author={Steven M. Tobias and Katherine Dagon and J. B. Marston},
  journal={The Astrophysical Journal},
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… Expand
Direct Statistical Simulation of a Jet
rst explain the method and place it into context with other statistical procedures, some of which are described in this book. In so doing we shall describe the strengths and weaknesses of theExpand
Generalized quasilinear approximation of the interaction of convection and mean flows in a thermal annulus
In this paper, we examine the interaction of convection, rotation and mean flows in a thermal annulus. In this system, mean flows are driven by correlations induced by rotation leading to non-trivialExpand
Direct statistical simulation of jets and vortices in 2D flows
In this paper, we perform direct statistical simulations of a model of two-dimensional flow that exhibits a transition from jets to vortices. The model employs two-scale Kolmogorov forcing, withExpand
Advances in mean-field dynamo theories
  • V. Pipin
  • Physics
  • Proceedings of the International Astronomical Union
  • 2012
Abstract We give a short introduction to the subject and review advances in understanding the basic ingredients of the mean-field dynamo theory. The discussion includes the recent analytic andExpand
The turbulent dynamo
  • S. Tobias
  • Physics, Medicine
  • Journal of Fluid Mechanics
  • 2021
It is argued that progress in dynamo theory will be made in the future by utilising and advancing some of the current breakthroughs in neutral fluid turbulence such as those in transition, self-sustaining processes, turbulence/mean-flow interaction, statistical and data-driven methods and maintenance and loss of balance. Expand
Fluctuations and large deviations of Reynolds stresses in zonal jet dynamics
The Reynolds stress, or equivalently the average of the momentum flux, is key to understanding the statistical properties of turbulent flows. Both typical and rare fluctuations of the time averagedExpand
Interaction between mean flow and turbulence in two dimensions
  • G. Falkovich
  • Mathematics, Medicine
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2016
The analytical solutions for two-dimensional mean flows generated by an inverse turbulent cascade on a sphere and in planar domains of different aspect ratios are presented. Expand
Kinetic theory and quasilinear theories of jet dynamics
We review progress that has been made to construct a theory for the jet formation and maintenance in planetary atmospheres. The theory is built in the regime where velocity fluctuations around theExpand
Direct statistical simulation of low-order dynamosystems
In this paper, we investigate the effectiveness of direct statistical simulation (DSS) for two low-order models of dynamo action. The first model, which is a simple model of solar and stellar dynamoExpand
Large Scale Quasi-geostrophic Magnetohydrodynamics
We consider the ideal magnetohydrodynamics (MHD) of a shallow fluid layer on a rapidly rotating planet or star. The presence of a background toroidal magnetic field is assumed, and the "shallowExpand


A model of the entropy flux and Reynolds stress in turbulent convection
We propose a closure model for the transport of entropy and momentum in astrophysical turbulence, intended for application to rotating stellar convective regions. Our closure model is first presentedExpand
On the dynamics of magnetorotational turbulent stresses
The turbulent stresses that lead to angular momentum transport in accretion discs have often been treated as resulting from an isotropic effective viscosity, related to the pressure through the alphaExpand
Nonlinear phenomena in atmospheric and oceanic sciences
This volume is a collection of treatises contributed by distinguished physicists, mathematicians and geophysicists, concerning the fluid mechanical behaviour of atmospheres, oceans and relatedExpand
Compressible convection in the deep atmospheres of giant planets
Abstract Fast rotating giant planets such as Jupiter and Saturn possess alternate prograde and retrograde zonal winds which are stable over long periods of time. We consider a compressible model ofExpand
Large-Scale Dynamics of the Convection Zone and Tachocline
The past few decades have seen dramatic progress in our understanding of solar interior dynamics, prompted by the relatively new science of helioseismology and increasingly sophisticated numericalExpand
β-Plane Magnetohydrodynamic Turbulence in the Solar Tachocline
This Letter discusses the role of a weak toroidal magnetic field in modifying the turbulent transport properties of stably stratified rotating turbulence in the tachocline. A local two-dimensionalExpand
Turbulent Convection under the Influence of Rotation: Sustaining a Strong Differential Rotation
The intense turbulence present in the solar convection zone is a major challenge to both theory and simulation as one tries to understand the origins of the striking differential rotation profileExpand
High Rayleigh number β-convection
Abstract High resolution numerical simulations of thermal convection in a rapidly rotating channel with gravity perpendicular to the rotation vector are described. The convecting columns are subjectExpand
Saturation of the magnetorotational instability at large Elsasser number
The magnetorotational instability is investigated within the shearing box approximation in the large Elsasser number regime. In this regime, which is of fundamental importance to astrophysicalExpand
Recovery of atmospheric flow statistics in a general circulation model without nonlinear eddy-eddy interactions
The closure problem of turbulence arises because nonlinear interactions among turbulent fluctuations (eddies) lead to an infinite hierarchy of moment equations for flow statistics. Here weExpand