Universal mechanism for saturation of vorticity growth in fully developed fluid turbulence

2013 ◽  
Vol 728 ◽  
Author(s):  
Chakradhar Thantanapally ◽  
Dhiraj V. Patil ◽  
Sauro Succi ◽  
Santosh Ansumali
Keyword(s):  
Coherent Structures ◽  
Large Scale ◽  
Blow Up ◽  
Initial Conditions ◽  
Inviscid Flows ◽  
Collective Dynamics ◽  
Fluid Turbulence ◽  
Show Evidence ◽  
Long Time ◽  
Decaying Turbulence

AbstractNumerical results from large-scale, long-time, simulations of decaying homogeneous turbulence are reported, which indicate that blow-up of inviscid flows is tamed by the emergence of collective dynamics of coherent structures. The simulations also suggest that this collective dynamics might lead to universal behaviour during the transient evolution of turbulence. In particular, simulations with three different initial conditions show evidence of a ${k}^{- 3} \log k$ spectrum in the transient stage, before the Kolmogorov ${k}^{- 5/ 3} $ asymptotic regime is attained. Such a universal transient might serve as a spectral funnel to the time-asymptotic Kolmogorov spectrum, which is invariably observed in the late stage of all three simulations presented in this work. The present work is entirely based on simulation evidence. However, the statistical analysis of the coherent structures suggests an analogy with population dynamics, which might be conducive to new mathematical models of transient decaying turbulence.

scholarly journals The fate of random initial vorticity distributions for two-dimensional Euler equations on a sphere

2015 ◽  
Vol 786 ◽  
pp. 1-4 ◽  
Author(s):  
Paul K. Newton
Keyword(s):  
Numerical Simulations ◽  
Euler Equations ◽  
Large Scale ◽  
Initial Conditions ◽  
Infinite Family ◽  
Small Scale ◽  
Two Dimensional ◽  
Random Initial Conditions ◽  
Long Time ◽  
Initial Vorticity

The paper by Dritschel et al. (J. Fluid Mech., vol. 783, 2015, pp. 1–22) describes the long-time behaviour of inviscid two-dimensional fluid dynamics on the surface of a sphere. At issue is whether the flow settles down to an equilibrium or whether, for generic (random) initial conditions, the long-time solution is periodic, quasi-periodic or chaotic. While it might be surprising that this issue is not settled in the literature, it is important to keep in mind that the Euler equations form a dissipationless Hamiltonian system, hence the set of equations only redistributes the initial vorticity, generating smaller and smaller scales, while keeping kinetic energy, angular impulse and an infinite family of vorticity moments (Casimirs) intact. While special solutions that never settle down to an equilibrium state can be constructed using point vortices, vortex patches and other distributions, the fate of random initial conditions is a trickier problem. Previous statistical theories indicate that the long-time state should be a stationary large-scale distribution of vorticity. By carrying out careful numerical simulations using two different methods, the authors make a compelling case that the generic long-time state resembles a large-scale oscillating quadrupolar vorticity field, surrounded by persistent small-scale vortices. While numerical simulations can never conclusively settle this issue, the results might help guide future theories that seek to prove the existence of such an interesting dynamical long-time state.

Transform/oblique rift system : what have we learned from numerical modelling and what's next ?

2020 ◽  
Author(s):  
Laetitia Le Pourhiet ◽  
Anthony Jourdon
Keyword(s):  
Numerical Modelling ◽  
Large Scale ◽  
Initial Conditions ◽  
Strike Slip ◽  
Rift System ◽  
New Concepts ◽  
Long Time ◽  
3D Numerical Modelling ◽  
Transform Margin ◽  
Conjugate Margins

