scholarly journals General formalism for a reduced description and modelling of momentum and energy transfer in turbulence

2019 ◽  
Vol 866 ◽  
pp. 865-896 ◽  
Author(s):  
A. Cimarelli ◽  
A. Abbà ◽  
M. Germano
Keyword(s):  
Turbulent Viscosity ◽  
Small Scale ◽  
New Formalism ◽  
Classical Models ◽  
The Rich ◽  
Scale Turbulence ◽  
Subgrid Stresses ◽  
Definition Of ◽  
Stability Issues ◽  
Subgrid Stress

Based on hierarchies of filter lengths, the large eddy decomposition and the related subgrid stresses are recognized to represent generalized central moments for the study and modelling of the different modes composing turbulence. In particular, the subgrid stresses and the subgrid dissipation are shown to be alternative observables for quantitatively assessing the scale-dependent properties of momentum flux (subgrid stresses) and the energy exchange between the large and small scales (subgrid dissipation). In this work we present a theoretical framework for the study of the subgrid stress and dissipation. Starting from an alternative decomposition of the turbulent stresses, a new formalism for their approximation and understanding is proposed which is based on a tensorial turbulent viscosity. The derived formalism highlights that every decomposition of the turbulent stresses is naturally approximated by a general form of turbulent viscosity tensor based on velocity increments which is then recognized to be a peculiar property of small-scale stresses in turbulence. The analysis in a turbulent channel shows the rich physics of the small-scale stresses which is unveiled by the tensorial formalism and usually missed in scalar approaches. To further exploit the formalism, we also show how it can be used to derive new modelling approaches. The proposed models are based on the second- and third-order inertial properties of the grid element. The basic idea is that the structure of the integration volume for filtering (either implicit or explicit) impacts the anisotropy and inhomogeneity of the filtered-out motions and, hence, this information could be leveraged to improve the prediction of the main unknown features of small-scale turbulence. The formalism provides also a rigorous definition of characteristic lengths for the turbulent stresses, which can be computed in every type of computational elements, thus overcoming the rather elusive definition of filter length commonly employed in more classical models. A preliminary analysis in a turbulent channel shows reasonable results. In order to solve numerical stability issues, a tensorial dynamic procedure for the evolution of the model constants is also developed. The generality of the procedure is such that it can be employed also in more conventional closures.

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.

scholarly journals Spherical convective dynamos in the rapidly rotating asymptotic regime

2017 ◽  
Vol 813 ◽  
pp. 558-593 ◽  
Author(s):  
Julien Aubert ◽  
Thomas Gastine ◽  
Alexandre Fournier
Keyword(s):  
Large Scale ◽  
Scaling Laws ◽  
Numerical Solutions ◽  
Strong Field ◽  
Magnetic Reynolds Number ◽  
Small Scale ◽  
Asymptotic State ◽  
Asymptotic Regime ◽  
Classical Models ◽  
Definition Of

Self-sustained convective dynamos in planetary systems operate in an asymptotic regime of rapid rotation, where a balance is thought to hold between the Coriolis, pressure, buoyancy and Lorentz forces (the MAC balance). Classical numerical solutions have previously been obtained in a regime of moderate rotation where viscous and inertial forces are still significant. We define a uni-dimensional path in parameter space between classical models and asymptotic conditions from the requirements to enforce a MAC balance and to preserve the ratio between the magnetic diffusion and convective overturn times (the magnetic Reynolds number). Direct numerical simulations performed along this path show that the spatial structure of the solution at scales larger than the magnetic dissipation length is largely invariant. This enables the definition of large-eddy simulations resting on the assumption that small-scale details of the hydrodynamic turbulence are irrelevant to the determination of the large-scale asymptotic state. These simulations are shown to be in good agreement with direct simulations in the range where both are feasible, and can be computed for control parameter values far beyond the current state of the art, such as an Ekman number $E=10^{-8}$. We obtain strong-field convective dynamos approaching the MAC balance and a Taylor state to an unprecedented degree of accuracy. The physical connection between classical models and asymptotic conditions is shown to be devoid of abrupt transitions, demonstrating the asymptotic relevance of classical numerical dynamo mechanisms. The fields of the system are confirmed to follow diffusivity-free, power-based scaling laws along the path.

scholarly journals A new model of shoaling and breaking waves: one-dimensional solitary wave on a mild sloping beach

2019 ◽  
Vol 862 ◽  
pp. 552-591 ◽  
Author(s):  
M. Kazakova ◽  
G. L. Richard
Keyword(s):  
Solitary Wave ◽  
Large Scale ◽  
Turbulent Viscosity ◽  
Inertial Subrange ◽  
Small Scale ◽  
Sudden Increase ◽  
One Dimensional ◽  
Turbulent Reynolds Number ◽  
Scale Turbulence ◽  
Sloping Beach

We present a new approach to model coastal waves in the shoaling and surf zones. The model can be described as a depth-averaged large-eddy simulation model with a cutoff in the inertial subrange. The large-scale turbulence is explicitly resolved through an extra variable called enstrophy while the small-scale turbulence is modelled with a turbulent-viscosity hypothesis. The equations are derived by averaging the mass, momentum and kinetic energy equations assuming a shallow-water flow, a negligible bottom shear stress and a weakly turbulent flow assumption which is not restrictive in practice. The model is fully nonlinear and has the same dispersive properties as the Green–Naghdi equations. It is validated by numerical tests and by comparison with experimental results of the literature on the propagation of a one-dimensional solitary wave over a mild sloping beach. The wave breaking is characterized by a sudden increase of the enstrophy which allows us to propose a breaking criterion based on the new concept of virtual enstrophy. The model features three empirical parameters. The first one governs the turbulent dissipation and was found to be a constant. The eddy viscosity is determined by a turbulent Reynolds number depending only on the bottom slope. The third parameter defines the breaking criterion and depends only on the wave initial nonlinearity. These dependences give a predictive character to the model which is suitable for further developments.

