scholarly journals Interaction between mean flow and turbulence in two dimensions

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160287 ◽  
Author(s):  
Gregory Falkovich
Keyword(s):  
Short Note ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Mean Flow ◽  
Turbulence Statistics ◽  
Planar Domains ◽  
Developed Turbulence ◽  
Aspect Ratios ◽  
Simple Geometry ◽  
Turbulent Cascade

This short note is written to call attention to an analytic approach to the interaction of developed turbulence with mean flows of simple geometry (jets and vortices). It is instructive to compare cases in two and three dimensions and see why the former are solvable and the latter are not (yet). We present the analytical solutions for two-dimensional mean flows generated by an inverse turbulent cascade on a sphere and in planar domains of different aspect ratios. These solutions are obtained in the limit of small friction when the flow is strong while turbulence can be considered weak and treated perturbatively. I then discuss when these simple solutions can be realized and when more complicated flows may appear instead. The next step of describing turbulence statistics inside a flow and directions of possible future progress are briefly discussed at the end.

Compressible magnetoconvection in three dimensions: planforms and nonlinear behaviour

1995 ◽  
Vol 305 ◽  
pp. 281-305 ◽  
Author(s):  
P. C. Matthews ◽  
M. R. E. Proctor ◽  
N. O. Weiss
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Nonlinear Behaviour ◽  
Two Dimensional ◽  
Horizontal Shear ◽  
Mean Flow ◽  
The Magnetic Field

Convection in a compressible fiuid with an imposed vertical magnetic field is studied numerically in a three-dimensional Cartesian geometry with periodic lateral boundary conditions. Attention is restricted to the mildly nonlinear regime, with parameters chosen first so that convection at onset is steady, and then so that it is oscillatory.Steady convection occurs in the form of two-dimensional rolls when the magnetic field is weak. These rolls can become unstable to a mean horizontal shear flow, which in two dimensions leads to a pulsating wave in which the direction of the mean flow reverses. In three dimensions a new pattern is found in which the alignment of the rolls and the shear flow alternates.If the magnetic field is sufficiently strong, squares or hexagons are stable at the onset of convection. Both the squares and the hexagons have an asymmetrical topology, with upflow in plumes and downflow in sheets. For the squares this involves a resonance between rolls aligned with the box and rolls aligned digonally to the box. The preference for three-dimensional flow when the field is strong is a consequence of the compressibility of the layer- for Boussinesq magnetoconvection rolls are always preferred over squares at onset.In the regime where convection is oscillatory, the preferred planform for moderate fields is found to be alternating rolls - standing waves in both horizontal directions which are out of phase. For stronger fields, both alternating rolls and two-dimensional travelling rolls are stable. As the amplitude of convection is increased, either by dcereasing the magnetic field strength or by increasing the temperature contrast, the regular planform structure seen at onset is soon destroyed by secondary instabilities.

An asymptotic theory of the jet flap in three dimensions

1971 ◽  
Vol 46 (4) ◽  
pp. 705-726 ◽  
Author(s):  
Naoyuki Tokuda
Keyword(s):  
Order Approximation ◽  
Three Dimensional ◽  
Outer Region ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Simple Method ◽  
Aspect Ratios ◽  
Line Theory ◽  
Lifting Line ◽  
Lifting Line Theory

A uniformly valid asymptotic solution has been constructed for three-dimensional jet-flapped wings by the method of matched asymptotic expansions for high aspect ratios. The analysis assumes that the flow is inviscid and incompressible and is formulated on the thin airfoil theory in accordance with the well-established Spence (1961) theory in two dimensions.A simple method emerges in treating the bound vortices along the jet sheet which forms behind the wing with the aid of the following physical picture. Three distinct flow regions—namely inner, outer and Trefitz—exist in the problem. Close to the wing the flow approximates to that in two dimensions. Therefore, Spence's solution in two dimensions applies. In the outer region a wing shrinks to a line of singularities from which the main disturbances of flow in this region arise. In particular, we find that the shape of the jet sheet, hence the strength of vortices, is now predetermined by the strength of the singularities there. Hence a complete flow field in the outer region can now be determined first by evaluating the flow due to various degrees of singularities along this line and then adding the effect of the jet bound vortices which is now known. Far removed from the wing, the well-known Trefftz region exists in which calculations of aerodynamic forces can be most easily done.The result has been applied to various wing planforms such as cusped, elliptic and rectangular wings. The present result breaks down for rectangular wings. However, we can apply Stewartson's (1960) solution for lifting-line theory for semi-infinite rectangular wings, because, to this second-order approximation it is established that the jet sheet in the outer region makes no contribution to lift, with the direct contribution of the deflected jet at the exit being cancelled by the reduced circulation in the jet vortices. This result for the rectangular wing gives excellent agreement with the experiments made on a rectangular wing, while the result for elliptic wings underestimates them considerably.

