On the formation of geophysical and planetary zonal flows by near-resonant wave interactions

2007 ◽  
Vol 576 ◽  
pp. 405-424 ◽  
Author(s):  
YOUNGSUK LEE ◽  
LESLIE M. SMITH
Keyword(s):  
Large Scale ◽  
Reduced Model ◽  
Small Scale ◽  
Full System ◽  
Time Asymmetry ◽  
Zonal Flows ◽  
Reduced Models ◽  
Random Forcing ◽  
Resonant Triads ◽  
Triad Interactions

Numerical simulations on a β-plane are used to further understand the formation of zonal flows from small-scale fluctuations. The dynamics of ‘reduced models’ are computed by restricting the nonlinear term to include a subset of triad interactions in Fourier space. Reduced models of near-resonant triads are considered, as well as the complement set of non-resonant triads. At moderately small values of the Rhines number, near-resonant triad interactions are shown to be responsible for the generation of large-scale zonal flows from small-scale random forcing. Without large-scale drag, both the full system and the reduced model of near resonances produce asymmetry between eastward and westward jets, in favour of stronger westward jets. When large-scale drag is included, the long-time asymmetry is reversed in the full system, with eastward jets that are thinner and stronger than westward jets. Then the reduced model of near resonances exhibits a weaker asymmetry, but there are nevertheless more eastward jets stronger than a threshold value.

scholarly journals Equilibria and condensates in Rossby and drift wave turbulence

2021 ◽  
Author(s):  
Jonathan Skipp ◽  
Sergey Nazarenko
Keyword(s):  
Large Scale ◽  
Finite Size ◽  
Small Scale ◽  
Simple Explanation ◽  
Weakly Nonlinear ◽  
Zonal Flows ◽  
Drift Wave Turbulence ◽  
Third Invariant ◽  
Thermodynamic Potentials ◽  
Singular Limits

Abstract We study the thermodynamic equilibrium spectra of the Charney- Hasegawa-Mima (CHM) equation in its weakly nonlinear limit. In this limit, the equation has three adiabatic invariants, in contrast to the two invariants of the 2D Euler or Gross-Pitaevskii equations, which are examples for comparison. We explore how the third invariant considerably enriches the variety of equilibrium spectra that the CHM system can access. In particular we characterise the singular limits of these spectra in which condensates occur, i.e. a single Fourier mode (or pair of modes) accumulate(s) a macroscopic fraction of the total invariants. We show that these equilibrium condensates provide a simple explanation for the characteristic structures observed in CHM systems of finite size: highly anisotropic zonal flows, large-scale isotropic vortices, and vortices at small scale. We show how these condensates are associated with combinations of negative thermodynamic potentials (e.g. temperature).

scholarly journals Excitation of zonal flow by the modulational instability in electron temperature gradient driven turbulence

2008 ◽  
Vol 74 (3) ◽  
pp. 381-389 ◽  
Author(s):  
Yu. A. ZALIZNYAK ◽  
A. I. YAKIMENKO ◽  
V. M. LASHKIN
Keyword(s):  
Temperature Gradient ◽  
Electron Temperature ◽  
Large Scale ◽  
Modulational Instability ◽  
Zonal Flow ◽  
Finite Amplitude ◽  
Small Scale ◽  
Drift Waves ◽  
Zonal Flows ◽  
Electron Temperature Gradient

AbstractThe generation of large-scale zonal flows by small-scale electrostatic drift waves in electron temperature gradient driven turbulence model is considered. The generation mechanism is based on the modulational instability of a finite amplitude monochromatic drift wave. The threshold and growth rate of the instability as well as the optimal spatial scale of zonal flow are obtained.

scholarly journals Optimisation of confinement in a fusion reactor using a nonlinear turbulence model

2018 ◽  
Vol 84 (2) ◽  
Author(s):  
E. G. Highcock ◽  
N. R. Mandell ◽  
M. Barnes ◽  
W. Dorland
Keyword(s):  
First Principles ◽  
Figure Of Merit ◽  
Large Scale ◽  
Unit Volume ◽  
Fusion Reactor ◽  
Small Scale ◽  
Zonal Flows ◽  
Novel Approach ◽  
First Time ◽  
Turbulent Cascade

