MHD simulation of the distribution of the gasdynamic parameters and magnetic field behind the Earth’s bow shock under sharp variations in the solar wind dynamic pressure

The distributions of the gasdynamic parameters (density, pressure, and velocity) and the magnetic field behind the Earth’s bow shock (on the outer boundary of the magnetosheath) generated under sharp variations in the solar wind dynamic pressure are found in the three-dimensional non-planepolarized formulation with allowance for the interplanetary magnetic field within the framework of the ideal magnetohydrodynamic model using the solution to the MHD Riemann problem of breakdown of an arbitrary discontinuity. Such a discontinuity which depends on the inclination of an element of the bow shock surface arises when a contact discontinuity traveling together with the solar wind and on which the solar wind density and, consequently, the dynamic pressure, increases or decreases suddenly impinges on the Earth’s bow shock and propagates along its surface initiating the development of to six waves or discontinuities (shocks). The general interaction pattern is constructed for the entire bow shock surface as a mosaic of exact solutions to the MHD Riemann problem obtained on computer using an original software (MHD Riemann solver) so that the flow pattern is a function of the angular surface coordinates (latitude and longitude). The calculations are carried out for various jumps in density on the contact discontinuity and characteristics parameters of the solar wind and interplanetary magnetic field at the Earth’s orbit. It is found that there exist horseshoe zones on the bow shock in which the increase in the density and the magnetic field strength in the fast shock waves or their reduced decrease in the fast rarefaction waves penetrating into the magnetosheath and arising as a result of sharp variation in the solar wind dynamic pressure is superposed on significant drop in the density and growth in the magnetic field strength in slow rarefaction waves. The distributions of the hydrodynamic parameters and the magnetic field can be used to interpret measurements carried out on spacecraft in the solar wind at the libration point and orbiters in the neighborhood of the Earth’s magnetosphere.     

Collision of an interplanetary shock wave with the Earth’s bow shock. Hydrodynamic parameters and magnetic field

Hydrodynamic parameters and magnetic field generated in each of the waves in neighborhood of the Earth’s bow shock when an interplanetary shock wave impinges on it and propagates along its surface are found in the three-dimensional non-plane-polarized formulation within the framework of the ideal magnetohydrodynamic model. The interaction pattern is constructed in the quasi-steady-state formulation as a mosaic of exact solutions, obtained by means of a computer, to the Riemann problem of breakdown of a discontinuity between the states downstream of the impinging wave and the bow shock on the traveling line of intersection of their fronts. The calculations are carried out for typical parameters of the quiescent solar wind and the interplanetary magnetic field in the Earth’s orbit when the plane front of a shock wave moves along the Sun-Earth radius with various given velocities. The solutions obtained can be used to interpret measurements carried out by spacecraft in the solar wind and in neighborhood of the Earth’s magnetosphere.     

Three-dimensional magnetohydrodynamic description of the process of impingement of a solar wind rotational discontinuity on the Earth’s bow shock

The impact of the plane front of a rotational discontinuity, which has a circular polarization and propagates in the solar wind along the Sun-Earth radius, on the Earth’s bow shock and the magnetosheath is first investigated in the three-dimensional formulation. The most characteristic values of the solar wind parameters and the interplanetary magnetic field strength in the Earth’s orbit are considered. The global three-dimensional pattern of the flow is constructed as a function of the latitude and longitude of points on the bow shock and the intensities of all the waves appearing in the interaction which significantly depend on the angle of rotation of the magnetic field are found. The solution obtained is necessary to interpret the solar wind parameters and the interplanetary magnetic field measured by spacecraft located in the neighborhood of the Lagrange point and the Earth’s magnetosphere.     

Three-dimensional magnetohydrodynamic description of the process of collision of a solar wind shock wave and the Earth’s bow shock

The propagation of a solar wind shock wave along the surface of the Earth’s bow shock is investigated within the framework of an ideal magnetohydrodynamic model in the three-dimensional non-plane-polarized formulation. The most characteristic values of the solar wind parameters and the interplanetary magnetic field strength are considered for the plane front of a solar wind shock wave moving at various velocities along the Sun-Earth radius. The global three-dimensional pattern of the interaction is constructed as a function of the angle of inclination of the surface of the bow shock to the solar wind velocity and the azimuthal angle along the curve of intersection of the fronts of the interacting shock waves. The evolution of the flow developed in the neighborhood of the bow shock is investigated and the parameters of the medium and magnetic field are calculated.     