Oscillatory two- and three-dimensional thermocapillary convection

1998 ◽  
Vol 364 ◽  
pp. 187-209 ◽  
Author(s):  
JIEYONG XU ◽  
ABDELFATTAH ZEBIB
Keyword(s):  
Reynolds Number ◽  
Critical Points ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Unstable Region ◽  
Infinite Layer ◽  
Aspect Ratios ◽  
Neutral Curves ◽  
Prandtl Numbers

The character and stability of two- and three-dimensional thermocapillary driven convection are investigated by numerical simulations. In two dimensions, Hopf bifurcation neutral curves are delineated for fluids with Prandtl numbers (Pr) 10.0, 6.78, 4.4 and 1.0 in the Reynolds number (Re)–cavity aspect ratio (Ax) plane corresponding to Re[les ]1.3×104 and Ax[les ]7.0. It is found that time-dependent motion is only possible if Ax exceeds a critical value, Axcr, which increases with decreasing Pr. There are two coexisting neutral curves for Pr[ges ]4.4. Streamline and isotherm patterns are presented at different Re and Ax corresponding to stationary and oscillatory states. Energy analyses of oscillatory flows are performed in the neighbourhood of critical points to determine the mechanisms leading to instability. Results are provided for flows near both critical points of the first unstable region with Ax=3.0 and Pr=10.In three dimensions, attention is focused on the influence of sidewalls, located at y=0 and y=Ay, and spanwise motion on the transition. In general, sidewalls have a damping effect on oscillations and hence increase the magnitude of the first critical Re. However, the existence of spanwise waves can reduce this critical Re. At large aspect ratios Ax=Ay=15, our results with Pr=13.9 at the lower critical Reynolds number of the first unstable region are in good agreement with those from infinite layer linear stability analysis.

A theory of the jet flap in three dimensions

1959 ◽  
Vol 251 (1266) ◽  
pp. 407-425 ◽  
Keyword(s):  
Aspect Ratio ◽  
Leading Edge ◽  
Elliptic Cylinder ◽  
Interpolation Formula ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Induced Drag ◽  
Aspect Ratios ◽  
The Difference

The treatment of two-dimensional jet-flapped wings in incompressible flow by the methods of thin-aerofoil theory given by one of the authors (Spence 1956) has been extended to the case of a thin wing of finite aspect ratio which possesses a deflected jet sheet of zero thickness emerging with a small angular deflexion at its trailing edge. The restriction is imposed that the streamlines of the jet flow lie in planes perpendicular to the wing-span, transverse momentum-transport being thus excluded. As in classical theories, the downwash field is assumed to arise from elementary horseshoe vortices proportional in strength to the local lift distribution; a new feature is the ability of the sheet formed by these elements to sustain a pressure difference on account of the longitudinal flux of momentum of the jet within it. The induced downwash w i ( x, y ) in the plane z = 0 at intermediate distances x from the wing cannot be calculated, and is therefore replaced by an interpolation formula having the correct values U ∞ α i at the wing and U ∞ α i ∞ far downstream. To ensure that the errors so introduced are small the aspect ratio A must be large, its permissible minimum increasing with the jet momentum coefficient C J . Two methods of interpolating to w i ( x, y ), both of which lead within close limits to the same expression for C L , are discussed. They are chosen so as to allow the two-dimensional equation for loading, whose solution is known, to be used to calculate the loading in a streamwise section in three dimensions. The spanwise variation of loading could be calculated for arbitrary planforms and jet-momentum distributions, but the present paper is confined to the case in which the loading and downwash distribution depend only on x/c , where x measures distance from the leading edge and c ( y ) is the local chord. This is shown to require both c and the jet-momentum flux per unit span to be elliptically distributed, the deflexion τ and incidence a being constant over the span. The relation between the coefficients of induced drag and lift is then C D i = C (2) L /( πA + 2 C J ) induced drag being defined as the difference between the thrust and the (constant) flux of momentum in the jet. (The interpolations for induced downwash are not used in deriving this relation.) The ratio of C L to the value C (2) L which it would have in two dimensions is C L / C (2) L = { A + (2/π) C J } / { A + 2/π ) (∂ C (2) L /∂α) - 2(1+ σ)}, where ∂ C (2) L /∂α is the two-dimensional derivative of lift with respect to incidence, a known function of C J and σ = 1 — α i /(½ α i ∞ ). An expression for σ is found in terms of known quantities by equating the induced drag calculated from the detailed forces on the wing to that given above. The results have been compared with experimental measurements made on an 8:1 elliptic cylinder of rectangular planform at aspect ratios 2⋅75, 6⋅8 and infinity. Remarkably close agreement with observed values of C L is obtained in all cases, and the difference C D — C Di = C D 0 , say, between the total- and induced-drag coefficients, is virtually independent of the aspect ratio. C D 0 represents the effects of the Reynolds number, section shape and jet configuration, which are excluded from the present theory.

scholarly journals Data on Orientation to Happiness in Higher Education Institutions from Mexico and El Salvador

