scholarly journals Three-dimensional rotating Couette flow via the generalised quasilinear approximation

2016 ◽  
Vol 810 ◽  
pp. 412-428 ◽  
Author(s):  
S. M. Tobias ◽  
J. B. Marston
Keyword(s):  
Couette Flow ◽  
Three Dimensional ◽  
Statistical Simulation ◽  
Nonlinear Interactions ◽  
Small Scales ◽  
Direct Statistical Simulation ◽  
Direct Numerical Solution ◽  
Point Correlation ◽  
Quasilinear Approximation ◽  
Significant Support

We examine the effectiveness of the generalised quasilinear (GQL) approximation introduced by Marston et al. (Phys. Rev. Lett., vol. 116 (21), 2016, 214501). This approximation splits the variables into large and small scales in directions where there is a translational symmetry and removes nonlinear interactions involving only small scales. We utilise as a paradigm problem three-dimensional, turbulent, rotating Couette flow. We compare the results obtained from direct numerical solution of the equations with those from quasilinear (QL) and GQL calculations. In this three-dimensional setting, there is a choice of cutoff wavenumber for the GQL approximation both in the streamwise and in the spanwise directions. We demonstrate that the GQL approximation significantly improves the accuracy of mean flows, spectra and two-point correlation functions over models that are quasilinear in any of the translationally invariant directions, even if only a few streamwise and spanwise modes are included. We argue that this provides significant support for a programme of direct statistical simulation utilising the GQL approximation.

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).

scholarly journals The vortex instability pathway in stratified turbulence

2013 ◽  
Vol 716 ◽  
pp. 1-4 ◽  
Author(s):  
Michael L. Waite
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Small Scale ◽  
Nonlinear Interactions ◽  
Stratified Turbulence ◽  
Transfer Energy ◽  
Columnar Vortex ◽  
Open Questions ◽  
Small Scales ◽  
Flow Transitions

AbstractThe parameter regime of strong stable density stratification and weak rotation is an important one in geophysical fluid dynamics. These conditions exist at intermediate length scales in the atmosphere and ocean (mesoscale and sub-mesoscale, respectively), and turbulence here links large-scale quasi-geostrophic motions with small-scale dissipation. While major advances in the theory of stratified turbulence have been made over the last few decades, many open questions remain, particularly about the nature of the energy cascade. Recent numerical experiments and analysis by Augier, Chomaz & Billant (J. Fluid Mech., vol. 713, 2012, pp. 86–108) present a remarkably vivid illustration of the nonlinear interactions that drive such turbulence. They consider a columnar vortex dipole, which naturally three-dimensionalizes under the influence of strong stratification. Kelvin–Helmholtz instabilities subsequently transfer energy directly to small scales, where the flow transitions into three-dimensional turbulence. This direct link between large and small scales is quite distinct from the usual picture of a turbulent cascade, in which nonlinear interactions are local in scale. But how important is this mechanism in the atmosphere and ocean?

A Liquid Metal Flow Between Two Coaxial Cylinders System

2019 ◽  
Vol 11 (1) ◽  
pp. 79-86
Author(s):  
Abdelkrim Merah ◽  
Ridha Kelaiaia ◽  
Faiza Mokhtari
Keyword(s):  
Couette Flow ◽  
Metal Flow ◽  
Three Dimensional ◽  
Liquid Sodium ◽  
Taylor Vortex ◽  
Turbulent Regime ◽  
Coaxial Cylinders ◽  
Concentric Cylinders ◽  
Ideal Tool ◽  
The Stability

Abstract The Taylor-Couette flow between two rotating coaxial cylinders remains an ideal tool for understanding the mechanism of the transition from laminar to turbulent regime in rotating flow for the scientific community. We present for different Taylor numbers a set of three-dimensional numerical investigations of the stability and transition from Couette flow to Taylor vortex regime of a viscous incompressible fluid (liquid sodium) between two concentric cylinders with the inner one rotating and the outer one at rest. We seek the onset of the first instability and we compare the obtained results for different velocity rates. We calculate the corresponding Taylor number in order to show its effect on flow patterns and pressure field.

scholarly journals Application of stakeholder theory to corporate environmental disclosures

2009 ◽  
Vol 7 (1) ◽  
pp. 394-410 ◽  
Author(s):  
Pamela Kent ◽  
Christopher Chan
Keyword(s):  
Social Responsibility ◽  
Stakeholder Theory ◽  
Mission Statement ◽  
Three Dimensional ◽  
Annual Reports ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Environmental Disclosures ◽  
Significant Support

Ullmann’s (1985) three-dimensional model of social responsibility disclosure is tested to determine whether it can be operationalized to help explain the quantity and quality of environmental disclosures in Australian annual reports. The stakeholder power dimension of Ullmann’s framework is significant in explaining environmental disclosures while content of the mission statement and existence or otherwise of environmental or social responsibility committees also find strong statistically significant support in the results. Ullmanns’ stakeholder theory has previously been applied to explain social disclosures in general (Roberts, 1992) and is an important theory because it introduces a measure of strategy. The current paper demonstrates how this theory can be applied to a specific social disclosure using variables that are idiosyncratically applicable to the types of disclosures.

Three-Dimensional Simulation of Taylor-Couette Flow

1989 ◽  
pp. 366-370 ◽  
Author(s):  
N. Matsumoto ◽  
S. Shirayama ◽  
K. Kuwahara ◽  
F. Hussain
Keyword(s):  
Couette Flow ◽  
Three Dimensional ◽  
Taylor Couette ◽  
Dimensional Simulation ◽  
Taylor Couette Flow

scholarly journals A note on the mirror-symmetric coherent structure in plane Couette flow

2013 ◽  
Vol 727 ◽  
Author(s):  
M. Nagata
Keyword(s):  
Couette Flow ◽  
Coherent Structure ◽  
Rotation Rate ◽  
Symmetric Solution ◽  
Three Dimensional ◽  
Plane Couette Flow ◽  
System Rotation ◽  
The Way

AbstractWe note that the mirror-symmetric solution in plane Couette flow, found recently by Gibson, Halcrow & Cvitanović (J. Fluid Mech., vol. 611, 2009, pp. 107–130) and Itano & Generalis (Phys. Rev. Lett., vol. 102, 2009, p. 114501), belongs to the solution group classified as ‘ribbon’ in rotating-plane Couette flow (RPCF). It represents a subcritical (in terms of the system rotation) solution at zero rotation rate on the three-dimensional tertiary flow branch which bifurcates from thesecondstreamwise-independent flow in RPCF. The way of its appearance is similar to that of the Nagata solution (J. Fluid Mech., vol. 217, 1990, pp. 519–527), which lies on the subcritical three-dimensional tertiary flow branch bifurcating from thefirststreamwise-independent flow in RPCF.

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