity, combustion-induced buoyancy has a further positive impact on the noise level in the high-frequency region. The jet preferred instability caused by external disturbance can improve the intensity of the sound source and may further be amplified as the noise peak, depending on the buoyancy level. An acoustic transfer function was therefore analyzed to characterize the different acoustic responses. The results showed that there is a positive correlation between the buoyancy level and the acoustical response rate of external disturbance, and the high-frequency disturbance is much easier to be amplified by flame than that with low frequency, especially in the downstream flow field.

Magnetic Buoyancy and Magnetorotational Instabilities in Stellar Tachoclines for Solar- and Antisolar-type Differential Rotation

Abstract We present results from an analytical model for magnetic buoyancy and rotational instabilities in full spherical shell stellar tachoclines that include rotation, differential rotation of either solar or antisolar type, and toroidal field. We find that in all cases, for latitudes where the tachocline vertical rotation gradient is positive, toroidal fields can be stored against magnetic buoyancy up to a limit that is proportional to the square root of the local vertical rotation gradient. For solar magnitude differential rotation, this limit is about 9 kG. For fixed percentage differential rotation, storage capacity varies linearly with the rotation rate. Faster rotators with the same percentage differential rotation can store larger fields, and slower rotators can store smaller fields. At latitudes where the vertical rotation gradient is negative, vigorous magnetorotational instability for even weak (≪1 kG) toroidal fields prevents such storage. We infer from these results that for stars with solar-type latitudinal differential rotation (fast equator, slow poles), any starspots present should be found in low latitudes, similar to the Sun. For antisolar differential rotation, any spots present should be found in mid- and high latitudes, perhaps with a peak of occurrence near 55°. These results hopefully provide some guidance for making and interpreting observations of stellar activity and differential rotation on stars with convection zones and tachoclines.

Influence of Lake Erie on a Lake Ontario Lake-Effect Snowstorm

AbstractAnnual lake-effect snowstorms, which develop through surface buoyant instability and upward moisture transport from the Laurentian Great Lakes, lead to important local increases in snowfall to the south and east. Surface wind patterns during cold-air outbreaks often result in areas where the air is modified by more than one Great Lake. While it is known that boundary layer air that has crossed multiple lakes can produce particularly intense snow, few observations are available on the process by which this occurs. This study examines unique observations taken during the Ontario Winter Lake-effect Systems (OWLeS) field project to document the process by which Lake Erie influenced snowfall that was produced over Lake Ontario on 28 January 2014. During the event, lake-effect clouds and snow that developed over Lake Erie extended northeastward toward Lake Ontario. OWLeS and operational observations showed that the clouds from Lake Erie disappeared (and snow greatly decreased) as they approached the Lake Ontario shoreline. This clear-air zone was due to mesoscale subsidence, apparently due to the divergence of winds moving from land to the smoother lake surface. However, the influence of Lake Erie in producing a deeper lake-effect boundary layer, thicker clouds, increased turbulence magnitudes, and heavier snow was identified farther downwind over Lake Ontario. It is hypothesized that the combination of a low-stability, high-moisture boundary layer as well as convective eddies and limited snow particles crossing the mesoscale subsidence region locally enhanced the lake-effect system over Lake Ontario within the plume of air originating over Lake Erie.

Experimental study on the flame propagation and laminar combustion characteristics of landfill gas

Biogas is the least expensive renewable energy source with an almost neutral balance of CO2 emissions. As a type of biogas, landfill gas could potentially be used in the internal combustion engines, gas turbines, and industrial furnaces. However, the combustion characteristics of landfill gas, which are the foundations of further use of the landfill gas, are not clear. In this paper, the flame propagation characteristics of landfill gas were measured in a constant volume combustion chamber using a schlieren system. The experiments were conducted over the equivalence ratio range of 0.7–1.4, the pressure range of 0.1–0.5 MPa, the temperature range of 290–380 K, and the methane contents of 47%, 55.5% and 59%. The main influencing factors of the combustion stability and laminar combustion velocity of landfill gas in laminar combustion were also investigated. The results showed that the preferential diffusion or buoyancy instability appeared during the flame propagation process, and flame front exhibited irregular cellular structure and protuberances or the flame core moved upward under the condition that the Markstein number was small or the laminar burning velocity was lower than 0.15 m/s. At the same time, the Markstein number and the stability of the flame front decreased with a lower equivalence ratio and methane content or higher initial pressure. However, the effect of the initial temperature on the Markstein number was not obvious. The unstretched flame velocity and the laminar combustion velocity initially increased and then gradually decreased with the increase of the equivalence ratio, and the maximum values were measured under the condition that the equivalence ratio was 1.1. Furthermore, the laminar combustion velocity of landfill gas decreased with a higher initial pressure or lower initial temperature and methane content.

