scholarly journals Exploiting self-organized criticality in strongly stratified turbulence

2021 ◽  
Vol 933 ◽  
Author(s):  
Gregory P. Chini ◽  
Guillaume Michel ◽  
Keith Julien ◽  
Cesar B. Rocha ◽  
Colm-cille P. Caulfield
Keyword(s):  
Large Scale ◽  
Ad Hoc ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Marginal Stability ◽  
Small Scale ◽  
Stratified Turbulence ◽  
Self Organized ◽  
Reduced Equations ◽  
Self Organized Criticality

A multiscale reduced description of turbulent free shear flows in the presence of strong stabilizing density stratification is derived via asymptotic analysis of the Boussinesq equations in the simultaneous limits of small Froude and large Reynolds numbers. The analysis explicitly recognizes the occurrence of dynamics on disparate spatiotemporal scales, yielding simplified partial differential equations governing the coupled evolution of slow large-scale hydrostatic flows and fast small-scale isotropic instabilities and internal waves. The dynamics captured by the coupled reduced equations is illustrated in the context of two-dimensional strongly stratified Kolmogorov flow. A noteworthy feature of the reduced model is that the fluctuations are constrained to satisfy quasilinear (QL) dynamics about the comparably slowly varying large-scale fields. Crucially, this QL reduction is not invoked as an ad hoc closure approximation, but rather is derived in a physically relevant and mathematically consistent distinguished limit. Further analysis of the resulting slow–fast QL system shows how the amplitude of the fast stratified-shear instabilities is slaved to the slowly evolving mean fields to ensure the marginal stability of the latter. Physically, this marginal stability condition appears to be compatible with recent evidence of self-organized criticality in both observations and simulations of stratified turbulence. Algorithmically, the slaving of the fluctuation fields enables numerical simulations to be time-evolved strictly on the slow time scale of the hydrostatic flow. The reduced equations thus provide a solid mathematical foundation for future studies of three-dimensional strongly stratified turbulence in extreme parameter regimes of geophysical relevance and suggest avenues for new sub-grid-scale parametrizations.

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.

scholarly journals Self-organized criticality and the fractal scaling of a predator-prey interaction

1992 ◽  
Vol 6 ◽  
pp. 11-11
Author(s):  
Richard B. Aronson
Keyword(s):  
Large Scale ◽  
Interactive Systems ◽  
Small Scale ◽  
Biological Interactions ◽  
Ecological Processes ◽  
The Bahamas ◽  
Fractal Scaling ◽  
Self Organized ◽  
Predation Effects ◽  
Self Organized Criticality

In many cases, it is not possible to explain evolutionary-scale patterns by analogy to ecological processes. However, in at least some cases, biological interactions appear amenable to such extrapolation. The paleobiological literature contains examples of predation, competition, and herbivory in which the dynamics are similar on multiple spatiotemporal scales.Dense populations of epifaunal, suspension-feeding ophiuroids, or brittlestar beds, are widely distributed, but they are rare and are restricted in their habitat distribution. On a small scale (meters to kilometers, hours to days), brittlestar bed distribution in the British Isles and the Bahamas is limited by predatory fishes and crabs. On an intermediate scale (tens to hundreds of kilometers, decades to centuries), predation by seastars may cause cycles of ophiuroid abundance in the western English Channel, beyond the stringent restrictions imposed by fish and crab predators. On a large scale (globally, millions to tens of millions of years), the Jurassic decline of brittlestar beds is associated with the diversification of predatory teleosts, neoselachian sharks, and decapod crustaceans.Small-scale predator-ophiuroid interactions sum to produce analogous intermediate- and large-scale interactions. Predation effects on brittlestar beds appear to be scale-independent, or fractal. Fractal scaling may be a consequence of self-organized criticality, an inherent property of large, interactive systems.

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?

scholarly journals Mean flow evolution of saturated forced shear flows in polytropic atmospheres

2019 ◽  
Vol 82 ◽  
pp. 259-269
Author(s):  
V. Witzke ◽  
L.J. Silvers
Keyword(s):  
Large Scale ◽  
Shear Flows ◽  
Three Dimensional ◽  
Relaxation Method ◽  
Marginal Stability ◽  
Small Scale ◽  
Mean Flow ◽  
Physical Processes ◽  
Flow Evolution ◽  
Stellar Interiors