<p>For very long time, transform margins have been treated and described  based on oceanic transform fault concepts. Their was no change in kinematics nor structures with time and thermally speaking, it was hypothesed that the margin was reheated as the mid-oceanic ridge translated passively along the margin.  In the last 10 years, 3D numerical modelling has been made available and numbers of studies have challenged this view. It is time to review the concepts that have emerge. Interrestingly, many modelling contributions have tackled the obliquity at very different scales, with initial conditions varying from simple flat layered homogeneous lithosphere to subduction of opposite vergence. Moreover some contributions have focus on rheological aspect and other on inheritance at different scale and different physical coupling have been used. Some models were targeting at reproducing the oceanic transform concepts, other at exploring how large scale structure can emerge.  I will therefore try to review  the state of art in numerical modelling of transform margin and oblique extensional system based on my own work and literature review. I will try to emphize the important differences and similarities used in the different modelling. Using different models with different boundary conditions and scale I will try to introduce a new conceptual model of transform margin which captures important characteristics like the delay in continental break-up highlighted by the tracing of sediments and water-depth as well as the obliquity between syn-rift and post-rift subsidence.  Some models of oblique extension have also been producing new type of strike slip ocean continent transition which somehow could be interpreted as steep transform margins but appears to be mainly strike slip and have no conjugate margins. To conclude, all these 3D numerical modelling  allow us today to present a very different view of transform margins than 10 years ago. Some of the new concepts that have emerged  mendate to re assess our interpretation of exisiting datasets.</p>

Asymptotic Effect of Initial and Upstream Conditions on Turbulence

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
William K. George
Keyword(s):  
New York ◽  
Turbulent Flows ◽  
Coherent Structures ◽  
Large Scale ◽  
Initial Conditions ◽  
Single Point ◽  
Building Blocks ◽  
The Self ◽  
Asymptotic Independence ◽  
Small Scale

More than two decades ago the first strong experimental results appeared suggesting that turbulent flows might not be asymptotically independent of their initial (or upstream) conditions (Wygnanski et al., 1986, “On the Large-Scale Structures in Two-Dimensional Smalldeficit, Turbulent Wakes,” J. Fluid Mech., 168, pp. 31–71). And shortly thereafter the first theoretical explanations were offered as to why we came to believe something about turbulence that might not be true (George, 1989, “The Self-Preservation of Turbulent Flows and its Relation to Initial Conditions and Coherent Structures,” Advances in Turbulence, W. George and R. Arndt, eds., Hemisphere, New York, pp. 1–41). These were contrary to popular belief. It was recognized immediately that if turbulence was indeed asymptotically independent of its initial conditions, it meant that there could be no universal single point model for turbulence (George, 1989, “The Self-Preservation of Turbulent Flows and its Relation to Initial Conditions and Coherent Structures,” Advances in Turbulence, W. George and R. Arndt, eds., Hemisphere, New York, pp. 1–41; Taulbee, 1989, “Reynolds Stress Models Applied to Turbulent Jets,” Advances in Turbulence, W. George and R. Arndt, eds., Hemisphere, New York, pp. 29–73) certainly consistent with experience, but even so not easy to accept for the turbulence community. Even now the ideas of asymptotic independence still dominate most texts and teaching of turbulence. This paper reviews the substantial additional evidence - experimental, numerical and theoretical - for the asymptotic effect of initial and upstream conditions that has accumulated over the past 25 years. Also reviewed is evidence that the Kolmogorov theory for small scale turbulence is not as general as previously believed. Emphasis has been placed on the canonical turbulent flows (especially wakes, jets, and homogeneous decaying turbulence), which have been the traditional building blocks for our understanding. Some of the important outstanding issues are discussed; and implications for the future of turbulence modeling and research, especially LES and turbulence control, are also considered.

