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 Turbulent 2.5-dimensional dynamos

2016 ◽  
Vol 799 ◽  
pp. 246-264 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Two Dimensional Flow

We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components $(u(x,y,t),v(x,y,t),w(x,y,t))$ that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier–Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers $Re$, magnetic Reynolds numbers $Rm$ and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows $Pm=Rm/Re$, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of $Re$ and the asymptotic behaviour in the large $Rm$ limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

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.

scholarly journals Persistent magnetic vortex flow at a supergranular vertex

2018 ◽  
Vol 610 ◽  
pp. A84 ◽  
Author(s):  
Iker S. Requerey ◽  
Basilio Ruiz Cobo ◽  
Milan Gošić ◽  
Luis R. Bellot Rubio
Keyword(s):  
Magnetic Fields ◽  
Large Scale ◽  
Vortex Flow ◽  
Spatial Scales ◽  
Magnetic Vortex ◽  
Magnetic Feature ◽  
Magnetic Element ◽  
Flow Maps ◽  
Wide Range ◽  
Intensity Images

Context. Photospheric vortex flows are thought to play a key role in the evolution of magnetic fields. Recent studies show that these swirling motions are ubiquitous in the solar surface convection and occur in a wide range of temporal and spatial scales. Their interplay with magnetic fields is poorly characterized, however. Aims. We study the relation between a persistent photospheric vortex flow and the evolution of a network magnetic element at a supergranular vertex. Methods. We used long-duration sequences of continuum intensity images acquired with Hinode and the local correlation-tracking method to derive the horizontal photospheric flows. Supergranular cells are detected as large-scale divergence structures in the flow maps. At their vertices, and cospatial with network magnetic elements, the velocity flows converge on a central point. Results. One of these converging flows is observed as a vortex during the whole 24 h time series. It consists of three consecutive vortices that appear nearly at the same location. At their core, a network magnetic element is also detected. Its evolution is strongly correlated to that of the vortices. The magnetic feature is concentrated and evacuated when it is caught by the vortices and is weakened and fragmented after the whirls disappear. Conclusions. This evolutionary behavior supports the picture presented previously, where a small flux tube becomes stable when it is surrounded by a vortex flow.

scholarly journals EXPRESS: Sources of Variation In Search and Foraging A Theoretical Perspective

2021 ◽  
pp. 174702182110503
Author(s):  
Alastair David Smith ◽  
Carlo De Lillo
Keyword(s):  
Spatial Scales ◽  
Theoretical Perspective ◽  
Search Space ◽  
Visual Exploration ◽  
Two Dimensional ◽  
Search Behaviour ◽  
Wide Range ◽  
Search Processes ◽  
Sources Of Variation ◽  
The Individual

Search – the problem of exploring a space of alternatives in order to identify target goals – is a fundamental behaviour for many species. Although its foundation lies in foraging, most studies of human search behaviour have been directed towards understanding the attentional mechanisms that underlie the efficient visual exploration of two-dimensional scenes. With this review, we aim to characterise how search behaviour can be explained across a wide range of contexts, environments, spatial scales, and populations, both typical and atypical. We first consider the generality of search processes across psychological domains. We then review studies of interspecies differences in search. Finally, we explore in detail the individual and contextual variables that affect visual search and related behaviours in established experimental psychology paradigms. Despite the heterogeneity of the findings discussed, we identify that variations in control processes, along with the ability to regulate behaviour as a function of the structure of search space and the sampling processes adopted, to be central to explanations of variations in search behaviour. We propose a tentative theoretical model aimed at integrating these notions and close by exploring questions that remain unaddressed.

A new model of shoaling and breaking waves. Part 2. Run-up and two-dimensional waves

2019 ◽  
Vol 867 ◽  
pp. 146-194 ◽  
Author(s):  
G. L. Richard ◽  
A. Duran ◽  
B. Fabrèges
Keyword(s):  
Large Scale ◽  
Turbulent Viscosity ◽  
Breaking Waves ◽  
Small Scale ◽  
Two Dimensional ◽  
Numerical Resolution ◽  
Wide Range ◽  
Scale Turbulence ◽  
Run Up ◽  
Averaged Model

We derive a two-dimensional depth-averaged model for coastal waves with both dispersive and dissipative effects. A tensor quantity called enstrophy models the subdepth large-scale turbulence, including its anisotropic character, and is a source of vorticity of the average flow. The small-scale turbulence is modelled through a turbulent-viscosity hypothesis. This fully nonlinear model has equivalent dispersive properties to the Green–Naghdi equations and is treated, both for the optimization of these properties and for the numerical resolution, with the same techniques which are used for the Green–Naghdi system. The model equations are solved with a discontinuous Galerkin discretization based on a decoupling between the hyperbolic and non-hydrostatic parts of the system. The predictions of the model are compared to experimental data in a wide range of physical conditions. Simulations were run in one-dimensional and two-dimensional cases, including run-up and run-down on beaches, non-trivial topographies, wave trains over a bar or propagation around an island or a reef. A very good agreement is reached in every cases, validating the predictive empirical laws for the parameters of the model. These comparisons confirm the efficiency of the present strategy, highlighting the enstrophy as a robust and reliable tool to describe wave breaking even in a two-dimensional context. Compared with existing depth-averaged models, this approach is numerically robust and adds more physical effects without significant increase in numerical complexity.

