Small-scale structure and energy transfer in homogeneous turbulence

2018 ◽  
Vol 854 ◽  
pp. 505-543 ◽  
Author(s):  
Douglas W. Carter ◽  
Filippo Coletti
Keyword(s):  
Energy Transfer ◽  
Large Scale ◽  
Probability Distributions ◽  
Physical Space ◽  
Energy Cascade ◽  
Homogeneous Turbulence ◽  
Small Scale ◽  
Mean Flow ◽  
Number Range ◽  
Wide Range

We use high-resolution velocity measurements in a jet-stirred zero-mean-flow facility to investigate the topology and energy transfer properties of homogeneous turbulence over the Reynolds number range $Re_{\unicode[STIX]{x1D706}}\approx 300$–500. The probability distributions of the enstrophy and strain-rate fields show long tails associated with the most intense events, while the weaker events behave as random variables. The high-enstrophy and high-strain structures are shaped as tube-like and sheet-like objects, respectively, the latter often wrapped around the former. Both types of structures have thickness that scales in Kolmogorov units, and display self-similar topology over a wide range of scales. The small-scale turbulence activity is found to be strongly correlated with the large-scale activity, suggesting that the phenomenon of amplitude modulation (previously observed in advection-dominated shear flows) is not limited to specific production mechanisms. Observing the significant variations in spatially averaged enstrophy, we heuristically define hyperactive and sleeping states of the flow: these also correspond to, respectively, high and low levels of large-scale velocity gradients. Moreover, the hyperactive and sleeping states contribute very differently to the inter-scale energy flux, characterized via the nonlinear transfer term in the Kármán–Howarth–Monin equation. While the energy cascades to smaller scales along the jet-axis direction, a weaker but sizable inverse transfer is observed along the transverse direction; a behaviour so far only observed in spatially developing flows. The hyperactive states are characterized by very intense energy transfers, while the sleeping states account for weaker fluxes, largely directed from small to large scales. This implies that the form of energy cascade depends on the presence (or absence) of intense turbulent structures. These results are at odds with the classic concept of the energy cascade between adjacent scales, but are compatible with the view of a cascade in physical space.

Signatures of midlatitude heat waves in Rossby wave variability spectra 

2021 ◽  
Author(s):  
Iana Strigunova ◽  
Richard Blender ◽  
Frank Lunkeit ◽  
Nedjeljka Žagar
Keyword(s):  
Rossby Wave ◽  
Large Scale ◽  
Rossby Waves ◽  
Heat Waves ◽  
Probability Distributions ◽  
Physical Space ◽  
Mean Flow ◽  
Single Wave ◽  
Fourier Decomposition ◽  
Latitude Belt

<p>This work aims at identifying extreme circulation conditions such as heat waves in modal space which is defined by eigensolutions of the linearized primitive equations. Here, the Rossby waves are represented in terms of Hough harmonics that are an orthogonal and complete expansion set allowing Rossby wave diagnostics in terms of their total (kinetic and available potential) energies. We expect that this diagnostic provides a more clear picture of the Rossby wave variability spectra compared to the common Fourier decomposition along a latitude belt. </p> <p>The probability distributions of Rossby wave energies are analysed separately for the zonal mean flow, for the planetary and synoptic zonal wavenumbers. The robustness is ensured by considering the four reanalyses ERA5, ERA-Interim, JRA-55 and MERRA. A single wave is characterized by Gaussianity in the complex Hough amplitudes and by a chi-square distribution for the energies. We find that the distributions of the energy anomalies in the wavenumber space are non-Gaussian with almost the same positive skewness in the four reanalyses.  The skewness increases during persistent heat waves for all energy anomaly distributions, in agreement with the recent trend of increased subseasonal variance in large-scale Rossby waves and decreased variance at synoptic scales. The new approach offers a selective filtering to physical space. The reconstructed circulation during heat waves is dominated by large-scale anticyclonic systems in northeastern Europe with zonal wavenumbers 2 and 3, in agreement with previous studies, thereby demonstrating physical meaningfulness of the skewness. </p> <p> </p>

scholarly journals Statistical Analysis of Dynamic Subgrid Modeling Approaches in Large Eddy Simulation

