Geostrophic Turbulence

1998 ◽  
Author(s):  
Rick Salmon
Keyword(s):  
Large Scale ◽  
Bottom Topography ◽  
Single Layer ◽  
Two Dimensional ◽  
Homogeneous Fluid ◽  
Coriolis Parameter ◽  
Strongly Nonlinear ◽  
Geostrophic Turbulence ◽  
Large Scale Flow ◽  
Quasigeostrophic Equations

Strongly nonlinear, rapidly rotating, stably stratified flow is called geostrophic turbulence. This subject, which blends ideas from chapters 2,4, and 5, is relevant to the large-scale flow in the Earth’s oceans and atmosphere. The quasigeostrophic equations form the basis of the study of geostrophic turbulence. We view the quasigeostrophic equations as a generalization of the vorticity equation for two-dimensional turbulence to include the important effects of stratification, bottom topography, and varying Coriolis parameter. Thus the theory of geostrophic turbulence represents an extension of the theory of two dimensional turbulence. However, its richer physics and greater applicability to real geophysical flows make geostrophic turbulence a much more interesting and important subject. This chapter offers a very brief introduction to the theory of geostrophic turbulence. We illustrate the principal ideas by separately considering the effects of bottom topography, varying Coriolis parameter, and density stratification on highly nonlinear, quasigeostrophic flow. We make no attempt at a comprehensive review. In every case, the theory of geostrophic turbulence relies almost solely on two now-familiar components: a conservation principle that energy and potential vorticity are (nearly) conserved and an irreversibility principle in the form of an appealing assumption that breaks the time-reversal symmetry of the exact (inviscid) dynamics. This irreversibility assumption takes a great many superficially dissimilar forms, fostering the misleading impression of a great many competing explanations for the same phenomena. However, broadminded analysis inevitably reveals that these competing explanations are virtually equivalent. We begin by considering the quasigeostrophic flow of a single layer of homogeneous fluid over a bumpy bottom. No case better illustrates how diverse forms of the irreversibility principle lead to the same conclusions.

The emergence of isolated coherent vortices in turbulent flow

1984 ◽  
Vol 146 ◽  
pp. 21-43 ◽  
Author(s):  
James C. Mcwilliams
Keyword(s):  
Turbulent Flow ◽  
Turbulent Flows ◽  
Large Scale ◽  
Initial Conditions ◽  
Turnaround Time ◽  
Large Reynolds Number ◽  
Two Dimensional ◽  
Dominant Component ◽  
Geostrophic Turbulence ◽  
Large Scale Flow

A study is made of some numerical calculations of two-dimensional and geostrophic turbulent flows. The primary result is that, under a broad range of circumstances, the flow structure has its vorticity concentrated in a small fraction of the spatial domain, and these concentrations typically have lifetimes long compared with the characteristic time for nonlinear interactions in turbulent flow (i.e. an eddy turnaround time). When such vorticity concentrations occur, they tend to assume an axisymmetric shape and persist under passive advection by the large-scale flow, except for relatively rare encounters with other centres of concentration. These structures can arise from random initial conditions without vorticity concentration, evolving in the midst of what has been traditionally characterized as the ‘cascade’ of isotropic, homogeneous, large-Reynolds-number turbulence: the systematic elongation of isolines of vorticity associated with the transfer of vorticity to smaller scales, eventually to dissipation scales, and the transfer of energy to larger scales. When the vorticity concentrations are a sufficiently dominant component of the total vorticity field, the cascade processes are suppressed. The demonstration of persistent vorticity concentrations on intermediate scales - smaller than the scale of the peak of the energy spectrum and larger than the dissipation scales - does not invalidate many of the traditional characterizations of two-dimensional and geostrophic turbulence, but I believe it shows them to be substantially incomplete with respect to a fundamental phenomenon in such flows.