Reverse Engineering the Tropical Precipitation–Buoyancy Relationship

The tropical precipitation–moisture relationship, characterized by rapid increases in precipitation for modest increases in moisture, is conceptually recast in a framework relevant to plume buoyancy and conditional instability in the tropics. The working hypothesis in this framework links the rapid onset of precipitation to integrated buoyancy in the lower troposphere. An analytical expression that relates the buoyancy of an entraining plume to the vertical thermodynamic structure is derived. The natural variables in this framework are saturation and subsaturation equivalent potential temperatures, which capture the leading-order temperature and moisture variations, respectively. The use of layer averages simplifies the analytical and subsequent numerical treatment. Three distinct layers, the boundary layer, the lower free troposphere, and the midtroposphere, adequately capture the vertical variations in the thermodynamic structure. The influence of each environmental layer on the plume is assumed to occur via lateral entrainment, corresponding to an assumed mass-flux profile. The fractional contribution of each layer to the midlevel plume buoyancy (i.e., the layer weight) is estimated from TRMM 3B42 precipitation and ERA-Interim thermodynamic profiles. The layer weights are used to “reverse engineer” a deep-inflow mass-flux profile that is nominally descriptive of the tropical atmosphere through the onset of deep convection. The layer weights—which are nearly the same for each of the layers—constitute an environmental influence function and are also used to compute a free-tropospheric integrated buoyancy measure. This measure is shown to be an effective predictor of onset in conditionally averaged precipitation across the global tropics—over both land and ocean.

The Effect of Weak Resistivity and Weak Thermal Diffusion on Short-wavelength Magnetic Buoyancy Instability

Abstract Magnetic buoyancy instability in weakly resistive and thermally conductive plasma is an important mechanism of magnetic field expulsion in astrophysical systems. It is often invoked, e.g., in the context of the solar interior. Here, we revisit a problem introduc`ed by Gilman: the short-wavelength linear stability of a plane layer of compressible isothermal and weakly diffusive fluid permeated by a horizontal magnetic field of strength decreasing with height. In this physical setting, we investigate the effect of weak resistivity and weak thermal conductivity on the short-wavelength perturbations, localized in the vertical direction, and show that the presence of diffusion allows to establish the wavelength of the most unstable mode, undetermined in an ideal fluid. When diffusive effects are neglected, the perturbations are amplified at a rate that monotonically increases as the wavelength tends to zero. We demonstrate that, when the resistivity and thermal conduction are introduced, the wavelength of the most unstable perturbation is established and its scaling law with the diffusion parameters depends on gradients of the mean magnetic field, temperature, and density. Three main dynamical regimes are identified, with the wavelength of the most unstable mode scaling as either or or , where d is the layer thickness and is the ratio of the characteristic thermal diffusion velocity scale to the free-fall velocity. Our analytic results are backed up by a series of numerical solutions. The two-dimensional interchange modes are shown to dominate over three-dimensional ones when the magnetic field and/or temperature gradients are strong enough.

Modeling air-water heat transfer induced by buoyant convection

The instantaneous 2D velocity field obtained at the air-water interface in previously performed direct numerical simulations (DNS) of interfacial heat transfer driven by buoyant convective instability is used to estimate the heat transfer velocity [2]. After reconstructing the three-dimensional velocity field immediately underneath the surface, a Lagrangian particle tracking method was used to assess the surface age. The surface heat transfer velocity, obtained using Danckwerts’ surface renewal model, was found to underestimate the heat transfer velocity acquired directly from the DNS data by about 16%.

Magnetic Buoyancy and Rotational Instabilities in the Tachocline

Abstract We present results from an analytical model for magnetic buoyancy and rotational instabilities in a full spherical shell tachocline that includes rotation, differential rotation close to that observed helioseismically, and toroidal field. Perturbation solutions are found for the limit of large latitudinal wave number, a limit commonly used to maximize instability due to magnetic buoyancy. We find that at all middle and high latitudes vigorous rotational instability is induced by weak toroidal fields, particularly for high longitudinal wave number, even when the vertical rotation gradient is marginally stable without toroidal field. We infer that this instability will prevent much storage of toroidal fields in the tachocline at these latitudes, but could be responsible for the appearance of ephemeral active regions there. By contrast, the low-latitude vertical rotation gradient, opposite in sign to that at high latitudes, is not only stable itself but also prevents magnetic buoyancy instability until the peak toroidal field is raised above a threshold of about 9 kG at the equator, declining to zero where the vertical rotation gradient changes sign, at in our model. Thus this rotation gradient provides a previously unnoticed mechanism for storage of toroidal fields until they amplify by dynamo action to order 10 kG, whereupon they can overcome the rotation gradient to emerge as sunspots. These results provide a new explanation for why sunspots are seen only at low latitudes. The purely rotational instability at latitudes above 50°, even without toroidal fields, also suggests that the high-latitude tachocline should be much thicker, due to HD turbulence, than has been inferred for lower latitudes from helioseismic measurements.

