Dynamics of interaction of vortices in shear turbulent flows

2021 ◽  
Vol 102 (2) ◽  
pp. 56-67
Author(s):  
A.Zh. Turmukhambetov ◽  
◽  
S.B. Otegenova ◽  
K.A. Aitmanova ◽  
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Spatial Scales ◽  
Equations Of Motion ◽  
Vortex Structures ◽  
Small Scale ◽  
Two Dimensional ◽  
Practical Applications ◽  
Kinematic Effect ◽  
The One

The paper analyzes the results of a theoretical study of quasi-two-dimensional turbulence, two-dimensional equations of motion of which contain additional terms. The regularities of the dynamic interaction of vortex structures in shear turbulent flows of a viscous liquid are established. Based on the model of quasi-twodimensional turbulence, numerical values of the spatial scales of intermittency are determined as an alternation of large-scale and small-scale pulsations of dynamic characteristics. The experimentally observed alternation of vortex structures and the idea of their self-organization form the basis of the assumption of the existence of a geometric parameter determined by the size of the vortex core and the distance between their centers. Therefore, the main attention is paid to the theoretical calculation of the minimum spatial scales of the intermittency of vortex clusters. As a simplification, the vortex pairs are located in a reference frame, relative to which the centers of the vortices are stationary. Thus, the kinematic effect of the transfer of one vortex into the field of another is excluded from consideration. The symmetric and unsymmetric interactions of vortices, taking into account the one-sided and opposite directions of their rotation, are considered as realizable cases. A successful attempt is made to study the influence of the internal structure of vortex clusters on the numerical values of the minimum intermittency scales. The obtained results are satisfactorily confirmed by known theoretical and experimental data. Consequently, they can be used in all practical applications, without exception, where the structure of turbulence is taken into account, as well as for improving and expanding existing semi-empirical theories.

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.

On the survival of strong vortex filaments in ‘model’ turbulence

1999 ◽  
Vol 394 ◽  
pp. 261-279 ◽  
Author(s):  
ROBERTO VERZICCO ◽  
JAVIER JIMÉNEZ
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Spatial Scales ◽  
Axial Strain ◽  
Compact Object ◽  
Mean Value ◽  
Theoretical Explanation ◽  
Small Scale ◽  
Vortex Filaments ◽  
Single Scale

This paper discusses numerical experiments in which an initially uniform columnar vortex is subject to several types of axisymmetric forcing that mimic the strain field of a turbulent flow. The mean value of the strain along the vortex axis is in all cases zero, and the vortex is alternately stretched and compressed. The emphasis is on identifying the parameter range in which the vortex survives indefinitely. This extends previous work in which the effect of steady single-scale non-uniform strains was studied. In a first series of experiments the effect of the unsteadiness of the forcing is analysed, and it is found that the vortex survives as a compact object if the ratio between the oscillation frequency and the strain itself is low enough. A theoretical explanation is given which agrees with the numerical results. The strain is then generalized to include several spatial scales and oscillation frequencies, with characteristics similar to those in turbulent flows. The largest velocities are carried by the large scales, while the highest gradients and faster time scales are associated with the shorter wavelengths. Also in these cases ‘infinitely long’ vortices are obtained which are more or less uniform and compact. Vorticity profiles averaged along their axes are approximately Gaussian. The radii obtained from these profiles are proportional to the Burgers' radius of the r.m.s. (small-scale) axial strain, while the azimuthal velocities are proportional to the maximum (large-scale) axial velocity differences. The study is motivated by previous observations of intense vortex filaments in turbulent flows, and the scalings found in the present experiments are consistent with those found in the turbulent simulations.

scholarly journals Turbulence in Large-Scale Two-Dimensional Balanced Hard Sphere Gas Flow

Atmosphere ◽  
2021 ◽  
Vol 12 (11) ◽  
pp. 1520
Author(s):  
Rafail V. Abramov
Keyword(s):  
Turbulent Flows ◽  
Hard Sphere ◽  
Large Scale ◽  
Gas Flow ◽  
Spatial Scales ◽  
Mean Field ◽  
Current Work ◽  
Two Dimensional ◽  
Dynamical Mechanism ◽  
Wide Range

