All pages tagged magnetohydrodynamics

Exact laws derived for incompressible magnetohydrodynamics (IMHD) turbulence have been widely used to gain insight into the problem of solar wind (SW) heating through the estimation of the turbulent energy cascade rate. While the incompressibilty assumption can, to some extent, be justified to address large scale SW turbulence where alfv\'enic fluctuations dominate, it is likely to fail to accurately describe sub-ion scale physics, as well as other more compressible plasmas such as planetary magnetospheres or the interstellar medium. Here, we will review a set of recent analytical and numerical results obtained for compressible flows within the isothermal closure. First, we will discuss the new exact law derived for compressible MHD (CMHD) and emphasize the major differences with IMHD, in particular the role of the mean (background) magnetic field and plasma density. In the next step, we will discuss the extension of the laws to compressible Hall-MHD (CHMHD) and discuss the physics brought up by the new terms due to the Hall current. The incompressiblity limit is further studied using a more compact form that include only increments of the turbulent fields and compared to previous derivations. The validation of the various exact laws are done using 3D direct numerical simulations (GHOST code for the compressible flows and TURBO for the incompressible models). Potential applications of the models to estimate the energy cascade rate of turbulence over a broad range of scales that span both the inertial and sub-ion (dispersive) ranges in spacecraft data will be discussed.

Authors: E. Bello-Benítez, G. Sánchez-Arriaga, T. Passot, D. Laveder and E. Siminos. There exist a broad variety of nonlinear-wave phenomena in the solar wind. Different types of stable large-amplitude solitary waves are typically observed in these plasmas. The study of small amplitude waves can be described by well-known equations: Korteweg-de-Vries (KdV), modified KdV, Derivative Nonlinear Schrödinger (DNLS) and triple-degenerate DNLS. However, magnetohydrodynamic (MHD) fluid equations are more suitable for the analysis of large-amplitude structures, which is the approach used in this work [1] —to be precise, MHD equations with Hall effect and Finite Larmor Radius (FLR) corrections to the double adiabatic pressure tensor. Assuming travelling wave solutions, the system of partial differential equations yields a set of 5 ordinary differential equations (ODEs) governing the spatial profile of the velocity and magnetic-field vectors —if double adiabatic equations of state are used for the gyrotropic pressures. The procedure to derive these equations follows Ref. [2], but some discrepancies are shown [1]. The existence of solitary-wave solutions in different parametric regimes is rigorously proved in this system of ODEs using concepts and tools from the theory of dynamical systems. Two key features of the concerning ODEs are: (1) the system is reversible and (2) the existence of an invariant which allows reducing the effective dimension of the system from 5 to 4. These characteristics are guaranteed if equations of state are used for the pressures. Nevertheless, only stable structures have physical interests and are expected to be observed in space. The global stability of the solitary waves is investigated by numerical spectral simulations using two different closures for the pressures: (1) double adiabatic equations and (2) evolution equations including the FLR work terms [3], which guarantee energy conservation and better reproduces the real physics. In case (1), it is found that the solitary waves may have a stable core even if the background is unstable. The background instability seems to disappear when the energy-conserving model (2) is considered. In this case, stable solitary waves are found that survive long time without significant deformation.

References

[1] E. Bello-Benítez, G. Sánchez-Arriaga, T. Passot, D. Laveder and E. Siminos, Phys. Rev. E 99, 023202 (2019).

[2] E. Mjølhus, Nonlin. Proc. Geophys. 16, 251 (2009).

[3] P. L. Sulem and T. Passot, J. Plasma Phys. 81, 325810103 (2015).