The confinement of heat in the core of a magnetic fusion reactor is optimised using a multidimensional optimisation algorithm. For the first time in such a study, the loss of heat due to turbulence is modelled at every stage using first-principles nonlinear simulations which accurately capture the turbulent cascade and large-scale zonal flows. The simulations utilise a novel approach, with gyrofluid treatment of the small-scale drift waves and gyrokinetic treatment of the large-scale zonal flows. A simple near-circular equilibrium with standard parameters is chosen as the initial condition. The figure of merit, fusion power per unit volume, is calculated, and then two control parameters, the elongation and triangularity of the outer flux surface, are varied, with the algorithm seeking to optimise the chosen figure of merit. A twofold increase in the plasma power per unit volume is achieved by moving to higher elongation and strongly negative triangularity.

scholarly journals Investigations of non-hydrostatic, stably stratified and rapidly rotating flows

2016 ◽  
Vol 801 ◽  
pp. 430-458 ◽  
Author(s):  
David Nieves ◽  
Ian Grooms ◽  
Keith Julien ◽  
Jeffrey B. Weiss
Keyword(s):  
Large Scale ◽  
Boussinesq Equations ◽  
Reduced Model ◽  
Small Scale ◽  
Net Energy ◽  
Stratified Turbulence ◽  
Stochastic Forcing ◽  
Barotropic Mode ◽  
Energy Exchanges ◽  
Scale Turbulence

We present an investigation of rapidly rotating (small Rossby number $Ro\ll 1$) stratified turbulence where the stratification strength is varied from weak (large Froude number $Fr\gg 1$) to strong ($Fr\ll 1$). The investigation is set in the context of a reduced model derived from the Boussinesq equations that retains anisotropic inertia-gravity waves with order-one frequencies and highlights a regime of wave–eddy interactions. Numerical simulations of the reduced model are performed where energy is injected by a stochastic forcing of vertical velocity, which forces wave modes only. The simulations reveal two regimes: characterized by the presence of well-formed, persistent and thin turbulent layers of locally weakened stratification at small Froude numbers, and by the absence of layers at large Froude numbers. Both regimes are characterized by a large-scale barotropic dipole enclosed by small-scale turbulence. When the Reynolds number is not too large, a direct cascade of barotropic kinetic energy is observed, leading to total energy equilibration. We examine net energy exchanges that occur through vortex stretching and vertical buoyancy flux and diagnose the horizontal scales active in these exchanges. We find that the baroclinic motions inject energy directly to the largest scales of the barotropic mode, implying that the large-scale barotropic dipole is not the end result of an inverse cascade within the barotropic mode.

Rossby-wave driven zonal flows in the ionospheric E-layer

2007 ◽  
Vol 73 (1) ◽  
pp. 131-140 ◽  
Author(s):  
T. D. KALADZE ◽  
D. J. WU ◽  
O. A. POKHOTELOV ◽  
R. Z. SAGDEEV ◽  
L. STENFLO ◽  
...  
Keyword(s):  
Large Scale ◽  
Rossby Waves ◽  
Maximum Growth ◽  
Present Theory ◽  
Finite Amplitude ◽  
Maximum Growth Rate ◽  
Small Scale ◽  
Reynolds Stresses ◽  
Zonal Flows ◽  
Coupled Equations

Abstract.A novel mechanism for the generation of large-scale zonal flows by small-scale Rossby waves in the Earth's ionospheric E-layer is considered. The generation mechanism is based on the parametric excitation of convective cells by finite amplitude magnetized Rossby waves. To describe this process a generalized Charney equation containing both vector and scalar (Korteweg–de Vries type) nonlinearities is used. The magnetized Rossby waves are supposed to have arbitrary wavelengths (as compared with the Rossby radius). A set of coupled equations describing the nonlinear interaction of magnetized Rossby waves and zonal flows is obtained. The generation of zonal flows is due to the Reynolds stresses produced by finite amplitude magnetized Rossby waves. It is found that the wave vector of the fastest growing mode is perpendicular to that of the magnetized Rossby pump wave. Explicit expression for the maximum growth rate as well as for the optimal spatial dimensions of the zonal flows are obtained. A comparison with existing results is carried out. The present theory can be used for the interpretation of the observations of Rossby-type waves in the Earth's ionosphere.