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.

scholarly journals Condensates in thin-layer turbulence

2019 ◽  
Vol 864 ◽  
pp. 490-518 ◽  
Author(s):  
Adrian van Kan ◽  
Alexandros Alexakis
Keyword(s):  
Steady State ◽  
Layer Thickness ◽  
Turbulent Flows ◽  
Mean Field ◽  
Direct Numerical Simulations ◽  
Thin Layers ◽  
Scale Model ◽  
Two Dimensional ◽  
Critical Height ◽  
Basic Features

We examine the steady state of turbulent flows in thin layers using direct numerical simulations. It is shown that when the layer thickness is smaller than a critical height, an inverse cascade arises which leads to the formation of a steady state condensate where most of the energy is concentrated in the largest scale of the system. For layers of thickness smaller than a second critical height, the flow at steady state becomes exactly two-dimensional. The amplitude of the condensate is studied as a function of layer thickness and Reynolds number. Bi-stability and intermittent bursts are found close to the two critical points. The results are interpreted based on a mean-field three-scale model that reproduces some of the basic features of the numerical results.

scholarly journals Two-Dimensional Evaluation of ATHAM-Fluidity, a Nonhydrostatic Atmospheric Model Using Mixed Continuous/Discontinuous Finite Elements and Anisotropic Grid Optimization

2016 ◽  
Vol 144 (11) ◽  
pp. 4349-4372 ◽  
Author(s):  
Julien Savre ◽  
James Percival ◽  
Michael Herzog ◽  
Chris Pain
Keyword(s):  
Optimization Algorithm ◽  
Large Scale ◽  
Atmospheric Model ◽  
Computational Time ◽  
Limited Area ◽  
Test Cases ◽  
Two Dimensional ◽  
Element Discretization ◽  
Wide Range ◽  
Grid Optimization

Abstract This paper presents the first attempt to apply the compressible nonhydrostatic Active Tracer High-Resolution Atmospheric Model–Fluidity (ATHAM-Fluidity) solver to a series of idealized atmospheric test cases. ATHAM-Fluidity uses a hybrid finite-element discretization where pressure is solved on a continuous second-order grid while momentum and scalars are computed on a first-order discontinuous grid (also known as ). ATHAM-Fluidity operates on two- and three-dimensional unstructured meshes, using triangular or tetrahedral elements, respectively, with the possibility to employ an anisotropic mesh optimization algorithm for automatic grid refinement and coarsening during run time. The solver is evaluated using two-dimensional-only dry idealized test cases covering a wide range of atmospheric applications. The first three cases, representative of atmospheric convection, reveal the ability of ATHAM-Fluidity to accurately simulate the evolution of large-scale flow features in neutral atmospheres at rest. Grid convergence without adaptivity as well as the performances of the Hermite–Weighted Essentially Nonoscillatory (Hermite-WENO) slope limiter are discussed. These cases are also used to test the grid optimization algorithm implemented in ATHAM-Fluidity. Adaptivity can result in up to a sixfold decrease in computational time and a fivefold decrease in total element number for the same finest resolution. However, substantial discrepancies are found between the uniform and adapted grid results, thus suggesting the necessity to improve the reliability of the approach. In the last three cases, corresponding to atmospheric gravity waves with and without orography, the model ability to capture the amplitude and propagation of weak stationary waves is demonstrated. This work constitutes the first step toward the development of a new comprehensive limited area atmospheric model.

NEW CHALLENGES FACING INTEGRATIVE BIOLOGICAL SCIENCE IN THE POST-GENOMIC ERA

2006 ◽  
Vol 14 (02) ◽  
pp. 275-293 ◽  
Author(s):  
CHRISTOPHER S. OEHMEN ◽  
TJERK P. STRAATSMA ◽  
GORDON A. ANDERSON ◽  
GALYA ORR ◽  
BOBBIE-JO M. WEBB-ROBERTSON ◽  
...  
Keyword(s):  
Paradigm Shift ◽  
Large Scale ◽  
Experimental Testing ◽  
Spatial Scales ◽  
Geographical Area ◽  
Biological Data ◽  
Biological Research ◽  
Complex Data ◽  
Discovery Research ◽  
Wide Range

The future of biology will be increasingly driven by the fundamental paradigm shift from hypothesis-driven research to data-driven discovery research employing the growing volume of biological data coupled to experimental testing of new discoveries. But hardware and software limitations in the current workflow infrastructure make it impossible or intractible to use real data from disparate sources for large-scale biological research. We identify key technological developments needed to enable this paradigm shift involving (1) the ability to store and manage extremely large datasets which are dispersed over a wide geographical area, (2) development of novel analysis and visualization tools which are capable of operating on enormous data resources without overwhelming researchers with unusable information, and (3) formalisms for integrating mathematical models of biosystems from the molecular level to the organism population level. This will require the development of algorithms and tools which efficiently utilize high-performance compute power and large storage infrastructures. The end result will be the ability of a researcher to integrate complex data from many different sources with simulations to analyze a given system at a wide range of temporal and spatial scales in a single conceptual model.

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.

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