90 research outputs found
Turbulence spectra in the buoyancy subrange of thermally stratified shear flows
CER68-69JTL21.February 1969.Originally presented as the author's thesis, Colorado State University.Includes bibliographical references (pages 94-97).Prepared under Office of Naval Research, project no. NR 062-414/6-6-68(Code 438), U.S. Department of Defense.A generalized eddy-viscosity approximation is used to study the turbulence spectra of thermally stratified shear flows. For a stationary process in the wave number range investigated--the buoyancy subrange--under the assumption of local homogeneity of the flow, two governing spectral equations with six unknowns are derived from the equations of motion and energy. In order to reduce the number of unknowns to two so that the spectral equations can be solved, a generalized eddy-viscosity is used for expressing the integrated forms of the inertial transfers of energy and temperature inhomogeneity, the shear stress and vertical heat flux in terms of velocity spectrum ¢(k) and temperature spectrum ¢TT(k). Asymptotic solutions are obtained in the buoyancy subrange where the local production and local dissipation of turbulent energy is negligible as compared to the inertial transfer and vertical heat flux terms when the flow conditions satisfy the criterion ε|dT'/dz| << N g/T' or g/T'. |dT'/dz| << N/ε.(g/T)^2. In the buoyancy subrange of stably stratified turbulent flow, the power law for the velocity and temperature spectra is not universal but varies with the flow conditions in the way ¢(k) ~ k^n and ¢TT(k) ~ k^m where 11/5 ≥ n ≥ -3 and -1 ≥ m ≥ -7/5. According to the measurements of velocity spectra in the atmosphere (Pinus and Schcherbakova, 1966; Myrup, 1968), the dependence of the power law on the flow conditions was confirmed. The solutions of Bolgiano (1959) and Luialey-Shur (1964) are only two particular cases of the present results under cert ain flow conditions. In the case of the unstably stratified turbulent flow, the velocity spectrum exhibits a hump in the buoyancy subrange as a result of the energy input from the temperature field to the velocity field. In the left side of this hump the velocity spectrum approaches a +1 slope and the temperature spectrum shows a -3 slope. The measurements of the velocity spectra in the atmosphere (Ivanov and Ordanovich, 1967) confirms this tendency.Under contract no. N00014-68-A-0493-0001
On Isotropic Turbulence in the Dark Fluid Universe
As first part of this work, experimental information about the decay of
isotropic turbulence in ordinary hydrodynamics, u^2(t) proportional to
t^{-6/5}, is used as input in FRW equations in order to investigate how an
initial fraction f of turbulent kinetic energy in the cosmic fluid influences
the cosmological development in the late, quintessence/phantom, universe. First
order perturbative theory to the first order in f is employed. It turns out
that both in the Hubble factor, and in the energy density, the influence from
the turbulence fades away at late times. The divergences in these quantities
near the Big Rip behave essentially as in a non-turbulent fluid. However, for
the scale factor, the turbulence modification turns out to diverge
logarithmically. As second part of our work, we consider the full FRW equation
in which the turbulent part of the dark energy is accounted for by a separate
term. It is demonstrated that turbulence occurrence may change the future
universe evolution due to dissipation of dark energy. For instance,
phantom-dominated universe becomes asymptotically a de Sitter one in the
future, thus avoiding the Big Rip singularity.Comment: 10 pages, no figures, significant revision. Matches published versio
Bottleneck effect in three-dimensional turbulence simulations
At numerical resolutions around and above, three-dimensional energy
spectra from turbulence simulations begin to show noticeably shallower spectra
than near the dissipation wavenumber (`bottleneck effect'). This
effect is shown to be significantly weaker in one-dimensional spectra such as
those obtained in wind tunnel turbulence. The difference can be understood in
terms of the transformation between one-dimensional and three-dimensional
energy spectra under the assumption that the turbulent velocity field is
isotropic. Transversal and longitudinal energy spectra are similar and can both
accurately be computed from the full three-dimensional spectra. Second-order
structure functions are less susceptible to the bottleneck effect and may be
better suited for inferring the scaling exponent from numerical simulation
data.Comment: 8 pages, 6 figure
On traveling waves in lattices: The case of Riccati lattices
The method of simplest equation is applied for analysis of a class of
lattices described by differential-difference equations that admit
traveling-wave solutions constructed on the basis of the solution of the
Riccati equation. We denote such lattices as Riccati lattices. We search for
Riccati lattices within two classes of lattices: generalized Lotka - Volterra
lattices and generalized Holling lattices. We show that from the class of
generalized Lotka - Volterra lattices only the Wadati lattice belongs to the
class of Riccati lattices. Opposite to this many lattices from the Holling
class are Riccati lattices. We construct exact traveling wave solutions on the
basis of the solution of Riccati equation for three members of the class of
generalized Holing lattices.Comment: 17 pages, no figure
Publishers imprint. Printed in Malaysia. Analytical Investigation of the Onset of Bifurcation Cascade in Two Logistic-like Maps
Discrete Dynamics in Nature and Society, Vol. 6, pp. 31-35 Reprints available directly from the publisher Photocopying permitted by license onl
Random functions and turbulence
International Series of Monographs in Natural Philosophy, Volume 32: Random Functions and Turbulence focuses on the use of random functions as mathematical methods. The manuscript first offers information on the elements of the theory of random functions. Topics include determination of statistical moments by characteristic functions; functional transformations of random variables; multidimensional random variables with spherical symmetry; and random variables and distribution functions. The book then discusses random processes and random fields, including stationarity and ergodicity of rando
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Foreign Vulnerabilities, Domestic Risks: The Global Drivers of GDP-at-Risk
We study how foreign financial developments influence the conditional distribution of domestic GDP growth. Within a quantile regression setup, we propose a method to parsimoniously account for foreign vulnerabilities using bilateral-exposure weights when assessing downside macroeconomic risks. Using a panel dataset of advanced economies, we show that tighter foreign financial conditions and faster foreign credit-to-GDP growth are associated with a more severe left tail of domestic GDP growth, even when controlling for domestic indicators. The inclusion of foreign indicators significantly improves estimates of ‘GDP-at-Risk’, a summary measure of downside risks. In turn, this yields time-varying estimates of higher moments of GDP growth that demonstrate interpretable moves over the cycle. Decomposing historical estimates of GDP-at-Risk into domestic and foreign sources, we show that foreign shocks are a key driver of domestic macroeconomic tail risks
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