Two-dimensional Incompressible MHD Research Articles

Effects of different nanoparticles Cu, TiO2, and Ag on fluid flow and heat transfer over cylindrical surface subject to non-fourier heat flux model

The significance of this investigation is to optimize the heat transfer rate of magnetohydrodynamic bioconvective hybrid nanofluid flow in the presence of heat source and thermal convection. The main focus is to examine the two-dimensional incompressible MHD and / hybrid nanofluid flow across the stretching cylinder with the Cattaneo–Christov heat flux model. The response surface methodological approach and sensitivity analysis have been employed to statistically scrutinize the influences of concentration, bioconvection, and thermo-diffusion on heat transfer rate. By applying suitable similarity vectors in controlling the partial differential equations, a system of equations (ODEs) is formed. A well-known method Runge Kutta with shooting has used for numerical simulations. The role of various involving factors on heat and mass transfer rate and skin friction factor is illustrated using tables, figures, and surface plots. The three-dimensional graphs displayed the synchronized effect of involving factors on physical quantities. The heat transfer rate is least responsive to variations in the magnetic parameter and most sensitive to the fluctuations of the Biot number. It is perceived that the nanoparticle concentration and motile concentration profiles declined with the increasing effect of chemical reaction parameters. The legitimacy of the current conclusions is established by the excellent agreement concerning present and previous consequences.

On the asymptotic stability of a stratified flow of the 2D non-resistive incompressible MHD equations

The exponential stability of a stratified flow of the two-dimensional incompressible MHD equations on a periodic domain $${\mathbb {T}}^2=[0,1]\times [0,1]$$ is presented. The stability mechanism which makes our results possible is due to the dissipation which arose from the mixing effect from the background flow. More precisely, although the magnetic field potential is governed by a transport equation, by using the algebraic structure of the incompressible condition, it turns out that the linearized MHD equation around the given stratified flow retains a non-local damping mechanism. We established the stability by combining with the energy estimates and the decay estimates.

The Boundary Layer Problem of MHD System with the Non-characteristic Dirichlet Boundary Condition for Velocity

In this paper, we study the boundary layer problem for the two-dimensional incompressible MHD system with the non-characteristic Dirichlet boundary condition for the velocity and the perfect conducting wall boundary condition for the magnetic field. Using multiscale analysis and the elaborate energy methods, we rigorously prove that the solutions of the viscous and diffusive MHD system are approximated by the inner solutions with the boundary layers in the sense of $L^{2}$ norm when the viscosity and diffusion coefficient tend to zero.

A Sparse-Mode Spectral Method for the Simulation of Turbulent Flows

We propose a new algorithm belonging to the family of the sparse-mode spectral method to simulate turbulent flows. In this method the number of Fourier modeskincreases withkmore slowly thankD−1in dimensionD, while retaining the advantage of the fast Fourier transform. Examples of applications of the algorithm are given for the one-dimensional Burgers' equation and two-dimensional incompressible MHD flows.

Chaotic phenomenon in the magnetopause plasma

A model of the magnetopause plasma based on the two-dimensional incompressible MHD equations is considered. A new set of nonlinear differential equations for the model has been derived. The evolution of phase orbits with the time is studied when the Mach number M A is varied. Numerical analysis shows that in certain range of the Mach number the system exhibits chaotic behavior. It has also been observed intermittent motion to chaos. The results show that nonlinear interaction of flow field and magnetic field causes irregular change of velocity and magnetic field in the magnetopause, and chaotic phenomena occur in the magnetopause plasma. We think that the results obtained from our model can provide new insight into the results detected by ISEE and OGO-5.

Current sheet formation in two-dimensional incompressible MHD turbulence from a lagrangian point of view

Abstract Two dimensional ideal incompressible MHD turbulence is studied in a Lagrangian framework in which the non-local pressure forces are approximated to be locally isotropic. Within this model current sheet formation at null points and along field lines is observed. In the case of field lines, this behavior is found to be robust under addition of random pressure fluctuations from isotropy. The value of a quantity called the fluid balance of strain is found to be important in predicting where and when current sheet formation occurs.

The equations of reduced magnetohydrodynamics

The equations of high- and low-beta reduced magnetohydrodynamics (RMHD) are considered anew in order to elucidate the relationship between compressible MHD and RMHD and also to distinguish RMHD from recently developed models of nearly incompressible MHD. Our results, summarized in two theorems, provide the conditions under which RMHD represents a valid reduction of compressible MHD. The equations for low-beta RMHD and high-beta RMHD are shown to be identical. Furthermore, as a direct consequence of our analysis, the conditions under which both two-dimensional incompressible MHD (in terms of the spatial co-ordinates as well as the fluid variables) and 2½ dimensional incompressible MHD (i.e. only two-dimensional in the spatial co-ordinates) represent a valid reduction of three-dimensional compressible MHD are also formulated. It is found that the elimination of all high-frequency and long-wavelength modes from the magneto-fluid reduces the fully compressible MHD equations to either two-dimensional incompressible MHD in the plasma beta (β) limit β ≪ 1, or 2½-dimensional incompressible MHD for β ≈ 1. Our approach clarifies several inconsistencies to be found in previous investigations in that the reduction is exact. Our results and analysis are expected to be of interest for plasma fusion and space and solar physics.

