Dastgeer Shaikh

Driven dissipative whistler wave turbulence

Driven dissipative whistler wave turbulence in two-dimensional electron magnetohydrodynamics is investigated using very high resolution nonlinear fluid simulations. It is shown that a dual cascade phenomenon of mean magnetic potential and energy invariants is in agreement with predictions based on statistical ensemble and Kolmogorov’s theories. Turbulent length scales larger than the electron skin depth (whistler wave regime) exhibit a spectral break in the vicinity of the forcing wave number that separates the inverse and forward cascade regimes. On the other hand, length scales smaller than the electron skin depth behave like hydrodynamic eddies in which both small and large scale regimes exhibit identical turbulent spectra. In both cases, however, turbulent fluctuations follow an exact Kolmogorov-type spectra. While wave effects are strong in the whistler wave regime, they are absent entirely in the hydrodynamics regime of the driven electron magnetohydrodynamic turbulence.

Anisotropic Cascades in Interstellar Medium Turbulence

Anisotropic turbulent cascades in the solar wind and interstellar medium (ISM) are investigated using three-dimensional incompressible magnetohydrodynamic (MHD) simulations with a numerical resolution of 2563. In the absence of an external magnetic field (B0 = 0), the anisotropy in the MHD turbulent fluctuations is mediated primarily by the local magnetic field. The latter leads to a disparity in the spectral transfer of energy along and across the local mean magnetic field. While the anisotropic cascades give rise to the relationship ∥ ∝ between the parallel (∥ ~ 1/k∥) and perpendicular (⊥ ~ 1/k⊥) length scales of the eddies relative to the local magnetic field, the global energy is found to obey a Kolmogorov-like k-5/3 anisotropic spectrum in our simulations where turbulence is predominantly subcritical. In the latter, the turbulent cascades are dominated by the nonlinear eddy turnover timescales compared to the linear Alfven wave periods. The critical-balance criterion is therefore not necessarily satisfied in fully developed, strong, anisotropic, high plasma-β magnetofluid ISM turbulence.

Spectral features of solar wind turbulent plasma

Spectral properties of a fully compressible solar wind Hall magnetohydrodynamic (HMHD) plasma are investigated by means of time dependent three-dimensional (3D) HMHD simulations. Our simulations, in agreement with spacecraft data, identify a spectral break in turbulence spectra at characteristic length-scales associated with electromagnetic fluctuations that are smaller than the ion gyroradius. In this regime, our 3D simulations show that turbulent spectral cascades in the presence of a mean magnetic field follow an omnidirectional anisotropic inertial range spectrum close to k -7/3 . The onset of the spectral break in our simulations can be ascribed to the presence of non-linear Hall interactions that modify the spectral cascades. Our simulations further show that the underlying characteristic turbulent fluctuations are spectrally anisotropic, the extent of which depends critically on the local wavenumber. The fluctuations associated with length-scales smaller than the ion gyroradius are highly compressible and tend to exhibit a near equipartition in the velocity and magnetic fields. Finally, we find that the orientation of velocity and magnetic field fluctuations critically determine the character of non-linear interactions that predominantly govern a HMHD plasma, like the solar wind.

Whistler wave cascades in solar wind plasma

Non-linear, three-dimensional, time-dependent fluid simulations of whistler wave turbulence are performed to investigate role of whistler waves in solar wind plasma turbulence in which characteristic turbulent fluctuations are characterized typically by the frequency and length-scales that are, respectively, bigger than ion gyrofrequency and smaller than ion gyroradius. The electron inertial length is an intrinsic length-scale in whistler wave turbulence that distinguishably divides the high-frequency solar wind turbulent spectra into scales smaller and bigger than the electron inertial length. Our simulations find that the dispersive whistler modes evolve entirely differently in the two regimes. While the dispersive whistler wave effects are stronger in the large-scale regime, they do not influence the spectral cascades which are describable by a Kolmogorov-like k ―7/3 spectrum. By contrast, the small-scale turbulent fluctuations exhibit a Navier-Stokes-like evolution where characteristic turbulent eddies exhibit a typical k ―5/3 hydrodynamic turbulent spectrum. By virtue of equipartition between the wave velocity and magnetic fields, we quantify the role of whistler waves in the solar wind plasma fluctuations.

