Astrophysical Fluid Dynamics via Direct Statistical Simulation

Abstract

In this paper, we introduce the concept of direct statistical simulation for astrophysical flows. This technique may be appropriate for problems in astrophysical fluids where the instantaneous dynamics of the flows are of secondary importance to their statistical properties. We give examples of such problems including mixing and transport in planets, stars, and disks. The method is described for a general set of evolution equations, before we consider the specific case of a spectral method optimized for problems on a spherical surface. The method is illustrated for the simplest non-trivial example of hydrodynamics and magnetohydrodynamics on a rotating spherical surface. We then discuss possible extensions of the method both in terms of computational methods and the range of astrophysical problems that are of interest.

A tutorial introduction to the statistical theory of turbulent plasmas, a half-century after Kadomtsev’sPlasma Turbulenceand the resonance-broadening theory of Dupree and Weinstock

“…The dispersion relation (6.13) also follows from a superficially distinct closure theory, the so-called CE2 (second-order cumulant) closure (see Tobias, Dagon & Marston 2011, Srinivasan & Young 2012, and references therein). In this approximation, the small-scale turbulence is represented by merely an external white-noise forcing; otherwise, 'eddy-eddy interactions' are neglected and the retained interactions are between only the mean fields and the turbulence.…”

“…With white-noise forcing, (2.8) closes in terms of ψ (t), C(t, t), and the known strength of the forcing; the truncated form of (2.7) ensures that this approximation is realizable. Tobias et al (2011), Tobias & Marston (2013, and Marston, Qi & Tobias (2015) have referred to the numerical solutions of such truncated cumulant systems as 'direct statistical simulations '. Realizability is an important property of CE2. While one can define higher-order approximations CEn for n > 2, none of those are realizable.…”

Zonal Flow as Pattern Formation: Merging Jets and the Ultimate Jet Length Scale

“…This approach is distinct from time integration of Eq. (2) to a steady state, which is done in [21][22][23][24] within a finite spatial domain. Our procedure has two advantages, both related to the fact that ideal states exist for any q within a continuous band.…”

“…This is because the QL model neglects the nonlinear eddy-eddy term that would give rise to a closure problem. Alternatively, CE2 can be regarded as a drastically truncated statistical closure of the full QG model [21][22][23][24]. However, for present purposes we prefer the former interpretation.…”

“…CE2 has been studied extensively numerically [21][22][23][24]. Those simulations also exhibit merging jets [22].…”