Self-consistent derivation of subgrid stresses for large-scale fluid equations

2000 ◽  
Vol 61 (1) ◽  
pp. 429-434 ◽  
Author(s):  
Fernando O. Minotti
Keyword(s):  
Large Scale ◽  
Self Consistent ◽  
Fluid Equations ◽  
Subgrid Stresses

Large scale random phase calculations for direct self-consistent field wavefunctions

1993 ◽  
Vol 172 (1) ◽  
pp. 13-20 ◽  
Author(s):  
Henrik Koch ◽  
Hans Ågren ◽  
Poul Jørgensen ◽  
Trygve Helgaker ◽  
Hans Jørgen Aa. Jensen
Keyword(s):  
Large Scale ◽  
Random Phase ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

scholarly journals Generalised quasilinear approximation of the helical magnetorotational instability

2016 ◽  
Vol 82 (3) ◽  
Author(s):  
Adam Child ◽  
Rainer Hollerbach ◽  
Brad Marston ◽  
Steven Tobias
Keyword(s):  
Large Scale ◽  
Statistical Simulation ◽  
The Self ◽  
Energy Spectra ◽  
Magnetorotational Instability ◽  
Self Consistent ◽  
Small Scales ◽  
Direct Statistical Simulation ◽  
Quasilinear Approximation ◽  
Better Than

Motivated by recent advances in direct statistical simulation (DSS) of astrophysical phenomena such as out-of-equilibrium jets, we perform a direct numerical simulation (DNS) of the helical magnetorotational instability (HMRI) under the generalised quasilinear approximation (GQL). This approximation generalises the quasilinear approximation (QL) to include the self-consistent interaction of large-scale modes, interpolating between fully nonlinear DNS and QL DNS whilst still remaining formally linear in the small scales. In this paper we address whether GQL can more accurately describe low-order statistics of axisymmetric HMRI when compared with QL by performing DNS under various degrees of GQL approximation. We utilise various diagnostics, such as energy spectra in addition to first and second cumulants, for calculations performed for a range of Reynolds and Hartmann numbers (describing rotation and imposed magnetic field strength respectively). We find that GQL performs significantly better than QL in describing the statistics of the HMRI even when relatively few large-scale modes are kept in the formalism. We conclude that DSS based on GQL (GCE2) will be significantly more accurate than that based on QL (CE2).

Curvy steps for density matrix-based energy minimization: Application to large-scale self-consistent-field calculations

2003 ◽  
Vol 118 (14) ◽  
pp. 6144-6151 ◽  
Author(s):  
Yihan Shao ◽  
Chandra Saravanan ◽  
Martin Head-Gordon ◽  
Christopher A. White
Keyword(s):  
Density Matrix ◽  
Energy Minimization ◽  
Large Scale ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

From Kinetic Theory to Navier–Stokes Hydrodynamics

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Kinetic Theory ◽  
Knudsen Number ◽  
Asymptotic Expansions ◽  
Large Scale ◽  
Local Equilibrium ◽  
Navier Stokes ◽  
Fluid Equations ◽  
Scale Limit

This Chapter illustrates the derivation of the macroscopic fluid equations, starting from Boltzmann’s kinetic theory. Two routes are presented, the heuristic derivation based on the enslaving of fast modes to slow ones, and the Hilbert–Chapman–Enskog procedure, based on low-Knudsen number asymptotic expansions. The former is handier but mathematically less rigorous than the latter. Either ways, the assumption of weak departure from local equilibrium proves crucial in recovering hydrodynamics as a large-scale limit of kinetic theory.

scholarly journals Deep rotating convection generates the polar hexagon on Saturn

2020 ◽  
Vol 117 (25) ◽  
pp. 13991-13996 ◽  
Author(s):  
Rakesh K. Yadav ◽  
Jeremy Bloxham
Keyword(s):  
Flow Pattern ◽  
High Latitude ◽  
Large Scale ◽  
Three Dimensional ◽  
Giant Planets ◽  
Zonal Flows ◽  
Self Organized ◽  
Consistent Model ◽  
Self Consistent ◽  
Polygonal Pattern

Numerous land- and space-based observations have established that Saturn has a persistent hexagonal flow pattern near its north pole. While observations abound, the physics behind its formation is still uncertain. Although several phenomenological models have been able to reproduce this feature, a self-consistent model for how such a large-scale polygonal jet forms in the highly turbulent atmosphere of Saturn is lacking. Here, we present a three-dimensional (3D) fully nonlinear anelastic simulation of deep thermal convection in the outer layers of gas giant planets that spontaneously generates giant polar cyclones, fierce alternating zonal flows, and a high-latitude eastward jet with a polygonal pattern. The analysis of the simulation suggests that self-organized turbulence in the form of giant vortices pinches the eastward jet, forming polygonal shapes. We argue that a similar mechanism is responsible for exciting Saturn’s hexagonal flow pattern.

scholarly journals Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics

2017 ◽  
Vol 473 (2205) ◽  
pp. 20170388 ◽  
Author(s):  
C. J. Cotter ◽  
G. A. Gottwald ◽  
D. D. Holm
Keyword(s):  
Large Scale ◽  
Particle Dynamics ◽  
Homogenization Theory ◽  
Small Scale ◽  
Mean Flow ◽  
Time Dynamics ◽  
Fluid Equations ◽  
Diffusive Limit ◽  
The Mean ◽  
Stochastic Fluid

In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. ( doi:10.1098/rspa.2014.0963 )), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

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