In stellar interiors shear flows play an important role in many physical processes. So far helioseismology provides only large-scale measurements, and so the small-scale dynamics remains insufficiently understood. To draw a connection between observations and three-dimensional DNS of shear driven turbulence, we investigate horizontally averaged profiles of the numerically obtained mean state. We focus here on just one of the possible methods that can maintain a shear flow, namely the average relaxation method. We show that although some systems saturate by restoring linear marginal stability this is not a general trend. Finally, we discuss the reason that the results are more complex than expected.

scholarly journals Thermodynamic Analysis of Ocean Circulation

2007 ◽  
Vol 37 (8) ◽  
pp. 2038-2052 ◽  
Author(s):  
J. Nycander ◽  
J. Nilsson ◽  
K. Döös ◽  
G. Broström
Keyword(s):  
Ocean Circulation ◽  
Large Scale ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Ocean Model ◽  
Global Ocean ◽  
Small Scale ◽  
Ekman Pumping ◽  
Overturning Circulation ◽  
Thermodynamic Work

Abstract Calculating a streamfunction as function of depth and density is proposed as a new way of analyzing the thermodynamic character of the overturning circulation in the global ocean. The sign of an overturning cell in this streamfunction directly shows whether it is driven mechanically by large-scale wind stress or thermally by heat conduction and small-scale mixing. It is also shown that the integral of this streamfunction gives the thermodynamic work performed by the fluid. The analysis is also valid for the Boussinesq equations, although formally there is no thermodynamic work in an incompressible fluid. The proposed method is applied both to an idealized coarse-resolution three-dimensional numerical ocean model, and to the realistic high-resolution Ocean Circulation and Climate Advanced Model (OCCAM). It is shown that the overturning circulation in OCCAM between the 200- and 1000-m depth is dominated by a thermally indirect cell of 24 Sverdrups (1 Sv ≡ 106 m3 s−1), forced by Ekman pumping. In the densest and deepest waters there is a thermally direct cell of 18 Sv, which requires a forcing by around 100 GW of parameterized small-scale mixing.

scholarly journals Self-organization in a driven dissipative plasma system

2009 ◽  
Vol 76 (1) ◽  
pp. 107-116 ◽  
Author(s):  
DASTGEER SHAIKH ◽  
B. DASGUPTA ◽  
Q. HU ◽  
G. P. ZANK
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Spectral Energy ◽  
Small Scale ◽  
Plasma System ◽  
Self Organized ◽  
Wide Range ◽  
Characteristic Modes ◽  
Perpendicular Component ◽  
Migration Of Energy

AbstractWe perform a fully self-consistent three-dimensional numerical simulation for a compressible, dissipative magnetoplasma driven by large-scale perturbations, that contain a fairly broad spectrum of characteristic modes, ranging from largest scales to intermediate scales and down to the smallest scales, where the energy of the system is dissipated by collisional (ohmic) and viscous dissipations. Additionally, our simulation includes nonlinear interactions amongst a wide range of fluctuations that are initialized with random spectral amplitudes, leading to the cascade of spectral energy in the inertial range spectrum, and takes into account large-scale as well as small-scale perturbations that may have been induced by the background plasma fluctuations, as well as the non-adiabatic exchange of energy leading to the migration of energy from the energy-containing modes or randomly injected energy driven by perturbations and further dissipated by the smaller scales. Besides demonstrating the comparative decays of the total energy and the dissipation rate of the energy, our results show the existence of a perpendicular component of the current, thus clearly confirming that the self-organized state is non-force free.

scholarly journals Extensions to the IEEE 802.11 TSF for Efficient and Reliable Network Synchronization in Large Scale MANETs

2006 ◽  
Vol 2 (2) ◽  
pp. 110
Author(s):  
Peter Rauschert ◽  
Arasch Honarbacht ◽  
Anton Kummert
Keyword(s):  
Ad Hoc Networks ◽  
Ieee 802.11 ◽  
Large Scale ◽  
Ad Hoc ◽  
Small Scale ◽  
Distributed Coordination ◽  
Self Organized ◽  
Mobile Stations ◽  
Hoc Networks ◽  
Coordination Function

Designing new protocols for Mobile Ad hoc Networks (MANETs) is a great challenge due to their distributed and self organized nature. Though, aspects of approved algorithms for hierarchical topographies may be carried over to these flat networks. The IEEE 802.11 protocol supports ad hoc networks in small scale applications, but its performance in large scale environments is still under investigation. Besides the Distributed Coordination Function (DCF), the Timer Synchronization Function (TSF) can be significantly improved in order to increase the performance in large scale multihop networks. This article presents systematic extensions to the TSF that allow increasing the overall reliability and disburdening the network at the same time. The presented scheme may be tailored to specific applications and even supports mobile stations and herewith MANETs.