On non-self-similar regimes in homogeneous isotropic turbulence decay

2012 ◽  
Vol 711 ◽  
pp. 364-393 ◽  
Author(s):  
Marcello Meldi ◽  
Pierre Sagaut
Keyword(s):  
Energy Spectrum ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Initial Conditions ◽  
Self Similarity ◽  
Velocity Correlation ◽  
Turbulence Decay ◽  
Long Time ◽  
Self Similar ◽  
Decay Exponent

AbstractBoth theoretical analysis and eddy-damped quasi-normal Markovian (EDQNM) simulations are carried out to investigate the different decay regimes of an initially non-self-similar isotropic turbulence. Breakdown of self-similarity is due to the consideration of a composite three-range energy spectrum, with two different slopes at scales larger than the integral length scale. It is shown that, depending on the initial conditions, the solution can bifurcate towards a true self-similar decay regime, or sustain a non-self-similar state over an arbitrarily long time. It is observed that these non-self-similar regimes cannot be detected, restricting the observation to time exponents of global quantities such as kinetic energy or dissipation. The actual reason is that the decay is controlled by large scales close to the energy spectrum peak. This theoretical prediction is assessed by a detailed analysis of triadic energy transfers, which show that the largest scales have a negligible impact on the total transfers. Therefore, it is concluded that details of the energy spectrum near the peak, which may be related to the turbulence production mechanisms, are important. Since these mechanisms are certainly not universal, this may at least partially explain the significant discrepancies that exist between experimental data and theoretical predictions. Another conclusion is that classical self-similarity theories, which connect the asymptotic behaviour of either the energy spectrum $E(k\ensuremath{\rightarrow} 0)$ or the velocity correlation function $f(r\ensuremath{\rightarrow} + \infty )$ and the turbulence decay exponent, are not particularly relevant when the large-scale spectrum shape exhibits more than one range.

scholarly journals A model for simulating the deposition of water-lain sediments in dryland environments

2004 ◽  
Vol 8 (2) ◽  
pp. 122-134 ◽  
Author(s):  
M. A. Bunch ◽  
R. Mackay ◽  
J. H. Tellam ◽  
P. Turner
Keyword(s):  
Land Surface ◽  
Large Scale ◽  
Initial Conditions ◽  
Sedimentary Facies ◽  
Storm Event ◽  
Storm Events ◽  
Near Surface ◽  
Radial Profiles ◽  
Long Time ◽  
The Uk

Abstract. A numerical process-imitating model, the Discrete Storm Event Sedimentation Simulator (DSESS), has been developed to represent the climatic and hydraulic conditions of drylands in modelling their geomorphological development and sedimentary facies distributions. The ultimate aim is to provide insights into the lateral variability of permeability in the Triassic Sandstone aquifers of the UK for the study of solute movement. DSESS employs discrete storm-flood automata, released across a cellular landscape, to model sediment transport: erosion, migration and deposition. Sediment classes with different grain sizes can be modelled. Empirical process-based equations are used to quantify the movement of the automata, their erosion potential, sediment-carrying capacity and interaction with the underlying sediments. The approach emphasises the sequence of dryland storm events and associated floods rather than their timing. Flood events are assumed to be discrete in time. Preliminary tests carried out with DSESS using simple systems and idealised initial conditions produce lithological and land surface features characteristic of dryland settings and indicate the potential of the model for large-scale, long-time modelling of sedimentary facies development. Markedly different results are observed across the range of tests carried out in response to the non-linear interactions between the different elements of the landscape and the floodwaters simulated with DSESS. Simulations show that sediment accumulations develop concave upward radial profiles, plano-convex cross-profiles and possess a general lateral grading of sediment with distance from source. The internal grain size architecture shows evidence of both persistent and rapidly changing flow conditions, with both lateral and longitudinal stepping of coarse bodies produced by ‘scour and fill’ events and random avulsions. Armoured layers form so that near-surface sediments have increased likelihood of preservation. Future developments will include representation of aeolian deposition, mass wasting and hyper-concentrated (debris) flows. Keywords: avulsion, channel, deposition, drylands, erosion, gravel armouring, modelling, sheet-flood, transport capacity

scholarly journals Effects of initial conditions in decaying turbulence generated by passive grids