Data ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 27
Author(s):  
Domingo Villavicencio-Aguilar ◽  
Edgardo René Chacón-Andrade ◽  
Maria Fernanda Durón-Ramos
Keyword(s):  
Higher Education ◽  
El Salvador ◽  
Latin American ◽  
Higher Education Institutions ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Stepwise Multiple Regression ◽  
Teacher Student ◽  
And Gender ◽  
Student’S T

Happiness-oriented people are vital in every society; this is a construct formed by three different types of happiness: pleasure, meaning, and engagement, and it is considered as an indicator of mental health. This study aims to provide data on the levels of orientation to happiness in higher-education teachers and students. The present paper contains data about the perception of this positive aspect in two Latin American countries, Mexico and El Salvador. Structure instruments to measure the orientation to happiness were administrated to 397 teachers and 260 students. This data descriptor presents descriptive statistics (mean, standard deviation), internal consistency (Cronbach’s alpha), and differences (Student’s t-test) presented by country, population (teacher/student), and gender of their orientation to happiness and its three dimensions: meaning, pleasure, and engagement. Stepwise-multiple-regression-analysis results are also presented. Results indicated that participants from both countries reported medium–high levels of meaning and engagement happiness; teachers reported higher levels than those of students in these two dimensions. Happiness resulting from pleasure activities was the least reported in general. Males and females presented very similar levels of orientation to happiness. Only the population (teacher/student) showed a predictive relationship with orientation to happiness; however, the model explained a small portion of variance in this variable, which indicated that other factors are more critical when promoting orientation to happiness in higher-education institutions.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

scholarly journals On the forces that cable webs under tension can support and how to design cable webs to channel stresses

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180781 ◽  
Author(s):  
Guy Bouchitté ◽  
Ornella Mattei ◽  
Graeme W. Milton ◽  
Pierre Seppecher
Keyword(s):  
Linear Programming ◽  
Convex Hull ◽  
Structural Engineering ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finite Dimensional ◽  
Necessary And Sufficient

In many applications of structural engineering, the following question arises: given a set of forces f 1 ,  f 2 , …,  f N applied at prescribed points x 1 ,  x 2 , …,  x N , under what constraints on the forces does there exist a truss structure (or wire web) with all elements under tension that supports these forces? Here we provide answer to such a question for any configuration of the terminal points x 1 ,  x 2 , …,  x N in the two- and three-dimensional cases. Specifically, the existence of a web is guaranteed by a necessary and sufficient condition on the loading which corresponds to a finite dimensional linear programming problem. In two dimensions, we show that any such web can be replaced by one in which there are at most P elementary loops, where elementary means that the loop cannot be subdivided into subloops, and where P is the number of forces f 1 ,  f 2 , …,  f N applied at points strictly within the convex hull of x 1 ,  x 2 , …,  x N . In three dimensions, we show that, by slightly perturbing f 1 ,  f 2 , …,  f N , there exists a uniloadable web supporting this loading. Uniloadable means it supports this loading and all positive multiples of it, but not any other loading. Uniloadable webs provide a mechanism for channelling stress in desired ways.

scholarly journals PARALLEL DELAUNAY REFINEMENT: ALGORITHMS AND ANALYSES

2007 ◽  
Vol 17 (01) ◽  
pp. 1-30 ◽  
Author(s):  
DANIEL A. SPIELMAN ◽  
SHANG-HUA TENG ◽  
ALPER ÜNGÖR
Keyword(s):  
Mesh Size ◽  
Constant Factor ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Delaunay Refinement ◽  
Steiner Points ◽  
Input Domain ◽  
Set Of Points ◽  
Refinement Algorithm

We present a parallel Delaunay refinement algorithm for generating well-shaped meshes in both two and three dimensions. Like its sequential counterparts, the parallel algorithm iteratively improves the quality of a mesh by inserting new points, the Steiner points, into the input domain while maintaining the Delaunay triangulation. The Steiner points are carefully chosen from a set of candidates that includes the circumcenters of poorly-shaped triangular elements. We introduce a notion of independence among possible Steiner points that can be inserted simultaneously during Delaunay refinements and show that such a set of independent points can be constructed efficiently and that the number of parallel iterations is O( log 2Δ), where Δ is the spread of the input — the ratio of the longest to the shortest pairwise distances among input features. In addition, we show that the parallel insertion of these set of points can be realized by sequential Delaunay refinement algorithms such as by Ruppert's algorithm in two dimensions and Shewchuk's algorithm in three dimensions. Therefore, our parallel Delaunay refinement algorithm provides the same shape quality and mesh-size guarantees as these sequential algorithms. For generating quasi-uniform meshes, such as those produced by Chew's algorithms, the number of parallel iterations is in fact O( log Δ). To the best of our knowledge, our algorithm is the first provably polylog(Δ) time parallel Delaunay-refinement algorithm that generates well-shaped meshes of size within a constant factor of the best possible.

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