On the helium fingers in the intracluster medium

In this paper, we investigate the convection phenomenon in the intracluster medium (the weakly collisional magnetized inhomogeneous plasma permeating galaxy clusters) where the concentration gradient of the helium ions cannot be ignored. To this end, we build upon the general machinery employed to study the salt finger instability found in the oceans. The salt finger instability is a form of double diffusive convection where the diffusions of two physical quantities – heat and salt concentrations – occur with different diffusion rates. The analogous instability in the intracluster medium may result because of the magnetic field mediated anisotropic diffusions of the heat and the helium ions (in the sea of hydrogen ions and free electrons). These two diffusions have inherently different diffusion rates. Hence, the convection caused by the onset of this instability is an example of double diffusive convection in the astrophysical setting. A consequence of this instability is the formation of vertical filamentary structures that have a greater concentration of helium ions with respect to the immediate neighbourhoods of the filaments. We call these structures helium fingers in analogy with the salt fingers found in the case of the salt finger instability. Here we show that the width of a helium finger scales as one-fourth power of the radius of the inner region of the intracluster medium in the supercritical regime. We also determine the explicit mathematical expression of the criterion for the onset of the heat-flux-driven buoyancy instability modified by the presence of inhomogeneously distributed helium ions.

Grim: A Flexible, Conservative Scheme for Relativistic Fluid Theories

Abstract Hot, diffuse, relativistic plasmas such as sub-Eddington black-hole accretion flows are expected to be collisionless, yet are commonly modeled as a fluid using ideal general relativistic magnetohydrodynamics (GRMHD). Dissipative effects such as heat conduction and viscosity can be important in a collisionless plasma and will potentially alter the dynamics and radiative properties of the flow from that in ideal fluid models; we refer to models that include these processes as Extended GRMHD. Here we describe a new conservative code, grim, that enables all of the above and additional physics to be efficiently incorporated. grim combines time evolution and primitive variable inversion needed for conservative schemes into a single step using an algorithm that only requires the residuals of the governing equations as inputs. This algorithm enables the code to be physics agnostic as well as flexibility regarding time-stepping schemes. grim runs on CPUs, as well as on GPUs, using the same code. We formulate a performance model and use it to show that our implementation runs optimally on both architectures. grim correctly captures classical GRMHD test problems as well as a new suite of linear and nonlinear test problems with anisotropic conduction and viscosity in special and general relativity. As tests and example applications, we resolve the shock substructure due to the presence of dissipation, and report on relativistic versions of the magneto-thermal instability and heat flux driven buoyancy instability, which arise due to anisotropic heat conduction, and of the firehose instability, which occurs due to anisotropic pressure (i.e., viscosity). Finally, we show an example integration of an accretion flow around a Kerr black hole, using Extended GRMHD.

Influence of mesh non-orthogonality on numerical simulation of buoyant jet flows

In the present research, we discuss the influence of mesh non-orthogonality on numerical solution of a type of buoyant flow. Buoyant jet flows are simulated numerically with hexahedral and prismatic mesh elements in an open source Computational Fluid Dynamics (CFD) code called “OpenFOAM”. Buoyant jet instability obtained with the prismatic meshes may be overestimated compared to that obtained with the hexahedral meshes when non-orthogonal correction is not applied in the code. Although the non-orthogonal correction method can improve the instability generated by mesh non-orthogonality, it may increase computation time required to reach a convergent solution. Thus, we propose modified solvers that can reduce the influence of mesh non-orthogonality and reduce the computation time compared to the existing solvers in OpenFOAM. It is demonstrated that calculations for a buoyant jet with a large temperature difference are performed faster by the modified solver.

Rayleigh-Taylor and Parker instabilities in MHD fluids

We present a brief survey of recent mathematical results on the stability and instability of magnetohydrodynamic flows in the presence of a gravitational field, which include the incompressible magnetic Rayleigh-Taylor instability, and the Parker instability (i.e., the magnetic buoyancy instability) in compressible magnetohydrodynamics. In particular, the stabilizing effect of some factors (e.g., steady magnetic fields, boundary conditions, domains) are analyzed. In addition, the mathematical results on the Rayleigh-Taylor instability problem in viscoelastic flows are discussed.

ON HELIUM MIXING IN QUASI-GLOBAL SIMULATIONS OF THE INTRACLUSTER MEDIUM

ABSTRACT The assumption of a spatially uniform helium distribution in the intracluster medium (ICM) can lead to biases in the estimates of key cluster parameters if composition gradients are present. The helium concentration profile in galaxy clusters is unfortunately not directly observable. Current models addressing the putative sedimentation are one-dimensional and parametrize the presence of magnetic fields in a crude way, ignoring the weakly collisional, magnetized nature of the medium. When these effects are considered, a wide variety of instabilities can play an important role in the plasma dynamics. In a series of recent papers, we have developed the local, linear theory of these instabilities and addressed their nonlinear development with a modified version of Athena. Here, we extend our study by developing a quasi-global approach that we use to simulate the mixing of helium as induced by generalizations of the heat-flux-driven buoyancy instability (HBI) and the magnetothermal instability, which feed off thermal and composition gradients. In the inner region of the ICM, mixing can occur over a few gigayears, after which the average magnetic field inclination angle is ∼30°–50°, resulting in an averaged Spitzer parameter higher by about 20% than the value obtained in homogeneous simulations. In the cluster outskirts the instabilities are rather inefficient, due to the shallow gradients. This suggests that composition gradients in cluster cores might be shallower than one-dimensional models predict. More quantitative statements demand more refined models that can incorporate the physics driving the sedimentation process and simultaneously account for the weakly collisional nature of the plasma.