Large-scale structure of isotropic homogeneous turbulence

1983 ◽  
Vol 22 (1) ◽  
pp. 87-92 ◽  
Author(s):  
Gerald Rosen
Keyword(s):  
Large Scale ◽  
Large Scale Structure ◽  
Scale Structure ◽  
Homogeneous Turbulence

The large-scale structure of homogenous turbulence

1956 ◽  
Vol 248 (949) ◽  
pp. 369-405 ◽  
Keyword(s):  
Large Scale ◽  
Asymptotic Form ◽  
Large Scale Structure ◽  
Scale Structure ◽  
Homogeneous Turbulence ◽  
Wave Number ◽  
Initial Condition ◽  
Triple Correlation ◽  
Leading Term ◽  
Asymptotic Forms

The starting-point for this paper lies in some results obtained by Proudman & Reid (1954) for isotropic turbulence with zero fourth-order cumulants. They showed in that case that the quantity _ /*00 u2 r4f(r) dr is not a dynamical invariant and that the first time derivative of the triple correlation J0 k( r ) is of order r -4 when r is large. The customary assumption that all velocity cumulants in homogeneous turbulence are exponentially small for large separations, and the consequent results, about the large-scale structure of the motion and about the final period of decay of the turbulence, are thus suspect, and we have redeveloped the whole subject ab initio. The fallacy in the old assumption of exponentially small cumulants can be ascribed to the action of pressure forces, which are local in their effect but which have values determined instantaneously by the whole velocity field. If at some initial instant a finite region only of an infinite fluid is in motion, at subsequent instants pressure forces generate a surrounding irrotational velocity distribution that falls off as some integral power of the distance from the central region. Likewise, the action of pressure forces in homogeneous turbulence is to ensure the development of algebraic asymptotic forms of velocity cumulants, the analogue of the finite region of initial motion being a volume of the fluid over which the vorticity is effectively correlated. However, an essential difference between the two cases is that in homogeneous turbulence pressure forces also build up long-range statistical connexions in the vorticity distribution. Having recognized why the old assumption is wrong, it is necessary to consider what kinds of asymptotic forms of velocity cumulants (for large separation) are dynamically persistent, and to consider in particular what asymptotic forms are likely to occur when homogeneous turbulence is generated in the usual way by setting a regular array of rods across a uniform stream. We have been able to find only one kind of large-scale structure that is unchanged by dynamical action, and this is also the kind of large-scale structure that develops from a plausibly idealized initial condition representing the effect of the grid on the stream. This initial condition, according to the hypothesis on which the positive results of this paper are based, is that there is a virtual origin in time at which all integral moments of cumulants of the velocity field converge. The important consequence of this hypothesis is that the effect of pressure forces is subsequently to develop asymptotic forms that are integral power-laws. It is shown, from a consideration of all the time derivatives at the initial instant, that the velocity covariance u{u in general becomes of order r -5 when the separation r is large, the leading term having the property that it makes no contribution to the vorticity covariance 0^X0$> which becomes of order r -8 . This semi-irrotational property of the asymptotic form, which arises from the fact that pressure forces act only indirectly on the vorticity, allows the asymptotic form of to be determined explicitly. By methods that are new in turbulence theory and that involve a good deal of tensor manipulation, it is found that U'} = mnV2 “ $ $ $ V2 ~ drjdr) when r is large, where the coefficient Cpqmn is related to the fourth integral moment of in a known way. There is a corresponding expression for the leading term in the spectrum tensor at small wave-numbers, which is now not analytic. The spectrum function giving the distribution of energy with respect to wave-number magnitude k is in general of the form E(k) = a 4 + 0(^5 In k)9 when k is small. Corresponding expressions are found for the asymptotic forms of the various terms occurring in the dynamical equation giving the rate of change of Both the inertia and pressure terms in this equation are found to be of order r~5, and as a consequence the coefficient Cpqmn (and likewise C) is not a dynamical invariant. It is shown that the integral J*2qzqrmrwdr (which exists, despite the apparent logarithmic divergence at large r) is uniquely related to CpqmnJ and it too varies during the decay, contrary to past belief. The final period of decay is examined afresh, and it is found that the energy then varies as which is also the result found experimentally; the power ( — f) arises from the fact that the spectrum tensor is of order k2 when the wave-number k is small, and is unaffected by the non-analytic character of that leading term. The covariance tqw] does not have a simple form in the final period; it is determined by the parameter on the previous history of the decay in a complicated way. It is rather puzzling that measurements indicate that the longitudinal correlation coefficient has a simple Gaussian form in the final period of decay, as would be the case for an analytic spectrum. We suggest this observation may be true only for turbulence of very low initial Reynolds number, for which the non-analytic part of the spectrum tensor has little time to develop. Finally, the results are specialized to correspond to turbulence which is completely isotropic. For reasons related to the symmetry, is now no larger than 0 ( r -6 ) when r is large (we have been unable to determine the exact order), and the leading term in the spectrum tensor, of order k 2 , is analytic. As suggested by Proudman & Reid’s work, the triple correlation k { r ) is of order r -4 when r is large and d / r«> _ -j-u2 r*f(r) dr> = (w2)1 lim rAk{r)

Zeitstrukturen im Jazz

2014 ◽  
Vol 59 (1) ◽  
pp. 79-92
Author(s):  
Alexander Becker
Keyword(s):  
Large Scale ◽  
Large Scale Structure ◽  
Time Frame ◽  
Scale Structure ◽  
Classical Form ◽  
Jazz Music ◽  
The Moment

