11,583 research outputs found
On the validity of Kraichnan scalings for forced two-dimensional turbulence
We examine the validity of the scaling laws derived by Kraichnan (1967) for forced two-dimensional turbulence. We use a new numerical technique (Dritschel & Fontane 2010) to reach higher Reynolds number than previously accessible with classical pseudo-spectral methods. No large scale friction or hypo-diffusion is used in order to avoid any distortion of the inverse cascade and to be in agreement with the theoretical framework used by Kraichnan. Both spectral and spatial forcing are considered and statistical convergence is obtained through large simulation ensembles.
A steeper energy spectrum proportional to k^(-2) is observed for the inverse cascade in place of the classical k^(-5/3) prediction. This steepening is shown to be associated with a faster growth of energy at large scales, scaling like t^(-1) rather than Kraichnan's prediction of t^(-3/2). The deviation from Kraichnan's theory is related to the emergence of a vortex population dominating the distribution of energy across scales, and whose number density and vorticity distribution with respect to vortex area are related to the shape of the enstrophy spectrum
Effective degrees of nonlinearity in a family of generalized models of two-dimensional turbulence
We study the small-scale behavior of generalized two-dimensional turbulence
governed by a family of model equations, in which the active scalar
is advected by the incompressible flow
. The dynamics of this family are characterized by the
material conservation of , whose variance is
preferentially transferred to high wave numbers. As this transfer proceeds to
ever-smaller scales, the gradient $\nabla\theta$ grows without bound. This
growth is due to the stretching term $(\nabla\theta\cdot\nabla)\u$ whose
``effective degree of nonlinearity'' differs from one member of the family to
another. This degree depends on the relation between the advecting flow $\u$
and the active scalar $\theta$ and is wide ranging, from approximately linear
to highly superlinear. Linear dynamics are realized when $\nabla\u$ is a
quantity of no smaller scales than $\theta$, so that it is insensitive to the
direct transfer of the variance of $\theta$, which is nearly passively
advected. This case corresponds to $\alpha\ge2$, for which the growth of
$\nabla\theta$ is approximately exponential in time and non-accelerated. For
$\alpha<2$, superlinear dynamics are realized as the direct transfer of
entails a growth in \nabla\u, thereby enhancing the production
of . This superlinearity reaches the familiar quadratic
nonlinearity of three-dimensional turbulence at and surpasses that
for . The usual vorticity equation () is the border line,
where \nabla\u and are of the same scale, separating the linear and
nonlinear regimes of the small-scale dynamics. We discuss these regimes in
detail, with an emphasis on the locality of the direct transfer.Comment: 6 journal pages, to appear in Physical Review
Revisiting Batchelor's theory of two-dimensional turbulence
Recent mathematical results have shown that a central assumption in the theory of two-dimensional turbulence proposed by Batchelor (Phys. Fluids, vol. 12, 1969, p. 233) is false. That theory, which predicts a X-2/3 k(-1) enstrophy spectrum in the inertial range of freely-decaying turbulence, and which has evidently been successful in describing certain aspects of numerical simulations at high Reynolds numbers Re, assumes that there is a finite, non-zero enstrophy dissipation X in the limit of infinite Re. This, however, is not true for flows having finite vorticity. The enstrophy dissipation in fact vanishes. We revisit Batchelor's theory and propose a simple modification of it to ensure vanishing X in the limit Re -> infinity. Our proposal is supported by high Reynolds number simulations which confirm that X decays like 1/ln Re, and which, following the time of peak enstrophy dissipation, exhibit enstrophy spectra containing an increasing proportion of the total enstrophy (omega(2))/2 in the inertial range as Re increases. Together with the mathematical analysis of vanishing X, these observations motivate a straightforward and, indeed, alarmingly simple modification of Batchelor's theory: just replace Batchelor's enstrophy spectrum X(2/3)k(-1) with (omega(2))k(-1)(In Re)(-1).Publisher PDFPeer reviewe
Vortical control of forced two-dimensional turbulence
A new numerical technique for the simulation of forced two-dimensional turbulence (Dritschel and Fontane, 2010) is used to examine the validity of Kraichnan-Batchelor scaling laws at higher Reynolds number than previously accessible with classical pseudo-spectral methods,making use of large simulation ensembles to allow a detailed consideration of the inverse cascade in a quasi-steady state. Our results support the recent finding of Scott (2007), namely that when a direct enstrophy cascading range is well-represented numerically, a steeper energy spectrum proportional to k^(−2) is obtained in place of the classical k^(−5/3) prediction. It is further shown that this steep spectrum is associated with a faster growth of energy at large scales, scaling like t^(−1) rather than Kraichnan’s prediction of t^(−3/2). The deviation from Kraichnan’s theory is related to the emergence of a population of vortices that dominate the distribution of energy across scales, and whose number density and vorticity distribution with respect to vortex area are related to the shape of the enstrophy spectrum. An analytical model is proposed which closely matches the numerical spectra between the large scales and the forcing scale
Transmit Diversity Code Filter Sets (TDCFSs), an MISO Antenna Frequency Predistortion Scheme for ATSC 3.0
"(c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.")Transmit diversity code filter sets (TDCFSs) are a method of predistorting the common waveforms from multiple transmitters in the same frequency channel, as in a single frequency network, in order to minimize the possibility of cross-interference among the transmitted signals over the entire reception area. This processing is achieved using all-pass linear filters, allowing the resulting combination of predistortion and multipath to be properly compensated as part of the equalization process in the receiver. The filter design utilizes an iterative computational approach, which minimizes cross-correlation peak side lobe under the constraints of number of transmitters and delay spread, allowing customization for specific network configurations. This paper provides an overview of the TDCFS multiple-input single output antenna scheme adopted in ATSC 3.0, together with experimental analysis of capacity and specific worst-case conditions that illustrate the benefits of using the TDCFS approach.Lopresto, S.; Citta, R.; Vargas, D.; Gómez Barquero, D. (2016). Transmit Diversity Code Filter Sets (TDCFSs), an MISO Antenna Frequency Predistortion Scheme for ATSC 3.0. IEEE Transactions on Broadcasting. 62(1):271-280. doi:10.1109/TBC.2015.2505400S27128062
Gang members are entangled in a web of violence that leads the gunman of today to become the victim of tomorrow
While the media often portrays a stark line between the victims of crime and offenders the reality is much more blurred. New research from David Pyrooz, Richard K. Moule, and Scott H. Decker find that this is especially the case for gang members who find that they are twice as likely to be both victims and offenders as non-gang members. They argue that gang membership is a large risk factor in this victim-offender overlap, as single acts of violence between gang members often lead to acts of retribution between gangs as a whole
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