In recent works, we developed a model of balanced gas flow, where the momentum equation possesses an additional mean field forcing term, which originates from the hard sphere interaction potential between the gas particles. We demonstrated that, in our model, a turbulent gas flow with a Kolmogorov kinetic energy spectrum develops from an otherwise laminar initial jet. In the current work, we investigate the possibility of a similar turbulent flow developing in a large-scale two-dimensional setting, where a strong external acceleration compresses the gas into a relatively thin slab along the third dimension. The main motivation behind the current work is the following. According to observations, horizontal turbulent motions in the Earth atmosphere manifest in a wide range of spatial scales, from hundreds of meters to thousands of kilometers. However, the air density rapidly decays with altitude, roughly by an order of magnitude each 15–20 km. This naturally raises the question as to whether or not there exists a dynamical mechanism which can produce large-scale turbulence within a purely two-dimensional gas flow. To our surprise, we discover that our model indeed produces turbulent flows and the corresponding Kolmogorov energy spectra in such a two-dimensional setting.

scholarly journals Stable spike clusters for the one-dimensional Gierer–Meinhardt system

2016 ◽  
Vol 28 (4) ◽  
pp. 576-635 ◽  
Author(s):  
JUNCHENG WEI ◽  
MATTHIAS WINTER
Keyword(s):  
Large Scale ◽  
Spatial Scales ◽  
Small Scale ◽  
Biologically Relevant ◽  
Formula Group ◽  
Group A ◽  
Scale Inhomogeneity ◽  
The One ◽  
Image Position ◽  
Small Scale Structures

We consider the Gierer–Meinhardt system with precursor inhomogeneity and two small diffusivities in an interval $$\begin{equation*} \left\{ \begin{array}{ll} A_t=\epsilon^2 A''- \mu(x) A+\frac{A^2}{H}, &x\in(-1, 1),\,t>0,\\[3mm] \tau H_t=D H'' -H+ A^2, & x\in (-1, 1),\,t>0,\\[3mm] A' (-1)= A' (1)= H' (-1) = H' (1) =0, \end{array} \right. \end{equation*}$$$$\begin{equation*}\mbox{where } \quad 0<\epsilon \ll\sqrt{D}\ll 1, \quad \end{equation*}$$$$\begin{equation*} \tau\geq 0 \mbox{ and $\tau$ is independent of $\epsilon$. } \end{equation*}$$ A spike cluster is the combination of several spikes which all approach the same point in the singular limit. We rigorously prove the existence of a steady-state spike cluster consisting of N spikes near a non-degenerate local minimum point t0 of the smooth positive inhomogeneity μ(x), i.e. we assume that μ′(t0) = 0, μ″(t0) > 0 and we have μ(t0) > 0. Here, N is an arbitrary positive integer. Further, we show that this solution is linearly stable. We explicitly compute all eigenvalues, both large (of order O(1)) and small (of order o(1)). The main features of studying the Gierer–Meinhardt system in this setting are as follows: (i) it is biologically relevant since it models a hierarchical process (pattern formation of small-scale structures induced by a pre-existing large-scale inhomogeneity); (ii) it contains three different spatial scales two of which are small: the O(1) scale of the precursor inhomogeneity μ(x), the $O(\sqrt{D})$ scale of the inhibitor diffusivity and the O(ε) scale of the activator diffusivity; (iii) the expressions can be made explicit and often have a particularly simple form.