Wie erlebt der Hörer Jazz? Bei dieser Frage geht es unter anderem um die Art und Weise, wie Jazz die Zeit des Hörens gestaltet. Ein an klassischer Musik geschultes Ohr erwartet von musikalischer Zeitgestaltung, den zeitlichen Rahmen, der durch Anfang und Ende gesetzt ist, von innen heraus zu strukturieren und neu zu konstituieren. Doch das ist keine Erwartung, die dem Jazz gerecht wird. Im Jazz wird der Moment nicht im Hinblick auf ein Ziel gestaltet, das von einer übergeordneten Struktur bereitgestellt wird, sondern so, dass er den Bewegungsimpuls zum nächsten Moment weiterträgt. Wie wirkt sich dieses Prinzip der Zeitgestaltung auf die musikalische Form im Großen aus? Der Aufsatz untersucht diese Frage anhand von Beispielen, an denen sich der Weg der Transformation von einer klassischen zu einer dem Jazz angemessenen Form gut nachverfolgen lässt.<br><br>How do listeners experience Jazz? This is a question also about how Jazz music organizes the listening time. A classically educated listener expects a piece of music to structure, unify and thereby re-constitute the externally given time frame. Such an expectation is foreign to Jazz music which doesn’t relate the moment to a goal provided by a large scale structure. Rather, one moment is carried on to the next, preserving the stimulus potentially ad infinitum. How does such an organization of time affect the large scale form? The paper tries to answer this question by analyzing two examples which permit to trace the transformation of a classical form into a form germane to Jazz music.

scholarly journals Mapping large-scale-structure evolution over cosmic times

2021 ◽  
Author(s):  
Marta B. Silva ◽  
Ely D. Kovetz ◽  
Garrett K. Keating ◽  
Azadeh Moradinezhad Dizgah ◽  
Matthieu Bethermin ◽  
...  
Keyword(s):  
Galaxy Formation ◽  
Large Scale ◽  
High Redshift ◽  
Formation Rate ◽  
Far Infrared ◽  
Large Scale Structure ◽  
Scale Structure ◽  
Structure Evolution ◽  
Intensity Mapping ◽  
Wide Range

AbstractThis paper outlines the science case for line-intensity mapping with a space-borne instrument targeting the sub-millimeter (microwaves) to the far-infrared (FIR) wavelength range. Our goal is to observe and characterize the large-scale structure in the Universe from present times to the high redshift Epoch of Reionization. This is essential to constrain the cosmology of our Universe and form a better understanding of various mechanisms that drive galaxy formation and evolution. The proposed frequency range would make it possible to probe important metal cooling lines such as [CII] up to very high redshift as well as a large number of rotational lines of the CO molecule. These can be used to trace molecular gas and dust evolution and constrain the buildup in both the cosmic star formation rate density and the cosmic infrared background (CIB). Moreover, surveys at the highest frequencies will detect FIR lines which are used as diagnostics of galaxies and AGN. Tomography of these lines over a wide redshift range will enable invaluable measurements of the cosmic expansion history at epochs inaccessible to other methods, competitive constraints on the parameters of the standard model of cosmology, and numerous tests of dark matter, dark energy, modified gravity and inflation. To reach these goals, large-scale structure must be mapped over a wide range in frequency to trace its time evolution and the surveyed area needs to be very large to beat cosmic variance. Only a space-borne mission can properly meet these requirements.

scholarly journals Higher order Hamiltonian Monte Carlo sampling for cosmological large-scale structure analysis

2021 ◽  
Vol 502 (3) ◽  
pp. 3976-3992
Author(s):  
Mónica Hernández-Sánchez ◽  
Francisco-Shu Kitaura ◽  
Metin Ata ◽  
Claudio Dalla Vecchia
Keyword(s):  
Fourth Order ◽  
Large Scale ◽  
Equations Of Motion ◽  
Large Scale Structure ◽  
Real Space ◽  
Higher Order ◽  
Second Order ◽  
Scale Structure ◽  
Integration Schemes ◽  
Reconstruction Methods

ABSTRACT We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic second-order leap-frog scheme (considering the single evaluation of the EoM) in a combination of even numbers of forward time integration steps with a single intermediate backward step. This largely reduces the number of evaluations and random gradient computations, as required in the usual second-order case for high-dimensional cases. We restrict this study to the lognormal-Poisson model, applied to a full volume halo catalogue in real space on a cubical mesh of 1250 h−1 Mpc side and 2563 cells. Hence, we neglect selection effects, redshift space distortions, and displacements. We note that those observational and cosmic evolution effects can be accounted for in subsequent Gibbs-sampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leap-frog scheme shortens the burn-in phase by a factor of at least ∼30. This implies that 75–90 independent samples are obtained while the fastest second-order method converges. After convergence, the correlation lengths indicate an improvement factor of about 3.0 fewer gradient computations for meshes of 2563 cells. In the considered cosmological scenario, the traditional leap-frog scheme turns out to outperform higher order integration schemes only when considering lower dimensional problems, e.g. meshes with 643 cells. This gain in computational efficiency can help to go towards a full Bayesian analysis of the cosmological large-scale structure for upcoming galaxy surveys.

scholarly journals Abell Clusters as Tracers of Large-Scale Structure: Alignments and Substructure

1988 ◽  
Vol 130 ◽  
pp. 536-536
Author(s):  
G. Rhee ◽  
P. Katgert
Keyword(s):  
Structure Data ◽  
Large Scale ◽  
Large Scale Structure ◽  
Scale Structure ◽  
Abell Clusters

Binggeli (A & A, 107, 338, 1982) showed that neighbouring Abell clusters with pair distances less than 30 to 40 h50−1 Mpc show directional correlation. Binggeli's result is based on structure data of 44 Abell clusters (all with zspectr < 0.1). Binggelli's result was questioned by Struble and Peebles (A.J., 90, 582, 1985). They produce a visual estimate of the direction of cluster elongation for 237 clusters. They did not observe reduced probability for small D large Θ pairs.

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