2007 ◽  
Vol 585 ◽  
pp. 395-420 ◽  
Author(s):  
P. LAVOIE ◽  
L. DJENIDI ◽  
R. A. ANTONIA
Keyword(s):  
Power Law ◽  
Large Scale ◽  
Velocity Structure ◽  
Isotropic Turbulence ◽  
Initial Conditions ◽  
Reynolds Numbers ◽  
Recent Analysis ◽  
Grid Turbulence ◽  
Power Law Exponent ◽  
Decaying Turbulence

The effects of initial conditions on grid turbulence are investigated for low to moderate Reynolds numbers. Four grid geometries are used to yield variations in initial conditions and a secondary contraction is introduced to improve the isotropy of the turbulence. The hot-wire measurements, believed to be the most detailed to date for this flow, indicate that initial conditions have a persistent impact on the large-scale organization of the flow over the length of the tunnel. The power-law coefficients, determined via an improved method, also depend on the initial conditions. For example, the power-law exponent m is affected by the various levels of large-scale organization and anisotropy generated by the different grids and the shape of the energy spectrum at low wavenumbers. However, the results show that these effects are primarily related to deviations between the turbulence produced in the wind tunnel and true decaying homogenous isotropic turbulence (HIT). Indeed, when isotropy is improved and the intensity of the large-scale periodicity, which is primarily associated with round-rod grids, is decreased, the importance of initial conditions on both the character of the turbulence and m is diminished. However, even in the case where the turbulence is nearly perfectly isotropic, m is not equal to −1, nor does it show an asymptotic trend in x towards this value, as suggested by recent analysis. Furthermore, the evolution of the second- and third-order velocity structure functions satisfies equilibrium similarity only approximately.

scholarly journals On the Semi-Analytical Solutions in Hydrodynamics of Ideal Fluid Flows Governed by Large-Scale Coherent Structures of Spiral-Type

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2307
Author(s):  
Sergey V. Ershkov ◽  
Alla Rachinskaya ◽  
Evgenii Yu. Prosviryakov ◽  
Roman V. Shamin
Keyword(s):  
Euler Equations ◽  
Coherent Structures ◽  
Large Scale ◽  
Stationary Solutions ◽  
Incompressible Fluids ◽  
Bottom Surface ◽  
Stationary Flows ◽  
Long Time ◽  
Partial Type ◽  
Spiral Type

We have presented here a clearly formulated algorithm or semi-analytical solving procedure for obtaining or tracing approximate hydrodynamical fields of flows (and thus, videlicet, their trajectories) for ideal incompressible fluids governed by external large-scale coherent structures of spiral-type, which can be recognized as special invariant at symmetry reduction. Examples of such structures are widely presented in nature in “wind-water-coastline” interactions during a long-time period. Our suggested mathematical approach has obvious practical meaning as tracing process of formation of the paths or trajectories for material flows of fallout descending near ocean coastlines which are forming its geometry or bottom surface of the ocean. In our presentation, we explore (as first approximation) the case of non-stationary flows of Euler equations for incompressible fluids, which should conserve the Bernoulli-function as being invariant for the aforementioned system. The current research assumes approximated solution (with numerical findings), which stems from presenting the Euler equations in a special form with a partial type of approximated components of vortex field in a fluid. Conditions and restrictions for the existence of the 2D and 3D non-stationary solutions of the aforementioned type have been formulated as well.

scholarly journals A New Surface Model for β-Plane Turbulence

2007 ◽  
Vol 64 (7) ◽  
pp. 2717-2725 ◽  
Author(s):  
Iordanka N. Panayotova
Keyword(s):  
Large Scale ◽  
Initial Conditions ◽  
Potential Temperature ◽  
Three Dimensional ◽  
Wave Turbulence ◽  
Surface Model ◽  
Surface Cooling ◽  
Rigid Boundary ◽  
Coriolis Parameter ◽  
Decaying Turbulence

