Steady-State Magnetohydrodynamic Flow Around an Unmagnetized Conducting Sphere

The non-collisional interaction between conducting obstacles and magnetized plasma winds can be found in different scenarios, from the interaction occurring between regions inside galaxy clusters to the interaction between the solar wind and Mars, Venus, active comets or even the interaction between Titan and the Saturnian's magnetospheric flow. These objects generate, through several current systems, perturbations in the streaming magnetic field leading to its draping around the obstacle's effective conducting surface. Recent observational results suggest that several properties associated with the magnetic field draping, such as the location of the polarity reversal layer of the induced magnetotail, are affected by variations in the conditions of the streaming magnetic field. To improve our understanding of these phenomena, we perform a characterization of several magnetic field draping signatures by analytically solving an ideal problem in which a perfectly conducting magnetized plasma (with frozen-in magnetic field conditions) flows around a spherical body for various orientations of the streaming magnetic field. In particular, we compute the shift of the inverse polarity reversal layer as the orientation of the background magnetic field is changed.Comment: Preprint submitted to Astrophysical Journa

Periodically driven circulation near the shore of a lake

Solutions are found for a linear model of the circulation near the shore of a lake that is subject to two diurnal forcing mechanisms. The first is the day/night heating/cooling induced horizontal pressure gradient. The second is an unsteady surface stress modelling a sea breeze/gully wind pattern. The two forcing mechanisms can oppose or reinforce each other depending on their relative phase. The interplay of different dynamic balances at different times and locations in the domain lead to complex circulation patterns especially during the period of flow reversal

Energy Balance in the Solar Transition Region. IV. Hydrogen and Helium Mass Flows With Diffusion

In this paper we have extended our previous modeling of energy balance in the chromosphere-corona transition region to cases with particle and mass flows. The cases considered here are quasi-steady, and satisfy the momentum and energy balance equations in the transition region. We include in all equations the flow velocity terms and neglect the partial derivatives with respect to time. We present a complete and physically consistent formulation and method for solving the non-LTE and energy balance equations in these situations, including both particle diffusion and flows of H and He. Our results show quantitatively how mass flows affect the ionization and radiative losses of H and He, thereby affecting the structure and extent of the transition region. Also, our computations show that the H and He line profiles are greatly affected by flows. We find that line shifts are much less important than the changes in line intensity and central reversal due to the effects of flows. In this paper we use fixed conditions at the base of the transition region and in the chromosphere because our intent is to show the physical effects of flows and not to match any particular observations. However, we note that the profiles we compute can explain the range of observed high spectral and spatial resolution Lyman alpha profiles from the quiet Sun. We suggest that dedicated modeling of specific sequences of observations based on physically consistent methods like those presented here will substantially improve our understanding of the energy balance in the chromosphere and corona.Comment: 50 pages + 20 figures; submitted to ApJ 9/10/01; a version with higher resolution figures is available at http://cfa-www.harvard.edu/~avrett

A general method for unsteady stagnation region heat transfer and results for model turbine flows

Recent experiments suggest that the heat-transfer characteristics of stator blades are influenced by the frequency of passing of upstream rotor blades. The calculation of these effects requires that the movement of the stagnation point with variations in freestream velocity is properly represented together with the possible effects of turbulence characteristics on the thin leading-edge boundary layer. A procedure to permit the achievement of these purposes is described for laminar flows in this paper together with results of its application to two model problems which demonstrate its abilities and quantify the influence of wake characteristics on fluid-dynamic and heat-transfer properties of the flow and their effects on surface heat transfer

Microstructure of strongly sheared suspensions and its impact on rheology and diffusion

The effects of Brownian motion alone and in combination with an interparticle force of hard-sphere type upon the particle configuration in a strongly sheared suspension are analysed. In the limit Pe[rightward arrow][infty infinity] under the influence of hydrodynamic interactions alone, the pair-distribution function of a dilute suspension of spheres has symmetry properties that yield a Newtonian constitutive behaviour and a zero self-diffusivity. Here, Pe=[gamma][ogonek]a2/2D is the Péclet number with [gamma][ogonek] the shear rate, a the particle radius, and D the diffusivity of an isolated particle. Brownian diffusion at large Pe gives rise to an O(aPe[minus sign]1) thin boundary layer at contact in which the effects of Brownian diffusion and advection balance, and the pair-distribution function is asymmetric within the boundary layer with a contact value of O(Pe0.78) in pure-straining motion; non-Newtonian effects, which scale as the product of the contact value and the O(a3Pe[minus sign]1) layer volume, vanish as Pe[minus sign]0.22 as Pe[rightward arrow][infty infinity]

Electro-osmotic flow in coated nanocapillaries: a theoretical investigation

Motivated by recent experiments, we present a theoretical investigation of how the electro-osmotic flow occurring in a capillary is modified when its charged surfaces are coated by charged polymers. The theoretical treatment is based on a three dimensional model consisting of a ternary fluid-mixture, representing the solvent and two species for the ions, confined between two parallel charged plates decorated by a fixed array of scatterers representing the polymer coating. The electro-osmotic flow, generated by a constant electric field applied in a direction parallel to the plates, is studied numerically by means of Lattice Boltzmann simulations. In order to gain further understanding we performed a simple theoretical analysis by extending the Stokes-Smoluchowski equation to take into account the porosity induced by the polymers in the region adjacent the walls. We discuss the nature of the velocity profiles by focusing on the competing effects of the polymer charges and the frictional forces they exert. We show evidence of the flow reduction and of the flow inversion phenomenon when the polymer charge is opposite to the surface charge. By using the density of polymers and the surface charge as control variables, we propose a phase diagram that discriminates the direct and the reversed flow regimes and determine its dependence on the ionic concentration.Comment: 15 pages, 6 figures in Physical Chemistry Chemical Physics, 201

Finite element methodology for integrated flow-thermal-structural analysis

Papers entitled, An Adaptive Finite Element Procedure for Compressible Flows and Strong Viscous-Inviscid Interactions, and An Adaptive Remeshing Method for Finite Element Thermal Analysis, were presented at the June 27 to 29, 1988, meeting of the AIAA Thermophysics, Plasma Dynamics and Lasers Conference, San Antonio, Texas. The papers describe research work supported under NASA/Langley Research Grant NsG-1321, and are submitted in fulfillment of the progress report requirement on the grant for the period ending February 29, 1988

Planetary magnetic fields

As a consequence of the smallness of the electronic fine structure constant, the characteristic time scale for the free diffusive decay of a magnetic field in a planetary core is much less than the age of the Solar System, but the characteristic time scale for thermal diffusion is greater than the age of the Solar System. Consequently, primordial fields and permanent magnetism are small and the only means of providing a substantial planetary magnetic field is the dynamo process. This requires a large region which is fluid, electrically conducting and maintained in a non-uniform motion that includes a substantial RMS vertical component. The attributes of fluidity and conductivity are readily provided in the deep interiors of all planets and most satellites, either in the form of an Fe alloy with a low eutectic temperature (e.g. Fe-S-O in terrestrial bodies and satellites) or by the occupation of conduction states in fluid hydrogen or 'ice' (H2O-NH3-CH4) in giant planets. It is argued that planetary dynamos are almost certainly maintained by convection (compositional and/or thermal)

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

Convection in the Earth's 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 Y2² 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 Earth's core