Forward-in-time Differencing for Fluids: Simulation of Geophysical Turbulence

Smolarkiewicz, Piotr K.; Prusa, Joseph M.

doi:10.1007/0-306-48421-8_8

Cited by 35 publications

(77 citation statements)

References 44 publications

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“…From the practical point of view, however, their main advantage is that nonlinearly stable turbulent simulations can be produced on relatively coarse grids (Smolarkiewicz and Prusa, 2002;Domaradzki, Xiao, and Smolarkiewicz, 2003;Margolin, Smolarkiewicz, and Wyszogradzki, 2006;Smolarkiewicz and Margolin, 2007), which, in particular, allows long temporal integration, as required in the study of behaviors such as magnetic cycles, developping on timescales very much longer than the turbulent turnover time.…”

Section: The Global Simulationmentioning

confidence: 99%

Torsional Oscillations in a Global Solar Dynamo

et al. 2012

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We characterize and analyze rotational torsional oscillations developing in a large-eddy magnetohydrodynamical simulation of solar convection (Ghizaru, Charbonneau, and Smolarkiewicz, Astrophys. J. Lett. 715, L133 (2010); Racine et al., Astrophys. J. 735, 46 (2011)) producing an axisymmetric largescale magnetic field undergoing periodic polarity reversals. Motivated by the many solar-like features exhibited by these oscillations, we carry out an analysis of the large-scale zonal dynamics. We demonstrate that simulated torsional oscillations are not driven primarily by the periodically-varying large-scale magnetic torque, as one might have expected, but rather via the magnetic modulation of angular-momentum transport by the large-scale meridional flow. This result is confirmed by a straightforward energy analysis. We also detect a fairly sharp transition in rotational dynamics taking place as one moves from the base of the convecting layers to the base of the thin tachocline-like shear layer formed in the stably stratified fluid layers immediately below. We conclude by discussing the implications of our analyses with regards to the mechanism of amplitude saturation in the global dynamo operating in the simulation, and speculate on the possible precursor value of torsional oscillations for the forecast of solar cycle characteristics.

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Section: The Global Simulationmentioning

confidence: 99%

Torsional Oscillations in a Global Solar Dynamo

et al. 2012

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“…Notably, among nonoscillatory schemes MPDATA appears to have unique dissipative properties [17] in mimicking the action of explicit subgrid-scale turbulence models where flow is underresolved -cf. [30][31][32][33] and references therein. This makes MPDATA methods suitable for direct numerical simulation (DNS) and largeeddy simulation (LES) as well as for implicit LES (ILES) [11].…”

Section: Fluid Solversmentioning

confidence: 99%

Iterated upwind schemes for gas dynamics

Smolarkiewicz

Szmelter

2009

Journal of Computational Physics

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A class of high-resolution schemes established in integration of anelastic equations is extended to fully compressible flows, and documented for unsteady (and steady) problems through a span of Mach numbers from zero to supersonic. The schemes stem from iterated upwind technology of the multidimensional positive definite advection transport algorithm (MPDATA). The derived algorithms employ standard and modified forms of the equations of gas dynamics for conservation of mass, momentum and either total or internal energy as well as potential temperature. Numerical examples from elementary wave-propagation, through computational aerodynamics benchmarks, to atmospheric small-and large-amplitude acoustics with intricate wave-flow interactions verify the approach for both structured and unstructured meshes, and demonstrate its flexibility and robustness.

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“…Transporting the auxiliary variable rather than the field variable alone has significant benefits for computational accuracy and stability (Smolarkiewicz et al 2001, Smolarkiewicz andPrusa 2002). The resulting numerical equations represent a system semi-implicit with respect to potential temperature and the wind field.…”

Section: Model Highlightsmentioning

confidence: 99%

Multi-scale waves in sound-proof global simulations with EULAG

Prusa¹,

Gutowski

2011

Acta Geophys.

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A b s t r a c t EULAG is a computational model for simulating flows across a wide range of scales and physical scenarios. A standard option employs an anelastic approximation to capture nonhydrostatic effects and simultaneously filter sound waves from the solution. In this study, we examine a localized gravity wave packet generated by instabilities in Held-Suarez climates. Although still simplified versus the Earth's atmosphere, a rich set of planetary wave instabilities and ensuing radiated gravity waves can arise. Wave packets are observed that have lifetimes ≤ 2 days, are negligibly impacted by Coriolis force, and do not show the rotational effects of differential jet advection typical of inertia-gravity waves. Linear modal analysis shows that wavelength, period, and phase speed fit the dispersion equation to within a mean difference of ∼ 4%, suggesting an excellent fit. However, the group velocities match poorly even though a propagation of uncertainty analysis indicates that they should be predicted as well as the phase velocities. Theoretical arguments suggest the discrepancy is due to nonlinearity -a strong southerly flow leads to a critical surface forming to the southwest of the wave packet that prevents the expected propagation.

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Forward-in-time Differencing for Fluids: Simulation of Geophysical Turbulence

Cited by 35 publications

References 44 publications

Torsional Oscillations in a Global Solar Dynamo

Torsional Oscillations in a Global Solar Dynamo

Iterated upwind schemes for gas dynamics

Multi-scale waves in sound-proof global simulations with EULAG

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