Abstract This paper introduces a new numerical model for studying wave–turbulence interactions in a continuously stratified rotating flow, having a uniform potential vorticity and a rigid boundary. The meridional variation in the Coriolis parameter (β effect), a channel geometry, and the first-order nonlinear terms in a small Rossby number expansion are included into the surface quasigeostrophic dynamics. The model contains important dynamical characteristics of three-dimensional flows such as advection by ageostrophic winds, and stretching and tilting of relative vorticity. Nevertheless, it has the computational economy of two-dimensional flows. Long-term direct numerical simulations are performed for decaying turbulence arising from random initial conditions. In addition to the formation of steady zonal jets, frequently reported as a possible end state under the β effect, this model exhibits several other realistic physical effects that were lacking in the previously studied β-plane models for wave–turbulence interactions. There is a significant contrast in the spatial and time scales of the formed eddies, resulting in high meridional asymmetry of the flow. Mean surface cooling and persistent large-scale blocking eddies are observed as well. The surface potential temperature variance spectrum exhibits a well-resolved k−5/3 inertial range.

Role of coherent structures in multiple self-similar states of turbulent planar wakes

2013 ◽  
Vol 731 ◽  
pp. 312-363 ◽  
Author(s):  
Jean-Pierre Hickey ◽  
Fazle Hussain ◽  
Xiaohua Wu
Keyword(s):  
Coherent Structures ◽  
Large Scale ◽  
Initial Conditions ◽  
Entrainment Rate ◽  
Bypass Transition ◽  
Spread Rate ◽  
Instability Modes ◽  
Self Similar ◽  
The Individual ◽  
Far Wake

AbstractWe study the nature of archetypal, incompressible, planar splitter-plate wakes, specifically the effects of the exit boundary layer state on multiple approximate self-similarity. Temporally developing direct numerical simulations, at a Reynolds number of 1500 based on the volume-flux defect, are performed to investigate three distinct wake evolution scenarios: Kelvin–Helmholtz transition, bypass transition in an asymmetric wake, and an initially fully turbulent wake. The differences in the evolution and far-wake statistics are analysed in detail. The individual approximately self-similar states exhibit a relative variation of up to 48 % in the spread rate, in second-order statistics, and in peak values of the energy budget terms. The multiplicity of self-similar states is tied to the non-universality of the large-scale coherent structures. These structures maintain the memory of the initial conditions. In the far wake, two distinct spanwise-coherent motions are identified: (i) staggered, segregated spanwise rollers on either side of the centreplane, dominant in wakes transitioning via anti-symmetric instability modes; and, (ii) larger spanwise rollers spanning across the centreplane, emerging in the absence of a near-wake characteristic length scale. The latter structure is characterized by strong spanwise coherence, cross-wake velocity correlations and a larger entrainment rate caused by deep pockets of irrotational fluid within the folds of the turbulent/non-turbulent interface. The mid-sized structures, primarily vortical rods, are generic for all initial conditions and are inclined at ∼$\pm 3{3}^{\circ } $ to the downstream, shallower than the preferential $\pm 4{5}^{\circ } $ inclination of the vorticity vector. The spread rate is driven by the inner-wake dynamics, more specifically the advective flux of spanwise vorticity across the centreplane, which depends on the large-scale coherent structures.

scholarly journals A glimpse of fluid turbulence from the molecular scale

2014 ◽  
Vol 25 (08) ◽  
pp. 1450034 ◽  
Author(s):  
Teruhisa S. Komatsu ◽  
Shigenori Matsumoto ◽  
Takashi Shimada ◽  
Nobuyasu Ito
Keyword(s):  
Large Scale ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Md Simulations ◽  
Energy Dissipation Rate ◽  
Coarse Grained ◽  
Fluid Turbulence ◽  
Molecular Scale ◽  
Decaying Turbulence ◽  
Three Dimensional Space

Large-scale molecular dynamics (MD) simulations of freely decaying turbulence in three-dimensional space are reported. Fluid components are defined from the microscopic states by eliminating thermal components from the coarse-grained fields. The energy spectrum of the fluid components is observed to scale reasonably well according to Kolmogorov scaling determined from the energy dissipation rate and the viscosity of the fluid, even though the Kolmogorov length is of the order of the molecular scale.

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