3D reconstruction of the flow and vortical field in a rotating sharp “U” turn channel

Particle image velocimetry experiments have been carried out to obtain visualizations and measurements of the main and secondary flow fields in a square channel with a sharp “U” turn. Both the main and the secondary flow fields have been used to perform a 3D reconstruction of the mean flow and vortical fields in the turn region and in the outlet duct. In order to study the influence of the rotation, tests both in stationary (absence of rotation, Re = 20,000) and in rotating (Re = 20,000 and Ro = 0.3) conditions have been performed. The results show that the Coriolis and centrifugal forces, caused by the rotation, yield strong modifications to the symmetrical flow and vortical fields that are generated, in the static case, only by the abrupt inversion of the flow direction.     

Investigation of generalized Fick’s and Fourier’s laws in the second-grade fluid flow

The second-grade fluid flow due to a rotating porous stretchable disk is modeled and analyzed. A porous medium is characterized by the Darcy relation. The heat and mass transport are characterized through Cattaneo-Christov double diffusions. The thermal and solutal stratifications at the surface are also accounted. The relevant nonlinear ordinary differential systems after using appropriate transformations are solved for the solutions with the homotopy analysis method (HAM). The effects of various involved variables on the temperature, velocity, concentration, skin friction, mass transfer rate, and heat transfer rate are discussed through graphs. From the obtained results, decreasing tendencies for the radial, axial, and tangential velocities are observed. Temperature is a decreasing function of the Reynolds number, thermal relaxation parameter, and Prandtl number. Moreover, the mass diffusivity decreases with the Schmidt number.     

Refinement of a global model for the Earth’s gravitational field using airborne gravimetry data

An algorithm for combining airborne gravimetry data with the data supplied by a global model of the Earth’s gravitational field is considered. The global model is specified by a spherical wavelet decomposition. An optimal guaranteed estimation of the wavelet coefficients for the gravitational field is used.     

Influence of the operation pressure on slug length in near horizontal gas–liquid pipe flow

Slug flow is commonly observed in gas production offshore fields. At high operation pressure only short hydrodynamic slugs are observed. However, as the offshore fields become older, the operation pressure becomes lower and long slugs may form. At near atmospheric pressures the long slugs may reach a size of 500 pipe diameters or more. Such slugs can cause serious operational failures due to the strong fluctuating pressure. Identifying the operation pressure conditions at which the long slugs appear, may reduce or prevent these negative effects.     

Influence of the spatial variation of Poisson’s ratio upon the elastic field in nonhomogeneous axisymmetric bodies

The effect of a nonconstant Poisson’s ratio upon the elastic field in functionally graded axisymmetric solids is analyzed. Both of the elastic coefficients, i.e. Young’s modulus and Poisson’s ratio, are permitted to vary in the radial direction. These elastic coefficients are considered to be functions of composition and are related on this basis. This allows a closed form solution for the stress function to be obtained. Two cases are discussed in this investigation: first, both Young’s modulus and Poisson’s ratio are allowed to vary across the radius and the effect of spatial variation of Poisson’s ratio upon the maximum radial displacement is investigated; secondly, Young’s modulus is taken as constant and the change in the maximum hoop stress resulting from a variable Poisson’s ratio is calculated.     

Effect of viscosity on the current layers emerging upon propagation of the Alfvén pulse in a hyperbolic magnetic field

The propagation of the Alfvén pulse in the vicinity of the X-point in the presence of viscosity is studied for the first time. It is shown that, in contrast to the case of magnetosonic perturbation, where the dynamic viscosity η (the point is that we are dealing with dimensionless quantities), which is small compared to the magnetic plasma viscosity ν, does not affect the flow, this influence is of primary importance in the Alfvén case. The magnitude of the steady-state current density is proportional to (vνη)^-1/4. It is also shown that at large times the distribution of the z-component of a magnetic field that is close to the distribution obtained in solving a linear problem is established in this significantly nonlinear problem. The effect of the heat conduction on this process is studied. Institute of Computational Technologies, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 11–16, November–December, 1999.     