2021 ◽  
Author(s):  
Mohammad Khalid Hossen ◽  
Asokan Mulayath Variyath ◽  
Jahrul M Alam
Keyword(s):  
Kinetic Energy ◽  
Large Eddy Simulation ◽  
Turbulent Flows ◽  
Large Scale ◽  
Physical Space ◽  
Statistical Characteristics ◽  
Small Scale ◽  
Eddy Simulation ◽  
Wide Range ◽  
Large Eddy

In large eddy simulation (LES) of turbulent flows, the most critical dynamical processes to be considered by dynamic subgrid models to account for an average cascade of kinetic energy from the largest to the smallest scales of the flow is not fully clear. Furthermore, evidence of vortex stretching being the primary mechanism of the cascade is not out of the question. In this article, we study some essential statistical characteristics of vortex stretching and its role in dynamic approaches of modeling subgrid-scale turbulence. We have compared the interaction of subgrid stresses with the filtered quantities among four models using invariants of the velocity gradient tensor. This technique is a single unified approach to studying a wide range of length scales in the turbulent flow. In addition, it also provides a rational basis for the statistical characteristics a subgrid model must serve in physical space to ensure an appropriate cascade of kinetic energy. Results indicate that the stretching mechanism extracts energy from the large-scale straining motion and passes it onto small-scale stretched vortices.

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.

Coupled Thermo-Hydro-Geochemical Models of Engineered Barrier Systems: The Febex Project

2000 ◽  
Vol 663 ◽  
Author(s):  
J. Samper ◽  
R. Juncosa ◽  
V. Navarro ◽  
J. Delgado ◽  
L. Montenegro ◽  
...  
Keyword(s):  
Large Scale ◽  
Reference Model ◽  
Numerical Models ◽  
Full Scale ◽  
Small Scale ◽  
Model Parameters ◽  
In Situ Test ◽  
Wide Range ◽  
Engineered Barrier

ABSTRACTFEBEX (Full-scale Engineered Barrier EXperiment) is a demonstration and research project dealing with the bentonite engineered barrier designed for sealing and containment of waste in a high level radioactive waste repository (HLWR). It includes two main experiments: an situ full-scale test performed at Grimsel (GTS) and a mock-up test operating since February 1997 at CIEMAT facilities in Madrid (Spain) [1,2,3]. One of the objectives of FEBEX is the development and testing of conceptual and numerical models for the thermal, hydrodynamic, and geochemical (THG) processes expected to take place in engineered clay barriers. A significant improvement in coupled THG modeling of the clay barrier has been achieved both in terms of a better understanding of THG processes and more sophisticated THG computer codes. The ability of these models to reproduce the observed THG patterns in a wide range of THG conditions enhances the confidence in their prediction capabilities. Numerical THG models of heating and hydration experiments performed on small-scale lab cells provide excellent results for temperatures, water inflow and final water content in the cells [3]. Calculated concentrations at the end of the experiments reproduce most of the patterns of measured data. In general, the fit of concentrations of dissolved species is better than that of exchanged cations. These models were later used to simulate the evolution of the large-scale experiments (in situ and mock-up). Some thermo-hydrodynamic hypotheses and bentonite parameters were slightly revised during TH calibration of the mock-up test. The results of the reference model reproduce simultaneously the observed water inflows and bentonite temperatures and relative humidities. Although the model is highly sensitive to one-at-a-time variations in model parameters, the possibility of parameter combinations leading to similar fits cannot be precluded. The TH model of the “in situ” test is based on the same bentonite TH parameters and assumptions as for the “mock-up” test. Granite parameters were slightly modified during the calibration process in order to reproduce the observed thermal and hydrodynamic evolution. The reference model captures properly relative humidities and temperatures in the bentonite [3]. It also reproduces the observed spatial distribution of water pressures and temperatures in the granite. Once calibrated the TH aspects of the model, predictions of the THG evolution of both tests were performed. Data from the dismantling of the in situ test, which is planned for the summer of 2001, will provide a unique opportunity to test and validate current THG models of the EBS.