Influence of non-monochromaticity on zonal-flow generation by magnetized Rossby waves in the ionospheric E-layer

2009 ◽  
Vol 75 (3) ◽  
pp. 345-357 ◽  
Author(s):  
T. D. KALADZE ◽  
H. A. SHAH ◽  
G. MURTAZA ◽  
L. V. TSAMALASHVILI ◽  
M. SHAD ◽  
...  
Keyword(s):  
Large Scale ◽  
Laboratory Experiments ◽  
Low Frequency ◽  
Zonal Flow ◽  
Present Theory ◽  
Resonant Interaction ◽  
Finite Amplitude ◽  
Small Scale ◽  
Zonal Flows ◽  
Flow Generation

AbstractThe influence of non-monochromaticity on low-frequency, large-scale zonal-flow nonlinear generation by small-scale magnetized Rossby (MR) waves in the Earth's ionospheric E-layer is considered. The modified parametric approach is used with an arbitrary spectrum of primary modes. It is shown that the broadening of the wave packet spectrum of pump MR waves leads to a resonant interaction with a growth rate of the order of the monochromatic case. In the case when zonal-flow generation by MR modes is prohibited by the Lighthill stability criterion, the so-called two-stream-like mechanism for the generation of sheared zonal flows by finite-amplitude MR waves in the ionospheric E-layer is possible. The growth rates of zonal-flow instabilities and the conditions for driving them are determined. The present theory can be used for the interpretation of the observations of Rossby-type waves in the Earth's ionosphere and in laboratory experiments.

scholarly journals Researches regarding scale reduced models for the optimisation of the aerodynamic coefficient

2019 ◽  
Vol 290 ◽  
pp. 04011
Author(s):  
Alexandru Lucian Stanciu ◽  
Nicoleta Pascu ◽  
Constantin Dogariu ◽  
Cristina Mohora
Keyword(s):  
Computer Aided Design ◽  
Original System ◽  
Vehicle Body ◽  
Reduced Model ◽  
Small Scale ◽  
Reduced Models ◽  
Simulation And Optimization ◽  
Optimization Stage ◽  
Computer Aided ◽  
Scale Modelling

Within the lifecycle of the product, the reduced models are very important for the experimental validation of the prototype. The modelling, simulation and optimization stage precedes the prototype realization, being part of the computer aided design (CAD), computer aided engineering (CAE). The physical model is a physical layout or test setup that reproduces, on a small scale, the features of the original system, in our case the vehicle body layout. The paper presents an automobile reduced model, with the aim to study the aerodynamic theory. The paper presents the algorithms of conceptual design of the scale reduced model, namely: 3D modelling, small scale modelling technology and geometric shape optimization solutions using different CAD-CAE programs.

scholarly journals Random forcing with a constant power input for two-dimensional gyrokinetic simulations

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Ryusuke Numata
Keyword(s):  
Large Scale ◽  
Scaling Laws ◽  
Power Input ◽  
Small Scale ◽  
Two Dimensional ◽  
Constant Power ◽  
Random Forcing ◽  
Constant Rate ◽  
Set Up ◽  
Gyrokinetic Simulations

A method of random forcing with a constant power input for two-dimensional gyrokinetic turbulence simulations is developed for the study of stationary plasma turbulence. The property that the forcing term injects the energy at a constant rate enables turbulence to be set up in the desired range and energy dissipation channels to be assessed quantitatively in a statistically steady state. Using the developed method, turbulence is demonstrated in the large-scale fluid and small-scale kinetic regimes, where the theoretically predicted scaling laws are reproduced successfully.

Drift wave driven zonal flows in electron–positron–ion plasmas

2010 ◽  
Vol 76 (3-4) ◽  
pp. 635-643 ◽  
Author(s):  
T. D. KALADZE ◽  
O. A. POKHOTELOV ◽  
M. SHAD
Keyword(s):  
Growth Rate ◽  
Large Scale ◽  
Maximum Growth ◽  
Finite Amplitude ◽  
Maximum Growth Rate ◽  
Small Scale ◽  
Drift Waves ◽  
Zonal Flows ◽  
Electron Positron ◽  
Spatial Dimensions

AbstractThe generation of large-scale zonal flows by small-scale electrostatic drift waves in electron–positron–ion (EPI) plasma is considered. The generation mechanism is based on the parametric excitation of convective cells by finite amplitude drift waves. To describe this process, the Hasegawa–Mima equation generalized for the case of EPI plasma is used. Explicit expressions for the maximum growth rate as well as for the optimal spatial dimensions of the zonal flows are obtained. Dependence of the growth rate on the spectrum purity of the wave packet is also investigated. The relevant instability conditions are determined.

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