Enhanced dissipation for quasi-geostrophic motion over small-scale topography

2000 ◽  
Vol 407 ◽  
pp. 105-122 ◽  
Author(s):  
JACQUES VANNESTE
Keyword(s):  
Large Scale ◽  
Spatial Scales ◽  
Additional Term ◽  
Equation Of Motion ◽  
Small Scale ◽  
Two Dimensional ◽  
Turbulent Dissipation ◽  
Dissipative Term ◽  
History Of ◽  
Large Scale Flow

The effect of a small-scale topography on large-scale, small-amplitude oceanic motion is analysed using a two-dimensional quasi-geostrophic model that includes free-surface and β effects, Ekman friction and viscous (or turbulent) dissipation. The topography is two-dimensional and periodic; its slope is assumed to be much larger than the ratio of the ocean depth to the Earth's radius. An averaged equation of motion is derived for flows with spatial scales that are much larger than the scale of the topography and either (i) much larger than or (ii) comparable to the radius of deformation. Compared to the standard quasi-geostrophic equation, this averaged equation contains an additional dissipative term that results from the interaction between topography and dissipation. In case (i) this term simply represents an additional Ekman friction, whereas in case (ii) it is given by an integral over the history of the large-scale flow. The properties of the additional term are studied in detail. For case (i) in particular, numerical calculations are employed to analyse the dependence of the additional Ekman friction on the structure of the topography and on the strength of the original dissipation mechanisms.

Large-scale flow in two-dimensional turbulence at static pumping

JETP Letters ◽  
2017 ◽  
Vol 106 (10) ◽  
pp. 659-661 ◽  
Author(s):  
I. V. Kolokolov ◽  
V. V. Lebedev
Keyword(s):  
Large Scale ◽  
Two Dimensional ◽  
Large Scale Flow

scholarly journals The effect of asymmetric large-scale dissipation on energy and potential enstrophy injection in two-layer quasi-geostrophic turbulence

2012 ◽  
Vol 694 ◽  
pp. 493-523 ◽  
Author(s):  
Eleftherios Gkioulekas
Keyword(s):  
Large Scale ◽  
Bottom Layer ◽  
Two Dimensional ◽  
Interlayer Interaction ◽  
Open Questions ◽  
Small Scales ◽  
Scale Range ◽  
Geostrophic Turbulence ◽  
Enstrophy Cascade ◽  
Potential Enstrophy

AbstractIn the Nastrom–Gage spectrum of atmospheric turbulence, we observe a${k}^{\ensuremath{-} 3} $energy spectrum that transitions into a${k}^{\ensuremath{-} 5/ 3} $spectrum, with increasing wavenumber$k$. The transition occurs near a transition wavenumber${k}_{t} $, located near the Rossby deformation wavenumber${k}_{R} $. The Tung–Orlando theory interprets this spectrum as a double downscale cascade of potential enstrophy and energy, from large scales to small scales, in which the downscale potential enstrophy cascade coexists with the downscale energy cascade over the same length scale range. We show that, in a temperature-forced two-layer quasi-geostrophic model, the rates with which potential enstrophy and energy are injected place the transition wavenumber${k}_{t} $near${k}_{R} $. We also show that, if the potential energy dominates the kinetic energy in the forcing range, then the Ekman term suppresses the upscale cascading potential enstrophy more than it suppresses the upscale cascading energy, a behaviour contrary to what occurs in two-dimensional turbulence. As a result, the ratio$\eta / \varepsilon $of injected potential enstrophy over injected energy, in the downscale direction, decreases, thereby tending to decrease the transition wavenumber${k}_{t} $further. Using a random Gaussian forcing model, we reach the same conclusion, under the modelling assumption that the asymmetric Ekman term predominantly suppresses the bottom layer forcing, thereby disregarding a possible entanglement between the Ekman term and the nonlinear interlayer interaction. Based on these results, we argue that the Tung–Orlando theory can account for the approximate coincidence between${k}_{t} $and${k}_{R} $. We also identify certain open questions that require further investigation via numerical simulations.

scholarly journals Evolution of large-scale flow from turbulence in a two-dimensional superfluid

Science ◽  
2019 ◽  
Vol 364 (6447) ◽  
pp. 1267-1271 ◽  
Author(s):  
Shaun P. Johnstone ◽  
Andrew J. Groszek ◽  
Philip T. Starkey ◽  
Christopher J. Billington ◽  
Tapio P. Simula ◽  
...  
Keyword(s):  
Large Scale ◽  
Einstein Condensate ◽  
Quantized Vortices ◽  
Two Dimensional ◽  
Inverse Energy Cascade ◽  
Bose Einstein Condensate ◽  
Quantitative Studies ◽  
Interacting Systems ◽  
Large Scale Flow ◽  
Bose Einstein

