Binod Sreenivasan

Melting of the Earth's inner core.

The Earth’s magnetic field is generated by a dynamo in the liquid iron core, which convects in response to cooling of the overlying rocky mantle. The core freezes from the innermost surface outward, growing the solid inner core and releasing light elements that drive compositional convection. Mantle convection extracts heat from the core at a rate that has enormous lateral variations. Here we use geodynamo simulations to show that these variations are transferred to the inner-core boundary and can be large enough to cause heat to flow into the inner core. If this were to occur in the Earth, it would cause localized melting. Melting releases heavy liquid that could form the variable-composition layer suggested by an anomaly in seismic velocity in the 150 kilometres immediately above the inner-core boundary. This provides a very simple explanation of the existence of this layer, which otherwise requires additional assumptions such as locking of the inner core to the mantle, translation from its geopotential centre or convection with temperature equal to the solidus but with composition varying from the outer to the inner core. The predominantly narrow downwellings associated with freezing and broad upwellings associated with melting mean that the area of melting could be quite large despite the average dominance of freezing necessary to keep the dynamo going. Localized melting and freezing also provides a strong mechanism for creating seismic anomalies in the inner core itself, much stronger than the effects of variations in heat flow so far considered.

Azimuthal winds, convection and dynamo action in the polar regions of planetary cores

We investigate azimuthal winds in planetary cores using a thermal convection-driven dynamo. When inertial forces are not negligible in the equation of motion, the inertially driven thermal winds are cyclonic. When the Lorentz forces are strong enough, we find anticyclonic thermal winds as observed in the Earths polar region from secular variation data. Under strong thermal convection, the azimuthal flow is created by the magnetic mode with one or more coherent, strong upwellings inside the tangent cylinder (TC), offset from the polar axis. We also find that, as the convection in the TC becomes stronger, these vortex plumes shrink in size, consistent with the convection being controlled by the magnetic field. In addition, strong upwellings in the TC could expel magnetic field in its path, creating regions of weak or even reverse flux patches. These patches drift westward, but at a significantly slower angular speed than the rotation about the vortex itself. Calculations with electrically conducting and stress-free boundaries reveal that the mechanism of generation of polar thermal winds is fairly independent of the boundary conditions imposed, provided the Rayleigh number is high enough to excite the magnetic mode.

Hydrodynamics of a swirling fluidised bed

Abstract A novel variant of the fluidised bed, the swirling fluidised bed, featuring an annular bed and inclined injection of gas through the distributor blades, is studied in the present work. The hydrodynamic characteristics in the swirling regime of operation are studied in detail, experimentally as well as by an analytical model. Unlike a conventional bed, the swirling bed presents three, or sometimes four regimes of operation depending on the bed weight. Bed pressure drop studies have been carried out in a swirling bed for two different sizes of spherical PVC particles. A striking feature that distinguishes the swirling bed from a conventional fluidised bed is that, the bed pressure drop in the swirling mode, (Δp)b,s increases with air velocity. A physically plausible explanation for this behaviour is that, (Δp)b,s is proportional to the centrifugal weight of the bed. This idea leads to the development of an approximate model that predicts the mean angular velocity of the bed, and hence, (Δp)b,s, at a given air flow rate. The good agreement between the theoretical and experimentally obtained (Δp)b,s values at moderate air flow rates, and the results of an uncertainty analysis performed on the model indicate that the present model describes the fluidised regime of a swirling bed satisfactorily.

Dynamos with weakly convecting outer layers: implications for core-mantle boundary interaction

Convection in the Earths core is driven much harder at the bottom than the top. This is partly because the adiabatic gradient steepens towards the top, partly because the spherical geometry means the area involved increases towards the top, and partly because compositional convection is driven by light material released at the lower boundary and remixed uniformly throughout the outer core, providing a volumetric sink of buoyancy. We have therefore investigated dynamo action of thermal convection in a Boussinesq fluid contained within a rotating spherical shell driven by a combination of bottom and internal heating or cooling. We first apply a homogeneous temperature on the outer boundary in order to explore the effects of heat sinks on dynamo action; we then impose an inhomogeneous temperature proportional to a single spherical harmonic Y 2² in order to explore core-mantle interactions. With homogeneous boundary conditions and moderate Rayleigh numbers, a heat sink reduces the generated magnetic field appreciably; the magnetic Reynolds number remains high because the dominant toroidal component of flow is not reduced significantly. The dipolar structure of the field becomes more pronounced as found by other authors. Increasing the Rayleigh number yields a regime in which convection inside the tangent cylinder is strongly affected by the magnetic field. With inhomogeneous boundary conditions, a heat sink promotes boundary effects and locking of the magnetic field to boundary anomalies. We show that boundary locking is inhibited by advection of heat in the outer regions. With uniform heating, the boundary effects are only significant at low Rayleigh numbers, when dynamo action is only possible for artificially low magnetic diffusivity. With heat sinks, the boundary effects remain significant at higher Rayleigh numbers provided the convection remains weak or the fluid is stably stratified at the top. Dynamo action is driven by vigorous convection at depth while boundary thermal anomalies dominate in the upper regions. This is a likely regime for the Earths core.