The development and structure of turbulent plane jets

1978 ◽  
Vol 88 (3) ◽  
pp. 563-583 ◽  
Author(s):  
K. W. Everitt ◽  
A. G. Robins
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Equations Of Motion ◽  
Turbulent Jets ◽  
Small Scale ◽  
Turbulence Structure ◽  
Plane Jets ◽  
Turbulent Plane ◽  
Variable Eddy Viscosity ◽  
Highly Turbulent Flows

The structure and development of turbulent plane jets in still air and moving streams are described. The nature of the small-scale turbulence cannot be accurately ascertained because of the difficulties inherent in the measurement of dissipation in highly turbulent flows. Although correlation measurements in a jet in still air indicate a large-scale structure which can best be described as ‘local flapping’, measurements in a jet in a moving stream do not reveal a similar structure. The development of the turbulence structure in a jet in a moving parallel stream is described and the properties of turbulent jets and wakes are shown to be reasonably well predicted by the use of a variable-eddy-viscosity formula together with the formal self-preserving properties of the equations of motion.

scholarly journals 2D Nanomaterials for Effective Energy Scavenging

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Md Al Mahadi Hasan ◽  
Yuanhao Wang ◽  
Chris R. Bowen ◽  
Ya Yang
Keyword(s):  
Large Scale ◽  
Waste Heat ◽  
Material Selection ◽  
Power Supplies ◽  
Small Scale ◽  
Energy Scavenging ◽  
Power Sources ◽  
Practical Applications ◽  
2D Nanomaterials ◽  
Self Powered

AbstractThe development of a nation is deeply related to its energy consumption. 2D nanomaterials have become a spotlight for energy harvesting applications from the small-scale of low-power electronics to a large-scale for industry-level applications, such as self-powered sensor devices, environmental monitoring, and large-scale power generation. Scientists from around the world are working to utilize their engrossing properties to overcome the challenges in material selection and fabrication technologies for compact energy scavenging devices to replace batteries and traditional power sources. In this review, the variety of techniques for scavenging energies from sustainable sources such as solar, air, waste heat, and surrounding mechanical forces are discussed that exploit the fascinating properties of 2D nanomaterials. In addition, practical applications of these fabricated power generating devices and their performance as an alternative to conventional power supplies are discussed with the future pertinence to solve the energy problems in various fields and applications.

scholarly journals Enhancing ecosystem restoration efficiency through spatial and temporal coordination

2015 ◽  
Vol 112 (19) ◽  
pp. 6236-6241 ◽  
Author(s):  
Thomas M. Neeson ◽  
Michael C. Ferris ◽  
Matthew W. Diebel ◽  
Patrick J. Doran ◽  
Jesse R. O’Hanley ◽  
...  
Keyword(s):  
Great Lakes ◽  
Large Scale ◽  
Expert Knowledge ◽  
Spatial Scales ◽  
Small Scale ◽  
Space And Time ◽  
Ecosystem Connectivity ◽  
Breeding Grounds ◽  
Local Expert ◽  
Conservation Projects

In many large ecosystems, conservation projects are selected by a diverse set of actors operating independently at spatial scales ranging from local to international. Although small-scale decision making can leverage local expert knowledge, it also may be an inefficient means of achieving large-scale objectives if piecemeal efforts are poorly coordinated. Here, we assess the value of coordinating efforts in both space and time to maximize the restoration of aquatic ecosystem connectivity. Habitat fragmentation is a leading driver of declining biodiversity and ecosystem services in rivers worldwide, and we simultaneously evaluate optimal barrier removal strategies for 661 tributary rivers of the Laurentian Great Lakes, which are fragmented by at least 6,692 dams and 232,068 road crossings. We find that coordinating barrier removals across the entire basin is nine times more efficient at reconnecting fish to headwater breeding grounds than optimizing independently for each watershed. Similarly, a one-time pulse of restoration investment is up to 10 times more efficient than annual allocations totaling the same amount. Despite widespread emphasis on dams as key barriers in river networks, improving road culvert passability is also essential for efficiently restoring connectivity to the Great Lakes. Our results highlight the dramatic economic and ecological advantages of coordinating efforts in both space and time during restoration of large ecosystems.

scholarly journals Toward understanding the multiscale spatial spectrum of solar convection

2012 ◽  
Vol 8 (S294) ◽  
pp. 361-363
Author(s):  
A. V. Getling ◽  
O. S. Mazhorova ◽  
O. V. Shcheritsa
Keyword(s):  
Convective Instability ◽  
Convective Flow ◽  
Large Scale ◽  
Fluid Layer ◽  
Boussinesq Equations ◽  
Spatial Spectrum ◽  
Small Scale ◽  
Two Dimensional ◽  
Solar Convection

AbstractConvection is simulated numerically based on two-dimensional Boussinesq equations for a fluid layer with a specially chosen stratification such that the convective instability is much stronger in a thin subsurface sublayer than in the remaining part of the layer. The developing convective flow has a small-scale component superposed onto a basic large-scale roll flow.

