scholarly journals LOOP EQUATION AND AREA LAW IN TURBULENCE

1994 ◽  
Vol 09 (08) ◽  
pp. 1197-1238 ◽  
Author(s):  
A. A. MIGDAL
Keyword(s):  
Fluid Dynamics ◽  
Summer School ◽  
Spatial Scales ◽  
Inertial Range ◽  
Coordinate Space ◽  
Extended Version ◽  
Closed Loops ◽  
Loop Equation ◽  
Minimal Area ◽  
Area Law

This is an extended version of the preprint,4 based on the lectures given at Cargese Summer School and Chernogolovka Summer School in 1993. The incompressible fluid dynamics is reformulated as dynamics of closed loops C in coordinate space. We derive explicit functional equation for the pdf of the circulation PC (Γ) which allows the scaling solutions in the inertial range of spatial scales. The pdf decays as exponential of some power of Γ3/A2, where A is the minimal area inside the loop.

Modeling, Simulation, and Optimization of Geological Sequestration of CO2

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Ramesh K. Agarwal
Keyword(s):  
Fluid Dynamics ◽  
Co2 Sequestration ◽  
Spatial Scales ◽  
The United States ◽  
Co2 Injection ◽  
Temporal Scales ◽  
Simulation And Optimization ◽  
Modeling Simulation ◽  
Plume Migration ◽  
Basic Fluid

With heightened concerns on carbon dioxide (CO2) emissions from coal power plants, there has been a major emphasis in recent years on development of safe and economical geological carbon sequestration (GCS) technology. However, the detailed multiphase fluid dynamics and processes of GCS are not fully understood because various CO2 trapping mechanisms in geological formations have large variations in both spatial and temporal scales. As a result, there remain many uncertainties in determining the sequestration capacity of the reservoir and the safety of sequestered CO2 due to leakage. Furthermore, the sequestration efficiency is highly dependent on the CO2 injection strategy, which includes injection rate, injection pressure, and type of injection well, and its orientation, etc. The goal of GCS is to maximize the sequestration capacity and minimize the plume migration by optimizing the GCS operation. In this paper, first the basic fluid dynamics and trapping mechanisms for CO2 sequestration are briefly discussed. They are followed by a brief summary of current GCS projects worldwide with special emphasis on those in the United States. Majority of the paper is devoted to the numerical modeling, simulation, and optimization of CO2 sequestration in saline aquifers at macro spatial scales of a few to hundreds of kilometers and macro temporal scales of a few to hundreds of years. Examples of numerical simulations of a few large industrial scale projects are presented. The optimization studies include the investigation of various injection and well placement strategies to determine the optimal approach for maximizing the storage and minimizing the plume migration.

scholarly journals Stochastic generation of multi-site daily precipitation focusing on extreme events

2018 ◽  
Vol 22 (1) ◽  
pp. 655-672 ◽  
Author(s):  
Guillaume Evin ◽  
Anne-Catherine Favre ◽  
Benoit Hingray
Keyword(s):  
Extreme Precipitation ◽  
Daily Precipitation ◽  
Spatial Scales ◽  
Tail Dependence ◽  
Extended Version ◽  
Temporal Dependence ◽  
Heavy Tailed Distributions ◽  
Temporal And Spatial ◽  
Heavy Tailed ◽  
High Precipitation

Abstract. Many multi-site stochastic models have been proposed for the generation of daily precipitation, but they generally focus on the reproduction of low to high precipitation amounts at the stations concerned. This paper proposes significant extensions to the multi-site daily precipitation model introduced by Wilks, with the aim of reproducing the statistical features of extremely rare events (in terms of frequency and magnitude) at different temporal and spatial scales. In particular, the first extended version integrates heavy-tailed distributions, spatial tail dependence, and temporal dependence in order to obtain a robust and appropriate representation of the most extreme precipitation fields. A second version enhances the first version using a disaggregation method. The performance of these models is compared at different temporal and spatial scales on a large region covering approximately half of Switzerland. While daily extremes are adequately reproduced at the stations by all models, including the benchmark Wilks version, extreme precipitation amounts at larger temporal scales (e.g., 3-day amounts) are clearly underestimated when temporal dependence is ignored.

scholarly journals How Turbulent is the Magnetically Closed Corona?