Nonequilibrium interacting systems can evolve to exhibit large-scale structure and order. In two-dimensional turbulent flow, the seemingly random swirling motion of a fluid can evolve toward persistent large-scale vortices. To explain such behavior, Lars Onsager proposed a statistical hydrodynamic model based on quantized vortices. Here, we report on the experimental confirmation of Onsager’s model. We dragged a grid barrier through an oblate superfluid Bose–Einstein condensate to generate nonequilibrium distributions of vortices. We observed signatures of an inverse energy cascade driven by the evaporative heating of vortices, leading to steady-state configurations characterized by negative absolute temperatures. Our results open a pathway for quantitative studies of emergent structures in interacting quantum systems driven far from equilibrium.

scholarly journals Disordered hyperuniformity in two-dimensional amorphous silica

2020 ◽  
Vol 6 (16) ◽  
pp. eaba0826 ◽  
Author(s):  
Yu Zheng ◽  
Lei Liu ◽  
Hanqing Nan ◽  
Zhen-Xiong Shen ◽  
Ge Zhang ◽  
...  
Keyword(s):  
Amorphous Silica ◽  
Density Functional ◽  
Large Scale ◽  
Single Layer ◽  
Topological Defects ◽  
Density Functional Theory Calculations ◽  
Density Fluctuations ◽  
Atomic Scale ◽  
Two Dimensional ◽  
Wave Localization

Disordered hyperuniformity (DHU) is a recently proposed new state of matter, which has been observed in a variety of classical and quantum many-body systems. DHU systems are characterized by vanishing infinite-wavelength normalized density fluctuations and are endowed with unique novel physical properties. Here, we report the discovery of disordered hyperuniformity in atomic-scale two-dimensional materials, i.e., amorphous silica composed of a single layer of atoms, based on spectral-density analysis of high-resolution transmission electron microscopy images. Moreover, we show via large-scale density functional theory calculations that DHU leads to almost complete closure of the electronic bandgap compared to the crystalline counterpart, making the material effectively a metal. This is in contrast to the conventional wisdom that disorder generally diminishes electronic transport and is due to the unique electron wave localization induced by the topological defects in the DHU state.

Molecular Dynamics Simulation of the Thermal Conductivity of Silicon-Germanene Nanoribbon (SiGeNR): A Comparison with Silicene Nanoribbon (SiNR) and Germanene Nanoribbon (GeNR)

2015 ◽  
Vol 1105 ◽  
pp. 285-289 ◽  
Author(s):  
Jessa Mae P. Tagalog ◽  
Cachey Girly Alipala ◽  
Giovanni J. Paylaga ◽  
Naomi T. Paylaga ◽  
Rolando V. Bantaculo
Keyword(s):  
Thermal Conductivity ◽  
Molecular Dynamics ◽  
Silicon Germanium ◽  
Large Scale ◽  
Room Temperature ◽  
Single Layer ◽  
Dynamics Simulation ◽  
Two Dimensional ◽  
Silicon And Germanium ◽  
Dynamics Simulations

This study examines the nature of thermal transport properties of single layer two-dimensional honeycomb structures of silicon-germanene nanoribbon (SiGeNR), silicene nanoribbon (SiNR) and germanene nanoribbon (GeNR) which have not yet been characterized experimentally. SiGeNR, SiNR and GeNR are the allotropes of silicon-germanium, silicon and germanium, respectively, withsp2hybridization. The thermal conductivity of the materials has been investigated using Tersoff potential through LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) by performing the molecular-dynamics simulations. The temperature is varied (50 K, 77 K, 150 K, 300 K, 500 K, 700 K, 1000 K, and 1200 K) with fixed nanoribbon dimension of 50 nm × 10 nm. The length is also varied (10 nm, 20 nm, 30 nm, 40 nm, and 50 nm) while the temperature is fixed at room temperature and the width is also fixed at 10 nm. The obtained results showed that the thermal conductivity of SiGeNR at room temperature is approximately 10 times higher than GeNR and approximately 6 times higher compared to SiNR. The thermal conductivity increases as the temperature is increased from 50 K – 300 K, and as the temperature is further increased, the thermal conductivity decreases with temperature. Moreover, the thermal conductivity in SiGeNR, SiNR, and GeNR increases as the length is being increased. Predicting new features of SiGeNR, SiNR and GeNR open new possibilities for nanoelectronic device applications of group IV two-dimensional materials.