On the formation of cyclones and anticyclones in a rotating fluid

It is commonly observed that the columnar vortices that dominate the large scales in homogeneous, rapidly rotating turbulence are predominantly cyclonic. This has prompted us to ask how this asymmetry arises. To provide a partial answer to this we look at the process of columnar vortex formation in a rotating fluid and, in particular, we examine how a localized region of swirl (an eddy) can convert itself into a columnar structure by inertial wave propagation. We show that, when the Rossby number (Ro) is small, the vortices evolve into columnar eddies through the radiation of linear inertial waves. When the Rossby number is large, on the other hand, no such column is formed. Rather, the eddy bursts radially outward under the action of the centrifugal force. There is no asymmetry between cyclonic and anticyclonic eddies for these two regimes. However, cyclones and anticyclones behave differently in the intermediate regime of Ro∼1. Here we find that the transition from columnar vortex formation to radial bu...

Experimental study of a vortex in a magnetic field

It is well-known that magnetohydrodynamic (MHD) flows behave differently from conventional fluid flows in two ways: the magnetic field makes the flow field anisotropic in the sense that it becomes independent of the coordinate parallel to the field; and the flow of liquid across the field lines induces an electric current, leading to ohmic damping. In this paper, an experimental study is presented of the long-time decay of an initially three-dimensional flow structure subject to a steady magnetic field, when the ratio of the electromagnetic Lorentz forces to the nonlinear inertial forces, quantified by the magnetic interaction parameter, N 0 , takes large as well as moderate values. This investigation is markedly different from previous studies on quasi-two-dimensional MHD flows in thin layers of conducting fluids, where only Hartmann layer friction held the key to the dissipation of the flow. The initial ‘linear’ phase of decay of an MHD flow, characterized by dominant Lorentz forces and modelled extensively in the literature, has been observed for the first time in a laboratory experiment. Further, when N 0 is large compared to unity, a distinct regime of decay of a vortex follows this linear phase. This interesting trend can be explained in terms of the behaviour of the ratio of the actual magnitudes of the Lorentz to the nonlinear inertial forces – the true interaction parameter – which decreases to a constant of order unity towards the end of the linear phase of decay, and remains invariant during a subsequent ‘nonlinear’ phase.

On the control of surface waves by a vertical magnetic field

We consider the magnetic damping of surface gravity waves by a vertical magnetic field. The damping mechanism is, in principle, quite simple. The motion of a conducting fluid in the presence of an imposed magnetic field leads to electric currents, and hence to Ohmic dissipation. As the fluid heats up, there is a corresponding loss in the mechanical energy of the wave motion. When the fluid is infinite in the horizontal plane, or else bounded by perfectly conducting vertical walls, the induced currents have a simple spatial distribution and so the analysis of such waves is straightforward [L. E. Franekel, J. Fluid. Mech. 7, 81 (1959); P. Rivat, J. Etay, and M. Garnier, Eur. J. Mech. B/Fluids 10, 537 (1991)]. However, in most practical applications of magnetic damping the fluid is bounded by nonconducting vertical walls. This leads to a complex distribution of electric currents and to a much weaker form of damping. In this paper, we extend the simple classical theory to accommodate nonconducting sidewalls, ...

Heat transfer in a swirling fluidized bed with geldart type-D particles

A relatively new variant in fluidized bed technology, designated as the swirling fluidized bed (SFB), was investigated for its heat transfer characteristics when operating with Geldart type D particles. Unlike conventional fluidized beds, the SFB imparts secondary swirling motion to the bed to enhance lateral mixing. Despite its excellent hydrodynamics, its heat transfer characteristics have not been reported in the published literature. Hence, two different sizes of spherical PVC particles (2.61 mm and 3.65 mm) with the presence of a center body in the bed have been studied at different velocities of the fluidizing gas. The wall-to-bed heat transfer coefficients were measured by affixing a thin constantan foil heater on the bed wall. Thermocouples located at different heights on the foil show a decrease in the wall heat transfer coefficient with bed height. It was seen that only a discrete particle model which accounts for the conduction between the particle and the heat transfer surface and the gas-convective augmentation can adequately represent the mechanism of heat transfer in the swirling fluidized bed.

Confinement of rotating convection by a laterally varying magnetic field

Spherical shell dynamo models based on rotating convection show that the flow within the tangent cylinder is dominated by an off-axis plume that extends from the inner core boundary to high latitudes and drifts westward. Earlier studies explained the formation of such a plume in terms of the effect of a uniform axial magnetic field that significantly increases the lengthscale of convection in a rotating plane layer. However, rapidly rotating dynamo simulations show that the magnetic field within the tangent cylinder has severe lateral inhomogeneities that may influence the onset of an isolated plume. Increasing the rotation rate in our dynamo simulations (by decreasing the Ekman number

Onset of plane layer magnetoconvection at low Ekman number

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