Scale-to-scale anisotropy in homogeneous turbulence

2017 ◽  
Vol 827 ◽  
pp. 250-284 ◽  
Author(s):  
Douglas W. Carter ◽  
Filippo Coletti
Keyword(s):  
Large Scale ◽  
Velocity Structure ◽  
Longitudinal Velocity ◽  
Reynolds Numbers ◽  
Homogeneous Turbulence ◽  
Mean Flow ◽  
Spatially Correlated ◽  
Air Jets ◽  
Image Velocimetry ◽  
Definition Of

We experimentally investigate scale-to-scale anisotropy from the integral to the dissipative scales in homogeneous turbulence. We employ an apparatus in which two facing arrays of randomly actuated air jets generate turbulence with negligible mean flow and shear, over a volume several times larger than the energy-containing eddy size. The Reynolds number based on the Taylor microscale is varied in the range$Re_{\unicode[STIX]{x1D706}}\approx 300{-}500$, while the axial-to-radial ratio of the root mean square velocity fluctuations ranges between 1.38 and 1.72. Two velocity components are measured by particle image velocimetry at varying resolutions, capturing from the integral to the Kolmogorov scales and yielding statistics up to sixth order. Over the inertial range, the scaling exponents of the velocity structure functions are found to differ not only between the longitudinal and transverse components, but also between the axial and radial directions of separation. At the dissipative scales, the moments of the velocity gradients indicate that departure from isotropy is, at the present Reynolds numbers, significant and more pronounced for stronger large-scale anisotropy. The generalized flatness factors of the longitudinal velocity differences tend towards isotropy as the separation is reduced from the inertial to the near-dissipative scales (down to about$10\unicode[STIX]{x1D702}$,$\unicode[STIX]{x1D702}$being the Kolmogorov length), but become more anisotropic for even smaller scales which are characterized by high intermittency. At the large scales, the direction of turbulence forcing is associated with a larger integral length, defined as the distance over which the velocity component in a given direction is spatially correlated. Because of anisotropy, the definition of the integral length is not trivial and may lead to dissimilar conclusions on the qualitative behaviour of the large scales and on the quantitative values of the normalized dissipation. Alternative definitions of these quantities are proposed to account for the anisotropy. Overall, these results highlight the importance of evaluating both the different velocity components and the different spatial directions across all scales of the flow.

Buoyancy effects on large-scale motions in convective atmospheric boundary layers: implications for modulation of near-wall processes

2018 ◽  
Vol 856 ◽  
pp. 135-168 ◽  
Author(s):  
S. T. Salesky ◽  
W. Anderson
Keyword(s):  
Boundary Layer ◽  
Velocity Field ◽  
Boundary Layers ◽  
Vertical Velocity ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Small Scale ◽  
Convective Conditions ◽  
Wide Range