Two-dimensional turbulence above topography

1976 ◽  
Vol 78 (1) ◽  
pp. 129-154 ◽  
Author(s):  
Francis P. Bretherton ◽  
Dale B. Haidvogel
Keyword(s):  
Kinetic Energy ◽  
Large Scale ◽  
Two Dimensional ◽  
Constant Depth ◽  
The North ◽  
Beta Plane ◽  
Two Dimensional Flow ◽  
Large Scale Flow ◽  
Quadratic Integral ◽  
North And South

In a turbulent two-dimensional flow enstrophy systematically cascades to very small scales, at which it is dissipated. The kinetic energy, on the other hand, remains at large scales and the total kinetic energy is constant. Above random topography an initially turbulent flow tends to a steady state with streamlines parallel to contours of constant depth, anticyclonic around a bump. A numerical experiment verifies this prediction. In a closed basin on a beta-plane the solution with minimum enstrophy implies a westward flow in the interior, returning in narrow boundary layers to the north and south. This result is interpreted using a parameterization of the effects of the eddies on the large-scale flow. The numerical solution is in qualitative agreement, but corresponds to a minimum of a more complex measure of the total enstrophy than the usual quadratic integral.

scholarly journals Resolution extension by image summing in serial femtosecond crystallography of two-dimensional membrane-protein crystals

IUCrJ ◽  
2018 ◽  
Vol 5 (1) ◽  
pp. 103-117 ◽  
Author(s):  
Cecilia M. Casadei ◽  
Ching-Ju Tsai ◽  
Anton Barty ◽  
Mark S. Hunter ◽  
Nadia A. Zatsepin ◽  
...  
Keyword(s):  
Membrane Protein ◽  
Large Scale ◽  
Structural Changes ◽  
Signal To Noise Ratio ◽  
Three Dimensional ◽  
Single Layer ◽  
Protein Crystals ◽  
Single Shot ◽  
Two Dimensional ◽  
X Ray

Previous proof-of-concept measurements on single-layer two-dimensional membrane-protein crystals performed at X-ray free-electron lasers (FELs) have demonstrated that the collection of meaningful diffraction patterns, which is not possible at synchrotrons because of radiation-damage issues, is feasible. Here, the results obtained from the analysis of a thousand single-shot, room-temperature X-ray FEL diffraction images from two-dimensional crystals of a bacteriorhodopsin mutant are reported in detail. The high redundancy in the measurements boosts the intensity signal-to-noise ratio, so that the values of the diffracted intensities can be reliably determined down to the detector-edge resolution of 4 Å. The results show that two-dimensional serial crystallography at X-ray FELs is a suitable method to study membrane proteins to near-atomic length scales at ambient temperature. The method presented here can be extended to pump–probe studies of optically triggered structural changes on submillisecond timescales in two-dimensional crystals, which allow functionally relevant large-scale motions that may be quenched in three-dimensional crystals.

scholarly journals Visualizing large-scale flow using synthetic aperture PIV

2019 ◽  
Vol 61 (1) ◽  
Author(s):  
Josje van Houwelingen ◽  
Ad P. C. Holten ◽  
Herman J. H. Clercx ◽  
Rudie P. J. Kunnen ◽  
Jaap Molenaar ◽  
...  
Keyword(s):  
Large Scale ◽  
Particle Image ◽  
Synthetic Aperture ◽  
Vortex Rings ◽  
Two Dimensional ◽  
Vorticity Field ◽  
Image Velocimetry ◽  
Large Scale Flow ◽  
Small Bubbles ◽  
Proof Of Principle

Abstract We discuss the application of synthetic aperture particle image velocimetry for measuring the flow around human swimmers using small bubbles as tracer. We quantify the two-dimensional projection of the velocity field in planes perpendicular to the viewing direction of an array of six cameras. With help of simulations, modelled after the experiment, we address questions about depth selectivity and occlusion in dense bubble fields. Using vortex rings in the swimming pool, we provide a proof of principle of the method. It is further illustrated by the vorticity field produced by a human swimmer. Graphic abstract

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