2021 ◽  
Vol 8 ◽  
Author(s):  
James A. Klimchuk ◽  
Spiro K. Antiochos
Keyword(s):  
Magnetic Reconnection ◽  
Large Scale ◽  
Direct Relationship ◽  
Spatial Scales ◽  
Complex Structure ◽  
Inertial Range ◽  
Small Current ◽  
Current Sheets ◽  
Energy Flows ◽  
Turbulent Cascade

We argue that the magnetically closed corona evolves primarily quasi-statically, punctuated by many localized bursts of activity associated with magnetic reconnection at a myriad of small current sheets. The sheets form by various processes that do not involve a traditional turbulent cascade whereby energy flows losslessly through a continuum of spatial scales starting from the large scale of the photospheric driving. If such an inertial range is a defining characteristic of turbulence, then the magnetically closed corona is not a turbulent system. It nonetheless has a complex structure that bears no direct relationship to the pattern of driving.

Numerical Formulations for Computing Design Propagations of the Spatial Slider-Crank Mechanism

1996 ◽  
Author(s):  
Hong-Liu Zou ◽  
Karim Abdel-Malek ◽  
Jia-Yi Wang
Keyword(s):  
Spanning Tree ◽  
Design Parameters ◽  
Coordinate Space ◽  
Joint Position ◽  
Link Length ◽  
Closed Loops ◽  
Numerical Examples ◽  
Cartesian Space ◽  
Numerical Formulation ◽  
Crank Mechanism

Abstract A numerical formulation for studying the design of a spatial slider-crank mechanism is developed and illustrated. The mechanism is modeled using graph theory and closed loops are converted to a spanning tree structure by cutting joints and introducing new constraints. Variations of these constraints with respect to design parameters are derived. A change in link length or link orientation is propagated through the model and a new assembled configuration is computed hence redesigning the mechanism. Constraints are formulated in Cartesian space but computed in relative joint coordinate space. The Jacobian of the constraint is transformed to joint coordinate space in order to compute an assembled configuration for the cut-joint constraint formulation. The experimental code is illustrated through numerical examples where joint-position vectors and orientation matrices are altered.

scholarly journals AN EXACT SOLUTION OF THE LOOP EQUATION IN STRONG TURBULENCE

1996 ◽  
Vol 11 (39n40) ◽  
pp. 3113-3118 ◽  
Author(s):  
D.V. ANTONOV
Keyword(s):  
Initial Data ◽  
Jacobi Equation ◽  
Loop Space ◽  
Potential Term ◽  
Loop Equation ◽  
Strong Turbulence ◽  
Functional Derivatives ◽  
Random Forces ◽  
Hamilton Jacobi Equation ◽  
Area Law

The Hamilton–Jacobi equation for the loop effective action in strong turbulence with Gaussian random forces1,2 is solved by making use of the smearing procedure for the loop space functional Laplacian, proposed in Ref. 3. The solution obtained satisfies tensor- or scalar area law ansatz and depends on the initial data and the potential term in the loop Hamiltonian, averaged over loops. In the lowest order in the viscosity this average may be eliminated, and the solution is given by a certain linear combination of the initial data and the potential term and their functional derivatives.

scholarly journals Gravity Wave Instability Dynamics at High Reynolds Numbers. Part II: Turbulence Evolution, Structure, and Anisotropy

2009 ◽  
Vol 66 (5) ◽  
pp. 1149-1171 ◽  
Author(s):  
David C. Fritts ◽  
Ling Wang ◽  
Joe Werne ◽  
Tom Lund ◽  
Kam Wan
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Wave Breaking ◽  
Spatial Scales ◽  
Reynolds Numbers ◽  
Inertial Range ◽  
Stable Phase ◽  
Wave Instability ◽  
Intrinsic Frequency ◽  
High Reynolds

Abstract This paper examines the character, intermittency, and anisotropy of turbulence accompanying wave instability, breaking, and turbulence evolution and decay for gravity waves (GW) having a high intrinsic frequency, amplitudes above and below nominal convective instability, and a high Reynolds number. Wave breaking at both amplitudes leads to an extended inertial range of turbulence, with turbulence energies that maximize within ∼1 wave period of the onset of breaking. Turbulence sources include both shear and buoyancy, with shear being the major contributor. Turbulence displays considerable intermittency both within and across the phase of the breaking gravity wave and exhibits clear anisotropy throughout the evolution. Turbulence anisotropy is found at all spatial scales and all times but is most pronounced in the most statically stable phase of the GW and at late times as the turbulent flow restratifies.