A study of slow‐mode structures in the dayside magnetosheath

Recent observations indicate that a region of enhanced plasma pressure and decreased magnetic field intensity frequently occurs in front of the plasma depletion layer at the dayside magnetopause [Song et al., 1990]. This inverse relationship is characteristic of a slow‐mode wave. We have simulated this phenomenon with a two‐dimensional incompressible MHD simulation code. When a normal component of the interplanetary magnetic field is present (Bx≠0), the total magnetic field intensity tends to decrease in front of the depletion layer due to the bending of the magnetic field lines, and the plasma pressure is enhanced in this region. On the other hand, when Bx =0, this slow‐mode structure is not present in the simulation and only the plasma depletion layer is observed.

Resistive Instabilities in a Two-Dimensional MHD Turbulent Flow

Direct numerical simulations of decaying two-dimensional incompressible MHD flows at Reynolds numbers of several thousands are reported here, using resolutions of 10242 collocation points on a uniform grid. Spatial derivation is performed using Fourier decomposition, assuming periodic boundary conditions, and nonlinear terms are computed in configuration space. The time-stepping scheme is semi-implicit, Crank–Nicolson and third-order Runge–Kutta. The magnetic Prandtl number is equal to unity in all runs. Both deterministic and random initial conditions are used, concentrated in the large scales, with quasi–equipartition between kinetic and magnetic energy. The dynamic range in amplitude of the fields is 107, ensuring well–resolved current and vorticity sheets, over roughly 20 grid points. This leaves sufficient space for tearing instabilities to develop, embedded in a turbulent flow.

A study of multiple X line reconnection at the dayside magnetopause

Interaction between the interplanetary magnetic field and the earth's geomagnetic field at the dayside magnetopause is studied by a global two‐dimensional incompressible MHD simulation. It is found that for a large magnetic Reynolds number (Rm ≥400), the multiple X line reconnection (MXR) becomes the major dayside reconnection process, while for a small magnetic Reynolds number (Rm ≤100), the classical single X line reconnection takes place. Since the magnetic Reynolds number at the dayside magnetopause is probably very high (Rm >10³), it may be suggested that MXR will dominate the dayside reconnection pattern. As a result of the MXR process, magnetic islands are formed on the dayside magnetopause surface. The dependence of the dayside reconnection geometry on the solar wind Alfvén Mach number is also examined.

Simulation of multiple X-line reconnection at the dayside magnetopause

The multiple X-line reconnection process, which was proposed by Lee and Fu [1985] for the dayside magnetopause, is simulated based on a two-dimensional incompressible MHD model. It is found that when the system length is much larger than the thickness of the current layer, magnetic flux tubes are repeatedly formed and convected out of the system. Impulsive magnetic reconnections associated with the formation of magnetic flux tubes are observed. In the case of the dayside magnetopause, magnetic flux tubes with a cross-section of ∼ 1 RE² are found to be formed repeatedly every 5-10 minutes, consistent with satellite observations.

Analytical estimates of turbulent MHD transport coefficients

Turbulent transfer rates from small-scale MHD excitations to large-scale Fourier modes are calculated algebraically using the method of Biskamp and Welter (1983). Three cases are considered: two-dimensional Navier-Stokes flows, two-dimensional incompressible MHD, and the weakly three-dimensional Strauss equations. In all cases, an initially large spectral gap, between the small-scale and large-scale excitations is assumed, and attention focuses on the initial values of the back-transfer rates. The sign of the transfer is determined by the sign of an analytically calculable eddy viscosity and/or anomalous resistivity. The authors confirm the results of Biskamp and Welter for the case of two-dimensional MHD, but find some differences for the case of the Strauss equations. It is argued that the Strauss equations may not exhibit an inverse cascade phenomenon for the spatially periodic case unless their initial spectra are such that the behaviour is essentially that of two-dimensional MHD.

Magnetohydrodynamic flow past a circular cylinder

The steady, two-dimensional incompressible MHD flow past a circular cylinder with an applied magnetic field parallel to the main flow is calculated using the method of series truncation. The differential equations are solved numerically. The magnetic Reynolds number is assumed to be small. The results show that with an applied magnetic field the flow stays attached to the cylinder longer and in some cases does not separate until the rear stagnation point.