Modeling Extinction

2003 ◽  
Author(s):  
M. E. J. Newman ◽  
R. G. Palmer
Keyword(s):  
Evolutionary Biology ◽  
Large Scale ◽  
Competitive Exclusion ◽  
Applied Mathematics ◽  
Santa Fe ◽  
New Approach ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Extinction Events ◽  
Mass Extinction Events

Developed after a meeting at the Santa Fe Institute on extinction modeling, this book comments critically on the various modeling approaches. In the last decade or so, scientists have started to examine a new approach to the patterns of evolution and extinction in the fossil record. This approach may be called "statistical paleontology," since it looks at large-scale patterns in the record and attempts to understand and model their average statistical features, rather than their detailed structure. Examples of the patterns these studies examine are the distribution of the sizes of mass extinction events over time, the distribution of species lifetimes, or the apparent increase in the number of species alive over the last half a billion years. In attempting to model these patterns, researchers have drawn on ideas not only from paleontology, but from evolutionary biology, ecology, physics, and applied mathematics, including fitness landscapes, competitive exclusion, interaction matrices, and self-organized criticality. A self-contained review of work in this field.

Turbulent flow between counter-rotating concentric cylinders: a direct numerical simulation study

2008 ◽  
Vol 615 ◽  
pp. 371-399 ◽  
Author(s):  
S. DONG
Keyword(s):  
Turbulent Flow ◽  
Large Scale ◽  
Outer Cylinder ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Taylor Vortex ◽  
Small Scale ◽  
Mean Flow ◽  
Concentric Cylinders ◽  
High Reynolds

We report three-dimensional direct numerical simulations of the turbulent flow between counter-rotating concentric cylinders with a radius ratio 0.5. The inner- and outer-cylinder Reynolds numbers have the same magnitude, which ranges from 500 to 4000 in the simulations. We show that with the increase of Reynolds number, the prevailing structures in the flow are azimuthal vortices with scales much smaller than the cylinder gap. At high Reynolds numbers, while the instantaneous small-scale vortices permeate the entire domain, the large-scale Taylor vortex motions manifested by the time-averaged field do not penetrate a layer of fluid near the outer cylinder. Comparisons between the standard Taylor–Couette system (rotating inner cylinder, fixed outer cylinder) and the counter-rotating system demonstrate the profound effects of the Coriolis force on the mean flow and other statistical quantities. The dynamical and statistical features of the flow have been investigated in detail.

Large- and small-scale vortical motions in a shear layer perturbed by tabs

1999 ◽  
Vol 382 ◽  
pp. 307-329 ◽  
Author(s):  
JUDITH K. FOSS ◽  
K. B. M. Q. ZAMAN
Keyword(s):  
Shear Layer ◽  
Pitch Angle ◽  
Large Scale ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Small Scale ◽  
Streamwise Vortices ◽  
Streamwise Vorticity ◽  
Cross Sectional ◽  
Scale Population

The large- and small-scale vortical motions produced by ‘delta tabs’ in a two-stream shear layer have been studied experimentally. An increase in mixing was observed when the base of the triangular shaped tab was affixed to the trailing edge of the splitter plate and the apex was pitched at some angle with respect to the flow axis. Such an arrangement produced a pair of counter-rotating streamwise vortices. Hot-wire measurements detailed the velocity, time-averaged vorticity (Ωx) and small-scale turbulence features in the three-dimensional space downstream of the tabs. The small-scale structures, whose scale corresponds to that of the peak in the dissipation spectrum, were identified and counted using the peak-valley-counting technique. The optimal pitch angle, θ, for a single tab and the optimal spanwise spacing, S, for a multiple tab array were identified. Since the goal was to increase mixing, the optimal tab configuration was determined from two properties of the flow field: (i) the large-scale motions with the maximum Ωx, and (ii) the largest number of small-scale motions in a given time period. The peak streamwise vorticity magnitude [mid ]Ωx−max[mid ] was found to have a unique relationship with the tab pitch angle. Furthermore, for all cases examined, the overall small-scale population was found to correlate directly with [mid ]Ωx−max[mid ]. Both quantities peaked at θ≈±45°. It is interesting to note that the peak magnitude of the corresponding circulation in the cross-sectional plane occurred for θ≈±90°. For an array of tabs, the two quantities also depended on the tab spacing. An array of contiguous tabs acted as a solid deflector producing the weakest streamwise vortices and the least small-scale population. For the measurement range covered, the optimal spacing was found to be S≈1.5 tab widths.

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