Scaling of turbulence intensities up to Reτ=106 with a resolvent-based quasilinear approximation

2021 ◽  
Vol 6 (3) ◽  
Author(s):  
Nikolaos Skouloudis ◽  
Yongyun Hwang
Keyword(s):  
Quasilinear Approximation

Quasilinear Approximation and WKB

2004 ◽  
Vol 34 (1-3) ◽  
Author(s):  
R. Krivec ◽  
V. B. Mandelzweig ◽  
F. Tabakin
Keyword(s):  
Quasilinear 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 Reduced-Order Quasilinear Model of Ocean Boundary-Layer Turbulence

2020 ◽  
Vol 50 (3) ◽  
pp. 537-558 ◽  
Author(s):  
Joseph Skitka ◽  
J. B. Marston ◽  
Baylor Fox-Kemper
Keyword(s):  
Boundary Layer ◽  
Model Reduction ◽  
Turbulent Transport ◽  
Galerkin Projection ◽  
Surface Boundary ◽  
Reduced Basis ◽  
Surface Boundary Layer ◽  
Boundary Layer Turbulence ◽  
Basis Size ◽  
Quasilinear Approximation

AbstractThe combined effectiveness of model reduction and the quasilinear approximation for the reproduction of the low-order statistics of oceanic surface boundary layer turbulence is investigated. Idealized horizontally homogeneous problems of surface-forced thermal convection and Langmuir turbulence are studied in detail. Model reduction is achieved with a Galerkin projection of the governing equations onto a subset of modes determined by proper orthogonal decomposition (POD). When applied to boundary layers that are horizontally homogeneous, POD and a horizontally averaged quasilinear approximation both assume flow features that are horizontally wavelike, making the pairing very efficient. For less than 0.2% of the modes retained, the reduced quasilinear model is able to reproduce vertical profiles of horizontal mean fields as well as certain energetically important second-order turbulent transport statistics and energies to within 30% error. Reduced-basis quasilinear statistics must approach the full-basis statistics as the basis size approaches completion; however, some quasilinear statistics resemble those found in the fully nonlinear simulations at smaller basis truncations. Thus, model reduction could possibly improve upon the accuracy of quasilinear dynamics.

scholarly journals On non-local energy transfer via zonal flow in the Dimits shift

2017 ◽  
Vol 83 (5) ◽  
Author(s):  
Denis A. St-Onge
Keyword(s):  
Energy Transfer ◽  
Numerical Solutions ◽  
Zonal Flow ◽  
Two Dimensional ◽  
Transfer Energy ◽  
Wave Interactions ◽  
Local Mechanism ◽  
Non Local ◽  
Quasilinear Approximation ◽  
Mode Truncation

The two-dimensional Terry–Horton equation is shown to exhibit the Dimits shift when suitably modified to capture both the nonlinear enhancement of zonal/drift-wave interactions and the existence of residual Rosenbluth–Hinton states. This phenomenon persists through numerous simplifications of the equation, including a quasilinear approximation as well as a four-mode truncation. It is shown that the use of an appropriate adiabatic electron response, for which the electrons are not affected by the flux-averaged potential, results in an $\boldsymbol{E}\times \boldsymbol{B}$ nonlinearity that can efficiently transfer energy non-locally to length scales of the order of the sound radius. The size of the shift for the nonlinear system is heuristically calculated and found to be in excellent agreement with numerical solutions. The existence of the Dimits shift for this system is then understood as an ability of the unstable primary modes to efficiently couple to stable modes at smaller scales, and the shift ends when these stable modes eventually destabilize as the density gradient is increased. This non-local mechanism of energy transfer is argued to be generically important even for more physically complete systems.

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