We simulate forced quasi-static magnetohydrodynamic turbulence and investigate the anisotropy, energy spectrum, and energy flux of the flow, specially for large interaction parameters (N ). We show that the angular dependence of the energy spectrum is well quantified using Legendre polynomials. For large N , the energy spectrum is exponential. Our direct computation of energy flux reveals an inverse cascade of energy at low wavenumbers, similar to that in two-dimensional turbulence.We observe the flow be two-dimensional (2D) for moderate N (N ∼ 20), and two-

Tarang is a general-purpose pseudospectral parallel code for simulating flows involving fluids, magnetohydrodynamics, and Rayleigh-Bénard convection in turbulence and instability regimes. In this paper we present code validation and benchmarking results of Tarang. We performed our simulations on 1024 3 , 2048 3 , and 4096 3 grids using the HPC system of IIT Kanpur and Shaheen of KAUST. We observe good "weak" and "strong" scaling for Tarang on these systems.

We perform direct numerical simulations of quasi-static magnetohydrodynamic turbulence, and compute various energy transfers including the ring-to-ring and conical energy transfers, and the energy fluxes of the perpendicular and parallel components of the velocity field. We show that the rings with higher polar angles transfer energy to ones with lower polar angles. For large interaction parameters, the dominant energy transfer takes place near the equator (polar angle θ ≈ π 2 ). The energy transfers are local both in wavenumbers and angles. The energy flux of the perpendicular component is predominantly from higher to lower wavenumbers (inverse cascade of energy), while that of the parallel component is from lower to higher wavenumbers (forward cascade of energy). Our results are consistent with earlier results, which indicate quasi two-dimensionalization of quasi-static magnetohydrodynamic (MHD) flows at high interaction parameters.

Dynamo action in planetary cores has been extensively studied in the context of convectively driven flows. We show in this letter that mechanical forcings, namely, tides, libration, and precession, are also able to kinematically sustain a magnetic field against ohmic diffusion. Previous attempts published in the literature focused on the laminar response or considered idealized spherical configurations. In contrast, we focus here on the developed turbulent regime and we self‐consistently solve the magnetohydrodynamic equations in an ellipsoidal container. Our results open new avenues of research in dynamo theory where both convection and mechanical forcing can play a role, independently or simultaneously.

We investigate the origin of various convective patterns for Prandtl number P = 6.8 (for water at room temperature) using bifurcation diagrams that are constructed using direct numerical simulations (DNS) of Rayleigh–Bénard convection (RBC). Several complex flow patterns resulting from normal bifurcations as well as various instances of "crises" have been observed in the DNS. "Crises" play vital roles in determining various convective flow patterns. After a transition of conduction state to convective roll states, we observe time-periodic and quasiperiodic rolls through Hopf and Neimark–Sacker bifurcations at r ≃ 80 and r ≃ 500 respectively (where r is the normalized Rayleigh number). The system becomes chaotic at r ≃ 750, and the size of the chaotic attractor increases at r ≃ 840 through an "attractor-merging crisis" which results in traveling chaotic rolls. For 846 ≤ r ≤ 849, stable fixed points and a chaotic attractor coexist as a result of an inverse subcritical Hopf bifurcation. Subsequently the chaotic attractor disappears through a "boundary crisis" and only stable fixed points remain. These fixed points later become periodic and chaotic through another set of bifurcations which ultimately leads to turbulence. As a function of Rayleigh number, |W101| ~ (r - 1)0.62 and |θ101| ~ (r - 1)-0.34 (velocity and temperature Fourier coefficient for (1, 0, 1) mode). However the Nusselt number scales as (r - 1)0.33.

In quasi-static MHD, experiments and numerical simulations reveal that the energy spectrum is steeper than Kolmogorov's k −5/3 spectrum. To explain this observation, we construct turbulence models based on variable energy flux, which is caused by the Joule dissipation. In the first model, which is applicable to small interaction parameters, the energy spectrum is a power law, but with a spectral exponent steeper than -5/3. In the other limit of large interaction parameters, the second model predicts an exponential energy spectrum and flux. The model predictions are in good agreement with the numerical results. a)

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