scholarly journals Exposing the plural nature of molecular clouds

2019 ◽  
Vol 628 ◽  
pp. A33 ◽  
Author(s):  
J.-F. Robitaille ◽  
F. Motte ◽  
N. Schneider ◽  
D. Elia ◽  
S. Bontemps
Keyword(s):  
Power Spectrum ◽  
Turbulent Flows ◽  
Spectrum Analysis ◽  
Spatial Scales ◽  
Inertial Range ◽  
Power Spectrum Analysis ◽  
Characteristic Scale ◽  
Data Set ◽  
Analysis Technique ◽  
Non Gaussian

We present the Multiscale non-Gaussian Segmentation (MnGSeg) analysis technique. This wavelet-based method combines the analysis of the probability distribution function (PDF) of map fluctuations as a function of spatial scales and the power spectrum analysis of a map. This technique allows us to extract the non-Gaussianities identified in the multiscaled PDFs usually associated with turbulence intermittency and to spatially reconstruct the Gaussian and the non-Gaussian components of the map. This new technique can be applied on any data set. In the present paper, it is applied on a Herschel column density map of the Polaris flare cloud. The first component has by construction a self-similar fractal geometry similar to that produced by fractional Brownian motion (fBm) simulations. The second component is called the coherent component, as opposed to fractal, and includes a network of filamentary structures that demonstrates a spatial hierarchical scaling (i.e. filaments inside filaments). The power spectrum analysis of the two components proves that the Fourier power spectrum of the initial map is dominated by the power of the coherent filamentary structures across almost all spatial scales. The coherent structures contribute increasingly from larger to smaller scales, without producing any break in the inertial range. We suggest that this behaviour is induced, at least partly, by inertial-range intermittency, a well-known phenomenon for turbulent flows. We also demonstrate that the MnGSeg technique is itself a very sensitive signal analysis technique that allows the extraction of the cosmic infrared background (CIB) signal present in the Polaris flare submillimetre observations and the detection of a characteristic scale for 0.1 ≲ l ≲ 0.3 pc. The origin of this characteristic scale could partly be the transition of regimes dominated by incompressible turbulence versus compressible modes and other physical processes, such as gravity.

Toward bed state morphodynamics in gravel-bed rivers

2020 ◽  
Vol 44 (5) ◽  
pp. 700-726 ◽  
Author(s):  
David Lawson Adams
Keyword(s):  
Fluid Dynamics ◽  
Grain Size ◽  
Spatial Scales ◽  
Channel Stability ◽  
Channel Processes ◽  
Fluvial Systems ◽  
Gravel Bed ◽  
Relative Contribution ◽  
Gravel Bed Rivers ◽  
Channel Configuration

In fluvial geomorphology, one of the most pervasive paradigms is that the size of the grains present in a river exercises an important effect on its character. In gravel-bed rivers, there is considerable scatter in the relations between so-called “representative grain sizes” and basic channel processes and morphologies. Under a grain size paradigm, our ability to rationalize the characteristics of a given channel and predict how it will respond to a change in conditions is limited. In this paper, I deconstruct this paradigm by exploring its historical origins in geomorphology and fluid dynamics, and identify three of its underlying premises: (1) the association between grain diameter and fluid drag derived from Nikuradse’s experiments with sand-coated surfaces; (2) the use of grain size by early process geomorphologists to describe general trends across large samples of sand-bed rivers; and (3) a classificatory approach to discerning bed structures originally developed for bed configurations found in sand-bed rivers. The conflation of sand- and gravel-bed rivers limits our ability to understand gravel-bed morphodynamics. Longstanding critique of the grain size paradigm has generated alternative ideas but, due to technological and conceptual limitations, they have remained unrealized. One such unrealized idea is the morphology-based definition of bed state – an important degree of freedom within fluvial systems, particularly in reaches where adjustments to planform are not easily achieved. By embracing recent advancements in fluid dynamics and remote sensing, I present an alternative or complementary concept of bed state based on the notion that fluvial systems act to maximize flow resistance. The proposed quantitative index represents the relative contribution of morphologic adjustments occurring at different spatial scales (discriminated using a wavelet transform) to a stable channel configuration. By explicitly acknowledging the complexity of bed adjustments we can move toward a more complete understanding of channel stability in gravel-bed rivers.

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