Contesting the City

2017 ◽  
Author(s):  
Christian D. Liddy
Keyword(s):  
Urban Politics ◽  
Low Countries ◽  
Late Medieval ◽  
Urban Citizenship ◽  
Town Government ◽  
Medieval Europe ◽  
Political Narrative ◽  
Classical Models ◽  
The Rich ◽  
The City

The political narrative of late medieval English towns is often reduced to the story of the gradual intensification of oligarchy, in which power was exercised and projected by an ever smaller ruling group over an increasingly subservient urban population. This book takes its inspiration not from English historiography, but from a more dynamic continental scholarship on towns in the southern Low Countries, Germany, and France. Its premise is that scholarly debate about urban oligarchy has obscured contemporary debate about urban citizenship. It identifies from the records of English towns a tradition of urban citizenship, which did not draw upon the intellectual legacy of classical models of the ‘citizen’. This was a vernacular citizenship, which was not peculiar to England, but which was present elsewhere in late medieval Europe. It was a citizenship that was defined and created through action. There were multiple, and divergent, ideas about citizenship, which encouraged townspeople to make demands, to assert rights, and to resist authority. This book exploits the rich archival sources of the five major towns in England—Bristol, Coventry, London, Norwich, and York—in order to present a new picture of town government and urban politics over three centuries. The power of urban governors was much more precarious than historians have imagined. Urban oligarchy could never prevail—whether ideologically or in practice—when there was never a single, fixed meaning of the citizen.

Similarity of dissipation and enstrophy in particle-induced small-scale turbulence

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Zhuo Wang ◽  
Kun Luo ◽  
Junhua Tan ◽  
Dong Li ◽  
Jianren Fan
Keyword(s):  
Small Scale ◽  
Scale Turbulence

scholarly journals Reframing ‘integration’: acknowledging and addressing five core critiques

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Sarah Spencer ◽  
Katharine Charsley
Keyword(s):  
Empirical Research ◽  
Recent Criticism ◽  
Heuristic Model ◽  
Migration Studies ◽  
Methodological Nationalism ◽  
Narrow Focus ◽  
The Subject ◽  
The Rich ◽  
Definition Of

AbstractEmpirical and theoretical insights from the rich body of research on ‘integration’ in migration studies have led to increasing recognition of its complexity. Among European scholars, however, there remains no consensus on how integration should be defined nor what the processes entail. Integration has, moreover, been the subject of powerful academic critiques, some decrying any further use of the concept. In this paper we argue that it is both necessary and possible to address each of the five core critiques on which recent criticism has focused: normativity; negative objectification of migrants as ‘other’; outdated imaginary of society; methodological nationalism; and a narrow focus on migrants in the factors shaping integration processes. We provide a definition of integration, and a revised heuristic model of integration processes and the ‘effectors’ that have been shown to shape them, as a contribution to a constructive debate on the ways in which these challenges for empirical research can be overcome.

scholarly journals THE PROTECTION OF THE RICH AGAINST THE POOR: THE POLITICS OF ADAM SMITH’S POLITICAL ECONOMY

2020 ◽  
Vol 37 (1) ◽  
pp. 138-158
Author(s):  
James A. Harris
Keyword(s):  
Political Economy ◽  
Political Culture ◽  
The Political ◽  
Ordinary People ◽  
General Attitude ◽  
The Poor ◽  
Natural Forms ◽  
The Rich ◽  
Definition Of ◽  
Point Of Departure

AbstractMy point of departure in this essay is Smith’s definition of government. “Civil government,” he writes, “so far as it is instituted for the security of property, is in reality instituted for the defence of the rich against the poor, or of those who have some property against those who have none at all.” First I unpack Smith’s definition of government as the protection of the rich against the poor. I argue that, on Smith’s view, this is always part of what government is for. I then turn to the question of what, according to Smith, our governors can do to protect the wealth of the rich from the resentment of the poor. I consider, and reject, the idea that Smith might conceive of education as a means of alleviating the resentment of the poor at their poverty. I then describe how, in his lectures on jurisprudence, Smith refines and develops Hume’s taxonomy of the opinions upon which all government rests. The sense of allegiance to government, according to Smith, is shaped by instinctive deference to natural forms of authority as well as by rational, Whiggish considerations of utility. I argue that it is the principle of authority that provides the feelings of loyalty upon which government chiefly rests. It follows, I suggest, that to the extent that Smith looked to government to protect the property of the rich against the poor, and thereby to maintain the peace and stability of society at large, he cannot have sought to lessen the hold on ordinary people of natural sentiments of deference. In addition, I consider the implications of Smith’s theory of government for the question of his general attitude toward poverty. I argue against the view that Smith has recognizably “liberal,” progressive views of how the poor should be treated. Instead, I locate Smith in the political culture of the Whiggism of his day.

scholarly journals Role of large-scale advection and small-scale turbulence on vertical migration of gyrotactic swimmers

2019 ◽  
Vol 4 (12) ◽  
Author(s):  
C. Marchioli ◽  
H. Bhatia ◽  
G. Sardina ◽  
L. Brandt ◽  
A. Soldati
Keyword(s):  
Vertical Migration ◽  
Large Scale ◽  
Small Scale ◽  
Scale Turbulence
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