The Transition to Incompressibility from Compressible Magnetohydroynamic Turbulence

On the basis of three-dimensional time-dependent numerical simulations, we find that compressible magnetohydrodynamic fluids describing super-Alfvenic, supersonic, and strongly magnetized space and laboratory plasmas decay progressively to a state of near-incompressibility, characterized by a subsonic turbulent Mach number. This transition is mediated dynamically by disparate spectral energy dissipation rates in compressible magnetosonic and shear Alfvenic modes. Dissipation leads to super-Alfvenic turbulent motions decaying to a sub-Alfvenic regime that couples weakly with (magneto-) acoustic cascades. Consequently, the supersonic plasma motion dissipates into highly subsonic motion and density fluctuations experience a passive convection.

3D electron fluid turbulence at nanoscales in dense plasmas

We have performed three-dimensional (3D) nonlinear fluid simulations of electron fluid turbulence at nanoscales in an unmagnetized warm dense plasma in which mode coupling between wave function and electrostatic (ES) potential associated with underlying electron plasma oscillations (EPOs) lead to nonlinear cascades in inertial range. While the wave function cascades towards smaller length scales, ES potential follows an inverse cascade. We find from our simulations that the quantum diffraction effect associated with a Bohm potential plays a critical role in determining the inertial range turbulent spectrum and the subsequent transport level exhibited by the 3D EPOs.

Theory and simulations of whistler wave propagation

A linear theory of whistler waves is developed within the paradigm of a two-dimensional incompressible electron magnetohydrodynamics model. Exact analytic wave solutions are obtained for small-amplitude whistler waves that exhibit magnetic field topological structures consistent with the observations and our simulations in a linear regime. In agreement with experiment, we find that the parallel group velocity of the wave is large compared to its perpendicular counterpart. Numerical simulations of collisional interactions demonstrate that the wave magnetic field either coalesces or repels depending upon the polarity of the associated current. In the nonlinear regime, our simulations demonstrate that the evolution of the wave magnetic field is governed essentially by the nonlinear Hall force.

Theory and simulations of principle of minimum dissipation rate

We perform a self-consistent, time-dependent numerical simulations of dissipative turbulent plasmas at a higher Lundquist number, typically up to O(106), using full three-dimensional compressible magnetohydrodynamics code with a numerical resolution of 1283. Our simulations follow the time variation of global helicity, magnetic energy, and the dissipation rate and show that the global helicity remains approximately constant, while magnetic energy is decaying faster and the dissipation rate is decaying even faster than the magnetic energy. This establishes that the principle of minimum dissipation rate under the constraint of (approximate) conservation of global helicity is a viable approach for plasma relaxation.

ENERGY CASCADES IN A PARTIALLY IONIZED ASTROPHYSICAL PLASMA

A local turbulence model is developed to study energy cascades in the interstellar medium (ISM) based on self-consistent two-dimensional fluid simulations. The model describes a partially ionized magnetofluid ISM that couples a neutral hydrogen fluid with a plasma primarily through charge-exchange interactions. Charge-exchange interactions are ubiquitous in warm ISM plasma, and the strength of the interaction depends largely on the relative speed between the plasma and the neutral fluid. Unlike small-length scale linear collisional dissipation in a single fluid, charge-exchange processes introduce channels that can be effective on a variety of length scales that depend on the neutral and plasma densities, temperature, relative velocities, charge-exchange cross section, and the characteristic length scales. We find, from scaling arguments and nonlinear coupled fluid simulations, that charge-exchange interactions modify spectral transfer associated with large-scale energy-containing eddies. Consequently, the warm ISM turbulent cascade rate prolongs spectral transfer among inertial range turbulent modes. Turbulent spectra associated with the neutral and plasma ISM fluids are therefore steeper than those predicted by Kolmogorovs phenomenology.

Modulation of waves due to charge-exchange collisions in magnetized partially ionized space plasma

A nonlinear time dependent fluid simulation model is developed that describes the evolution of magnetohydrodynamic waves in the presence of collisional and charge exchange interactions of a partially ionized plasma. The partially ionized plasma consists of electrons, ions and a significant number of neutral atoms. In our model, the electrons and ions are described by a single fluid compressible magnetohydrodynamic (MHD) model and are coupled self-consistently to the neutral gas, described by the compressible hydrodynamic equations. Both the plasma and neutral fluids are treated with different energy equations that describe thermal energy exchange processes between them. Based on our self-consistent model, we find that propagating Alfvenic and fast/slow modes grow and damp alternately through a nonlinear modulation process. The modulation appears to be robust and survives strong damping by the neutral component.