A number of recent studies have demonstrated the existence of so-called large- and very-large-scale motions (LSM, VLSM) that occur in the logarithmic region of inertia-dominated wall-bounded turbulent flows. These regions exhibit significant streamwise coherence, and have been shown to modulate the amplitude and frequency of small-scale inner-layer fluctuations in smooth-wall turbulent boundary layers. In contrast, the extent to which analogous modulation occurs in inertia-dominated flows subjected to convective thermal stratification (low Richardson number) and Coriolis forcing (low Rossby number), has not been considered. And yet, these parameter values encompass a wide range of important environmental flows. In this article, we present evidence of amplitude modulation (AM) phenomena in the unstably stratified (i.e. convective) atmospheric boundary layer, and link changes in AM to changes in the topology of coherent structures with increasing instability. We perform a suite of large eddy simulations spanning weakly ($-z_{i}/L=3.1$) to highly convective ($-z_{i}/L=1082$) conditions (where$-z_{i}/L$is the bulk stability parameter formed from the boundary-layer depth$z_{i}$and the Obukhov length $L$) to investigate how AM is affected by buoyancy. Results demonstrate that as unstable stratification increases, the inclination angle of surface layer structures (as determined from the two-point correlation of streamwise velocity) increases from$\unicode[STIX]{x1D6FE}\approx 15^{\circ }$for weakly convective conditions to nearly vertical for highly convective conditions. As$-z_{i}/L$increases, LSMs in the streamwise velocity field transition from long, linear updrafts (or horizontal convective rolls) to open cellular patterns, analogous to turbulent Rayleigh–Bénard convection. These changes in the instantaneous velocity field are accompanied by a shift in the outer peak in the streamwise and vertical velocity spectra to smaller dimensionless wavelengths until the energy is concentrated at a single peak. The decoupling procedure proposed by Mathiset al.(J. Fluid Mech., vol. 628, 2009a, pp. 311–337) is used to investigate the extent to which amplitude modulation of small-scale turbulence occurs due to large-scale streamwise and vertical velocity fluctuations. As the spatial attributes of flow structures change from streamwise to vertically dominated, modulation by the large-scale streamwise velocity decreases monotonically. However, the modulating influence of the large-scale vertical velocity remains significant across the stability range considered. We report, finally, that amplitude modulation correlations are insensitive to the computational mesh resolution for flows forced by shear, buoyancy and Coriolis accelerations.

scholarly journals Self-Supervised Pre-Training of Transformers for Satellite Image Time Series Classification

2020 ◽  
Author(s):  
Yuan Yuan ◽  
Lei Lin
Keyword(s):  
Time Series ◽  
Deep Learning ◽  
Large Scale ◽  
Temporal Structure ◽  
Satellite Image ◽  
Fine Tuning ◽  
Small Scale ◽  
Model Parameters ◽  
Learning Approaches ◽  
Wide Range

Satellite image time series (SITS) classification is a major research topic in remote sensing and is relevant for a wide range of applications. Deep learning approaches have been commonly employed for SITS classification and have provided state-of-the-art performance. However, deep learning methods suffer from overfitting when labeled data is scarce. To address this problem, we propose a novel self-supervised pre-training scheme to initialize a Transformer-based network by utilizing large-scale unlabeled data. In detail, the model is asked to predict randomly contaminated observations given an entire time series of a pixel. The main idea of our proposal is to leverage the inherent temporal structure of satellite time series to learn general-purpose spectral-temporal representations related to land cover semantics. Once pre-training is completed, the pre-trained network can be further adapted to various SITS classification tasks by fine-tuning all the model parameters on small-scale task-related labeled data. In this way, the general knowledge and representations about SITS can be transferred to a label-scarce task, thereby improving the generalization performance of the model as well as reducing the risk of overfitting. Comprehensive experiments have been carried out on three benchmark datasets over large study areas. Experimental results demonstrate the effectiveness of the proposed method, leading to a classification accuracy increment up to 1.91% to 6.69%. <div><b>This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.</b></div>

scholarly journals Physical Transport Processes that Affect the Distribution of Oil in the Gulf of Mexico: Observations and Modeling

Oceanography ◽  
2021 ◽  
Vol 34 (1) ◽  
pp. 58-75
Author(s):  
Michel Boufadel ◽  
◽  
Annalisa Bracco ◽  
Eric Chassignet ◽  
Shuyi Chen ◽  
...  
Keyword(s):  
Gulf Of Mexico ◽  
Physical Environment ◽  
Large Scale ◽  
Transport Processes ◽  
Small Scale ◽  
Surface Mixed Layer ◽  
Physical Processes ◽  
Mixing Processes ◽  
Near Surface ◽  
Wide Range