Mycorrhizal fungal community relationship to root nitrogen concentration over a regional atmospheric nitrogen deposition gradient in the northeastern USA

2008 ◽  
Vol 38 (5) ◽  
pp. 1260-1266 ◽  
Author(s):  
Erik A. Lilleskov ◽  
Philip M. Wargo ◽  
Kristiina A. Vogt ◽  
Daniel J. Vogt
Keyword(s):  
Large Scale ◽  
Spatial Scales ◽  
Nitrogen Concentration ◽  
N Deposition ◽  
Small Scale ◽  
N Availability ◽  
Cenococcum Geophilum ◽  
Ectomycorrhizal Morphotypes ◽  
Deposition Gradient ◽  
Northeastern Usa

Increased nitrogen (N) input has been found to alter ectomycorrhizal fungal communities over short deposition gradients and in fertilization experiments; however, its effects over larger spatial scales have not been determined. To address this gap, we reanalyzed data from a study originally designed to examine the effects of soil aluminum/calcium (Al/Ca) ratios on the vitality of red spruce fine roots over a regional acid and N deposition gradient in the northeastern USA. We used root N as an indicator of stand N availability and examined its relationship with the abundance of ectomycorrhizal morphotypes. The dominant morphotypes changed in relative abundance as a function of stand N availability. As root N concentrations increased, Piloderma spp. - like, Cenococcum geophilum Fr., and other unidentified mycorrhizal morphotypes declined in abundance, while other smooth-mantled morphotypes increased. Root N concentration in the 1–2 mm diameter class was the best predictor of the abundance of multiple morphotypes. The morphotype responses were consistent with those found in experimental and small-scale studies, suggesting that N availability is altering ectomycorrhizal communities over broad spatial scales in this region. This finding provides an impetus to conduct a more detailed characterization of mycorrhizal community responses to N deposition across large-scale gradients.

The story of humanity and the challenge of posthumanity

2018 ◽  
Vol 32 (2) ◽  
pp. 101-120 ◽  
Author(s):  
Zoltán Boldizsár Simon
Keyword(s):  
Human Subject ◽  
Large Scale ◽  
Historical Narrative ◽  
Historical Narratives ◽  
Small Scale ◽  
Historical Understanding ◽  
New Era ◽  
And Gender ◽  
The One ◽  
Better Than

Today’s technological-scientific prospect of posthumanity simultaneously evokes and defies historical understanding. On the one hand, it implies a historical claim of an epochal transformation concerning posthumanity as a new era. On the other, by postulating the birth of a novel, better-than-human subject for this new era, it eliminates the human subject of modern Western historical understanding. In this article, I attempt to understand posthumanity as measured against the story of humanity as the story of history itself. I examine the fate of humanity as the central subject of history in three consecutive steps: first, by exploring how classical philosophies of history achieved the integrity of the greatest historical narrative of history itself through the very invention of humanity as its subject; second, by recounting how this central subject came under heavy criticism by postcolonial and gender studies in the last half-century, targeting the universalism of the story of humanity as the greatest historical narrative of history; and third, by conceptualizing the challenge of posthumanity against both the story of humanity and its criticism. Whereas criticism fragmented history but retained the possibility of smaller-scale narratives, posthumanity does not doubt the feasibility of the story of humanity. Instead, it necessarily invokes humanity, if only in order to be able to claim its supersession by a better-than-human subject. In that, it represents a fundamental challenge to the modern Western historical condition and the very possibility of historical narratives – small-scale or large-scale, fragmented or universal.

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