This work numerically investigates the role of viscosity and resistivity in Rayleigh–Taylor instabilities in magnetized high-energy-density (HED) plasmas for a high Atwood number and high plasma beta regimes surveying across plasma beta and magnetic Prandtl numbers. The numerical simulations are performed using the visco-resistive magnetohydrodynamic equations. Results presented here show that the inclusion of self-consistent viscosity and resistivity in the system drastically changes the growth of the Rayleigh–Taylor instability (RTI) as well as modifies its internal structure at smaller scales. It is seen here that the viscosity has a stabilizing effect on the RTI. Moreover, the viscosity inhibits the development of small-scale structures and also modifies the morphology of the tip of the RTI spikes. On the other hand, the resistivity reduces the magnetic field stabilization, supporting the development of small-scale structures. The morphology of the RTI spikes is seen to be unaffected by the presence of resistivity in the system. An additional novelty of this work is in the disparate viscosity and resistivity profiles that may exist in HED plasmas and their impact on RTI growth, morphology and the resulting turbulence spectra. Furthermore, this work shows that the dynamics of the magnetic field is independent of viscosity and likewise the resistivity does not affect the dissipation of enstrophy and kinetic energy. In addition, power law scalings of enstrophy, kinetic energy and magnetic field energy are provided in both the injection range and inertial sub-range, which could be useful for understanding RTI induced turbulent mixing in HED laboratory and astrophysical plasmas and could aid in the interpretation of observations of RTI-induced turbulence spectra.
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Extending a Physics-informed Machine-learning Network for Superresolution Studies of Rayleigh–Bénard Convection
Advancing our understanding of astrophysical turbulence is bottlenecked by the limited resolution of numerical simulations that may not fully sample scales in the inertial range. Machine-learning (ML) techniques have demonstrated promise in upscaling resolution in both image analysis and numerical simulations (i.e., superresolution). Here we employ and further develop a physics-constrained convolutional neural network ML model called “MeshFreeFlowNet” (MFFN) for superresolution studies of turbulent systems. The model is trained on both the simulation images and the evaluated partial differential equations (PDEs), making it sensitive to the underlying physics of a particular fluid system. We develop a framework for 2D turbulent Rayleigh–Bénard convection generated with the
- NSF-PAR ID:
- 10494974
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 964
- Issue:
- 1
- ISSN:
- 0004-637X
- Format(s):
- Medium: X Size: Article No. 2
- Size(s):
- ["Article No. 2"]
- Sponsoring Org:
- National Science Foundation
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Abstract A simulation of a supercell storm produced for a prior study on tornado predictability is reanalyzed for the purpose of examining the fine-scale details of tornadogenesis. It is found that the formation of a tornado-like vortex in the simulation differs from how such vortices have been understood to form in previous numerical simulations. The main difference between the present simulation and past ones is the inclusion of a turbulent boundary layer in the storm’s environment in the present case, whereas prior simulations have used a laminar boundary layer. The turbulent environment contains significant near-surface vertical vorticity (
ζ > 0.03 s−1atz = 7.5 m), organized in the form of longitudinal streaks aligned with the southerly ground-relative winds. Theζ streaks are associated with corrugations in the vertical plane in the predominantly horizontal, westward-pointing environmental vortex lines; the vortex-line corrugations are produced by the vertical drafts associated with coherent turbulent structures aligned with the aforementioned southerly ground-relative winds (longitudinal coherent structures in the surface layer such as these are well known to the boundary layer and turbulence communities). Theζ streaks serve as focal points for tornadogenesis, and may actually facilitate tornadogenesis, given how near-surfaceζ in the environment can rapidly amplify when subjected to the strong, persistent convergence beneath a supercell updraft.Significance Statement In high-resolution computer simulations of supercell storms that include a more realistic, turbulent environment, the means by which tornado-like vortices form differs from the mechanism identified in prior simulations using a less realistic, laminar environment. One possibility is that prior simulations develop intense vortices for the wrong reasons. Another possibility could be that tornadoes form in a wide range of ways in the real atmosphere, even within supercell storms that appear to be similar, and increasingly realistic computer simulations are finally now capturing that diversity.
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Abstract In a strongly magnetized, magnetically dominated relativistic plasma, Alfvénic turbulence can extend to scales much smaller than the particle inertial scales. It leads to an energy cascade somewhat analogous to inertial- or kinetic-Alfvén turbulent cascades existing in nonrelativistic space and astrophysical plasmas. Based on phenomenological modeling and particle-in-cell numerical simulations, we propose that the energy spectrum of such relativistic kinetic-scale Alfvénic turbulence is close to
k −3or slightly steeper than that due to intermittency corrections or Landau damping. We note the analogy of this spectrum with the Kraichnan spectrum corresponding to the enstrophy cascade in 2D incompressible fluid turbulence. Such turbulence strongly energizes particles in the direction parallel to the background magnetic field, leading to nearly one-dimensional particle momentum distributions. We find that these distributions have universal log-normal statistics. -
A numerical investigation of an asymptotically reduced model for quasigeostrophic Rayleigh-Bénard convection is conducted in which the depth-averaged flows are numerically suppressed by modifying the governing equations. At the largest accessible values of the Rayleigh number Ra, the Reynolds number and Nusselt number show evidence of approaching the diffusion-free scalings of Re ∼ RaE/Pr and Nu ∼ Pr−1/2Ra3/2E2, respectively, where E is the Ekman number and Pr is the Prandtl number. For large Ra, the presence of depth-invariant flows, such as large-scale vortices, yield heat and momentum transport scalings that exceed those of the diffusion-free scaling laws. The Taylor microscale does not vary significantly with increasing Ra, whereas the integral length scale grows weakly. The computed length scales remain O(1) with respect to the linearly unstable critical wave number; we therefore conclude that these scales remain viscously controlled. We do not find a point-wise Coriolis-inertia-Archimedean (CIA) force balance in the turbulent regime; interior dynamics are instead dominated by horizontal advection (inertia), vortex stretching (Coriolis) and the vertical pressure gradient. A secondary, subdominant balance between the Archimedean buoyancy force and the viscous force occurs in the interior and the ratio of the root mean square (rms) of these two forces is found to approach unity with increasing Ra. This secondary balance is attributed to the turbulent fluid interior acting as the dominant control on the heat transport. These findings indicate that a pointwise CIA balance does not occur in the high Rayleigh number regime of quasigeostrophic convection in the plane layer geometry. Instead, simulations are characterized by what may be termed a nonlocal CIA balance in which the buoyancy force is dominant within the thermal boundary layers and is spatially separated from the interior Coriolis and inertial forces.more » « less
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