Influence of conicity on the stress–strain state of a flexible orthotropic conical shell in a nonstationary magnetic field

A problem of magnetoelasticity for a flexible conical shell in a nonstationary magnetic field is solved. The effect of conicity on the stress–strain state of the shell is analyzed     

An improved correlation of the pressure drop in stenotic vessels using Lorentz’s reciprocal theorem

A mathematical model of the human cardiovascular system in conjunction with an accurate lumped model for a stenosis can provide better insights into the pressure wave propagation at pathological conditions. In this study, a theoretical relation between pressure drop and flow rate based on Lorentz’s reciprocal theorem is derived, which offers an identity to describe the relevance of the geometry and the convective momentum transport to the drag force. A voxelbased simulator V-FLOW VOF3 D, where the vessel geometry is expressed by using volume of fluid(VOF) functions, is employed to find the flow distribution in an idealized stenosis vessel and the identity was validated numerically. It is revealed from the correlation that the pressure drop of NS flow in a stenosis vessel can be decomposed into a linear term caused by Stokes flow with the same boundary conditions, and two nonlinear terms. Furthermore, the linear term for the pressure drop of Stokes flow can be summarized as a correlation by using a modified equation of lubrication theory, which gives favorable results compared to the numerical ones. The contribution of the nonlinear terms to the pressure drop was analyzed numerically, and it is found that geometric shape and momentum transport are the primary factors for the enhancement of drag force. This work paves a way to simulate the blood flow and pressure propagation under different stenosis conditions by using 1D mathematical model.     

Effects of magnetic field and variable viscosity on forced non‐darcy flow about a flat plate with variable wall temperature in porous media in the presence of suction and blowing

This paper presents a study of the effect of a magnetic field and variable viscosity on steady twodimensional laminar nonDarcy forced convection flow over a flat plate with variable wall temperature in a porous medium in the presence of blowing (suction). The fluid viscosity is assumed to vary as an inverse linear function of temperature. The derived fundamental equations on the assumption of small magnetic Reynolds number are solved numerically by using the finite difference method. The effects of variable viscosity, magnetic and suction (or injection) parameters on the velocity and temperature profiles as well as on the skinfriction and heattransfer coefficients were studied. It is shown that the magnetic field increases the wall skin friction while the heattransfer rate decreases.     

Kh. A. Rakhmatulin’s scientific legacy in the field of mechanics of deformable rigid bodies

Kh. A. Rakhmatulin’s scientific activity was aimed at solving the most important scientific and technical problems encountered by the country. Khalil Akhmetovich was a unique combination of a theorist and an experimenter, an engineer and an inventor, a talented teacher and a scientific research manager.     

Analyses of the driver’s anticipation effect in a new lattice hydrodynamic traffic flow model with passing

In this paper, we studied the effect of driver’s anticipation with passing in a new lattice model. The effect of driver’s anticipation is examined through linear stability analysis and shown that the anticipation term can significantly enlarge the stability region on the phase diagram. Using nonlinear stability analysis, we obtained the range of passing constant for which kink soliton solution of mKdV equation exist. For smaller values of passing constant, uniform flow and kink jam phase are present on the phase diagram and jamming transition occurs between them. When passing constant is greater than the critical value depending on the anticipation coefficient, jamming transitions occur from uniform traffic flow to kink-bando traffic wave through chaotic phase with decreasing sensitivity. The theoretical findings are verified using numerical simulation which confirm that traffic jam can be suppressed efficiently by considering the anticipation effect in the new lattice model.     

Framing conflicting scientific views of John Robison on the Euler’s column buckling problem in the socio-political context of the late XVIII century

Meccanica - The analytical approach of Leonhard Euler to the solution of an elastic column under compression is seen today as a landmark in buckling studies. However, this work was not well...     

Comment on the paper “Magnetohydrodynamic effects on natural convection flow of a nanofluid in the presence of heat source due to solar energy,N. Anbuchezhian,K. Srinivasan,K. Chandrasekaran,R. Kandasamy,Meccanica (2013) 48:307–321”

In the above paper a theoretical investigation of MHD convective flow and heat transfer of an incompressible viscous nanofluid past a porous vertical stretching sheet in the presence of variable stream condition is presented. The governing boundary layer equations are transformed by a Lie symmetry group transformation and the ordinary differential equations are solved numerically using Runge–Kutta Gill method.