Physical transport processes such as the circulation and mixing of waters largely determine the spatial distribution of materials in the ocean. They also establish the physical environment within which biogeochemical and other processes transform materials, including naturally occurring nutrients and human-made contaminants that may sustain or harm the region’s living resources. Thus, understanding and modeling the transport and distribution of materials provides a crucial substrate for determining the effects of biological, geological, and chemical processes. The wide range of scales in which these physical processes operate includes microscale droplets and bubbles; small-scale turbulence in buoyant plumes and the near-surface “mixed” layer; submesoscale fronts, convergent and divergent flows, and small eddies; larger mesoscale quasi-geostrophic eddies; and the overall large-scale circulation of the Gulf of Mexico and its interaction with the Atlantic Ocean and the Caribbean Sea; along with air-sea interaction on longer timescales. The circulation and mixing processes that operate near the Gulf of Mexico coasts, where most human activities occur, are strongly affected by wind- and river-induced currents and are further modified by the area’s complex topography. Gulf of Mexico physical processes are also characterized by strong linkages between coastal/shelf and deeper offshore waters that determine connectivity to the basin’s interior. This physical connectivity influences the transport of materials among different coastal areas within the Gulf of Mexico and can extend to adjacent basins. Major advances enabled by the Gulf of Mexico Research Initiative in the observation, understanding, and modeling of all of these aspects of the Gulf’s physical environment are summarized in this article, and key priorities for future work are also identified.

scholarly journals Dependence of Model Energy Spectra on Vertical Resolution

2016 ◽  
Vol 144 (4) ◽  
pp. 1407-1421 ◽  
Author(s):  
Michael L. Waite
Keyword(s):  
High Resolution ◽  
Large Scale ◽  
Vertical Mixing ◽  
Energy Spectra ◽  
Small Scale ◽  
Rossby Number ◽  
Vertical Resolution ◽  
Wide Range ◽  
Qualitative Shape ◽  
Vertical Grid

Abstract Many high-resolution atmospheric models can reproduce the qualitative shape of the atmospheric kinetic energy spectrum, which has a power-law slope of −3 at large horizontal scales that shallows to approximately −5/3 in the mesoscale. This paper investigates the possible dependence of model energy spectra on the vertical grid resolution. Idealized simulations forced by relaxation to a baroclinically unstable jet are performed for a wide range of vertical grid spacings Δz. Energy spectra are converged for Δz 200 m but are very sensitive to resolution with 500 m ≤ Δz ≤ 2 km. The nature of this sensitivity depends on the vertical mixing scheme. With no vertical mixing or with weak, stability-dependent mixing, the mesoscale spectra are artificially amplified by low resolution: they are shallower and extend to larger scales than in the converged simulations. By contrast, vertical hyperviscosity with fixed grid-scale damping rate has the opposite effect: underresolved spectra are spuriously steepened. High-resolution spectra are converged except for the stability-dependent mixing case, which are damped by excessive mixing due to enhanced shear over a wide range of horizontal scales. It is shown that converged spectra require resolution of all vertical scales associated with the resolved horizontal structures: these include quasigeostrophic scales for large-scale motions with small Rossby number and the buoyancy scale for small-scale motions at large Rossby number. It is speculated that some model energy spectra may be contaminated by low vertical resolution, and it is recommended that vertical-resolution sensitivity tests always be performed.

scholarly journals Gyrotactic swimmers in turbulence: shape effects and role of the large-scale flow

2018 ◽  
Vol 856 ◽  
Author(s):  
M. Borgnino ◽  
G. Boffetta ◽  
F. De Lillo ◽  
M. Cencini
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Preferential Sampling ◽  
Wide Range ◽  
Shape Effects ◽  
Dilute Suspensions ◽  
Large Scale Flow

We study the dynamics and the statistics of dilute suspensions of gyrotactic swimmers, a model for many aquatic motile microorganisms. By means of extensive numerical simulations of the Navier–Stokes equations at different Reynolds numbers, we investigate preferential sampling and small-scale clustering as a function of the swimming (stability and speed) and shape parameters, considering in particular the limits of spherical and rod-like particles. While spherical swimmers preferentially sample local downwelling flow, for elongated swimmers we observe a transition from downwelling to upwelling regions at sufficiently high swimming speed. The spatial distribution of both spherical and elongated swimmers is found to be fractal at small scales in a wide range of swimming parameters. The direct comparison between the different shapes shows that spherical swimmers are more clusterized at small stability and speed numbers, while for large values of the parameters elongated cells concentrate more. The relevance of our results for phytoplankton swimming in the ocean is briefly discussed.

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