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 Transition from geostrophic flows to inertia-gravity waves in the spectrum of a differentially heated rotating annulus experiment.

2020 ◽  
Author(s):  
Costanza Rodda ◽  
Uwe Harlander
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Small Scale ◽  
Turbulent Regime ◽  
Weakly Nonlinear ◽  
Geostrophic Flows ◽  
Balanced Flow ◽  
Energy And Momentum ◽  
Open Question ◽  
Inertia Gravity Waves

<p>Inertia-gravity waves (IGWs) are known to play an essential role in the terrestrial atmospheric dynamics as they can lead to energy and momentum flux when they propagate upwards. An open question is to which extent nearly linear IGWs contribute to the total energy and to flattening of the energy spectrum observed at the mesoscale.<br>In this work, we present an experimental investigation of the energy distribution between the large-scale balanced flow and the small-scale imbalanced flow. Weakly nonlinear IGWs emitted from baroclinic jets are observed in the differentially heated rotating annulus experiment. Similar to the atmospheric spectra, the experimental kinetic energy spectra reveal the typical subdivision into two distinct regimes with slopes <em>k</em><sup>-3</sup> for the large scales and <em>k<sup>-</sup></em><sup>5/3</sup> for smaller scales. By separating the spectra into a vortex and wave part, it emerges that at the largest scales in the mesoscale range the gravity waves observed in the experiment cause a flattening of the spectra and provide most of the energy. At smaller scales, our data analysis suggests a transition towards a turbulent regime with a forward energy cascade up to where dissipation by diffusive processes occurs.</p>

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 Tropical background and wave spectra: contribution of wave-wave interactions in a moderately nonlinear turbulent flow

2021 ◽  
Author(s):  
Chaim I Garfinkel ◽  
Ofer Shamir ◽  
Itzhak Fouxon ◽  
Nathan Paldor
Keyword(s):  
Power Spectrum ◽  
Large Scale ◽  
Water Model ◽  
Small Scale ◽  
Simple Explanation ◽  
External Forcing ◽  
Strong Response ◽  
Wave Interactions ◽  
Tropical Dynamics ◽  
Wave Modes

AbstractVariability in the tropical atmosphere is concentrated at wavenumber-frequency combinations where linear theory indicates wave-modes can freely propagate, but with substantial power in between. This study demonstrates that such a power spectrum can arise from small scale convection triggering large scale waves via wave-wave interactions in a moderately turbulent fluid. Two key pieces of evidence are provided for this interpretation of tropical dynamics using a nonlinear rotating shallow water model: a parameter sweep experiment in which the amplitude of an external forcing is gradually ramped up, and also an external forcing in which only symmetric or only anti-symmetric modes are forced. These experiments do not support a commonly accepted mechanism involving the forcing projecting directly onto the wave-modes with a strong response, yet still simulate a power spectrum resembling that observed, though the linear projection mechanism could still complement the mechanism proposed here in observations. Interpreting the observed tropical power spectrum using turbulence offers a simple explanation as to why power should be concentrated at the theoretical wave-modes, and also provides a solid footing for the common assumption that the back-ground spectrum is red, even as it clarifies why there is no expectation for a turbulent cascade with a specific, theoretically derived slope such as -5/3. However it does explain why the cascade should be towards lower wavenumbers, that is an inverse energy cascade, similar to the midlatitudes even as compressible wave-modes are important for tropical dynamics.

scholarly journals Transition from Geostrophic Flows to Inertia–Gravity Waves in the Spectrum of a Differentially Heated Rotating Annulus Experiment

2020 ◽  
Vol 77 (8) ◽  
pp. 2793-2806
Author(s):  
Costanza Rodda ◽  
Uwe Harlander
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Small Scale ◽  
Turbulent Regime ◽  
Weakly Nonlinear ◽  
Geostrophic Flows ◽  
Balanced Flow ◽  
Energy And Momentum ◽  
Open Question ◽  
Inertia Gravity Waves

Abstract Inertia–gravity waves (IGWs) play an essential role in the terrestrial atmospheric dynamics as they can lead to energy and momentum flux when propagating upward. An open question is to what extent IGWs contribute to the total energy and to the flattening of the energy spectrum observed at the mesoscale. In this work, we present an experimental investigation of the energy distribution between the large-scale balanced flow and the small-scale imbalanced flow. Weakly nonlinear IGWs emitted from baroclinic jets are observed in the differentially heated rotating annulus experiment. Similar to the atmospheric spectra, the experimental kinetic energy spectra reveal the typical subdivision into two distinct regimes with slopes k−3 for the large scales and k−5/3 for the small scales. By separating the spectra into the vortex and wave components, it emerges that at the large-scale end of the mesoscale the gravity waves observed in the experiment cause a flattening of the spectra and provide most of the energy. At smaller scales, our data analysis suggests a transition toward a turbulent regime with a forward energy cascade up to where dissipation by diffusive processes occurs.

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 Large- to submesoscale surface circulation and its implications on biogeochemical/biological horizontal distributions during the OUTPACE cruise (southwest Pacific)

2018 ◽  
Vol 15 (8) ◽  
pp. 2411-2431 ◽  
Author(s):  
Louise Rousselet ◽  
Alain de Verneil ◽  
Andrea M. Doglioli ◽  
Anne A. Petrenko ◽  
Solange Duhamel ◽  
...  
Keyword(s):  
Large Scale ◽  
Water Mass ◽  
Finite Size ◽  
Small Scale ◽  
General Direction ◽  
The North ◽  
Mesoscale Structures ◽  
Surface Circulation ◽  
Biogeochemical Parameters

Abstract. The patterns of the large-scale, meso- and submesoscale surface circulation on biogeochemical and biological distributions are examined in the western tropical South Pacific (WTSP) in the context of the OUTPACE cruise (February–April 2015). Multi-disciplinary original in situ observations were achieved along a zonal transect through the WTSP and their analysis was coupled with satellite data. The use of Lagrangian diagnostics allows for the identification of water mass pathways, mesoscale structures, and submesoscale features such as fronts. In particular, we confirmed the existence of a global wind-driven southward circulation of surface waters in the entire WTSP, using a new high-resolution altimetry-derived product, validated by in situ drifters, that includes cyclogeostrophy and Ekman components with geostrophy. The mesoscale activity is shown to be responsible for counter-intuitive water mass trajectories in two subregions: (i) the Coral Sea, with surface exchanges between the North Vanuatu Jet and the North Caledonian Jet, and (ii) around 170∘ W, with an eastward pathway, whereas a westward general direction dominates. Fronts and small-scale features, detected with finite-size Lyapunov exponents (FSLEs), are correlated with 25 % of surface tracer gradients, which reveals the significance of such structures in the generation of submesoscale surface gradients. Additionally, two high-frequency sampling transects of biogeochemical parameters and microorganism abundances demonstrate the influence of fronts in controlling the spatial distribution of bacteria and phytoplankton, and as a consequence the microbial community structure. All circulation scales play an important role that has to be taken into account not only when analysing the data from OUTPACE but also, more generally, for understanding the global distribution of biogeochemical components.

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