15,555 research outputs found
Temperature spectra in shear flow and thermal convection
We show that the P_u(\om) \propto \om^{-7/3} shear velocity power spectrum
gives rise to a P_\Theta (\om ) \propto \om^{-4/3} power spectrum for a
passively advected scalar, as measured in experiment [K. Sreenivasan, Proc. R.
Soc. London A {\bf 434}, 165 (1991)]. Applying our argument to high Rayleigh
number Rayleigh Benard flow, we can account for the measured scaling exponents
equally well as the Bolgiano Obukhov theory (BO59). Yet, of the two
explanations, only the shear approach might be able to explain why no classical
scaling range is seen in between the shear (or BO59) range and the viscous
subrange of the experimental temperature spectrum [I. Procaccia {\it et al.},
Phys. Rev. A {\bf 44}, 8091 (1991)].Comment: 9 pages, 1 figure, 1 tabl
Ontological Investigations of a Pragmatic Kind? A Reply to Lauer
This paper is a reply to Richard Lauer’s “Is Social Ontology Prior to Social Scientific Methodology?” (2019) and an attempt to contribute to the meta-social ontological discourse more broadly. In the first part, I will give a rough sketch of Lauer’s general project and confront his pragmatist approach with a fundamental problem. The second part of my reply will provide a solution for this problem rooted in a philosophy of the social sciences in practice
Flow organization in non-Oberbeck-Boussinesq Rayleigh-Benard convection in water
Non-Oberbeck-Boussinesq (NOB) effects on the flow organization in
two-dimensional Rayleigh-Benard turbulence are numerically analyzed. The
working fluid is water. We focus on the temperature profiles, the center
temperature, the Nusselt number, and on the analysis of the velocity field.
Several velocity amplitudes (or Reynolds numbers) and several kinetic profiles
are introduced and studied; these together describe the various features of the
rather complex flow organization. The results are presented both as functions
of the Rayleigh number Ra (with Ra up to 10^8) for fixed temperature difference
(Delta) between top and bottom plates and as functions of Delta
("non-Oberbeck-Boussinesqness") for fixed Ra with Delta up to 60 K. All results
are consistent with the available experimental NOB data for the center
temperature Tc and the Nusselt number ratio Nu_{NOB}/Nu_{OB} (the label OB
meaning that the Oberbeck-Boussinesq conditions are valid).
Beyond Ra ~ 10^6 the flow consists of a large diagonal center convection roll
and two smaller rolls in the upper and lower corners. In the NOB case the
center convection roll is still characterized by only one velocity scale.Comment: 31 pages, 22 figure
Switching in heteroclinic networks
We study the dynamics near heteroclinic networks for which all eigenvalues of
the linearization at the equilibria are real. A common connection and an
assumption on the geometry of its incoming and outgoing directions exclude even
the weakest forms of switching (i.e. along this connection). The form of the
global transition maps, and thus the type of the heteroclinic cycle, plays a
crucial role in this. We look at two examples in , the House and
Bowtie networks, to illustrate complex dynamics that may occur when either of
these conditions is broken. For the House network, there is switching along the
common connection, while for the Bowtie network we find switching along a
cycle
Scaling in thermal convection: A unifying theory
A systematic theory for the scaling of the Nusselt number and of the
Reynolds number in strong Rayleigh-Benard convection is suggested and
shown to be compatible with recent experiments. It assumes a coherent large
scale convection roll (``wind of turbulence'') and is based on the dynamical
equations both in the bulk and in the boundary layers. Several regimes are
identified in the Rayleigh number versus Prandtl number phase space, defined by
whether the boundary layer or the bulk dominates the global kinetic and thermal
dissipation, respectively. The crossover between the regimes is calculated. In
the regime which has most frequently been studied in experiment (Ra smaller
than 10^{11}) the leading terms are , for and , for . In most measurements these laws are modified
by additive corrections from the neighboring regimes so that the impression of
a slightly larger (effective) Nu vs Ra scaling exponent can arise. -- The
presented theory is best summarized in the phase diagram figure 1.Comment: 30 pages, latex, 7 figures, under review at Journal of Fluid Mec
On geometry effects in Rayleigh-Benard convection
Various recent experiments hint at a geometry dependence of scaling relations
in Rayleigh-B\'enard convection. Aspect ratio and shape dependences have been
found. In this paper a mechanism is offered which can account for such
dependences. It is based on Prandtl's theory for laminar boundary layers and on
the conservation of volume flux of the large scale wind. The mechanism implies
the possibility of different thicknesses of the kinetic boundary layers at the
sidewalls and the top/bottom plates, just as experimentally found by Qiu and
Xia (Phys. Rev. E58, 486 (1998)), and also different -scaling of the wind
measured over the plates and at the sidewalls. In the second part of the paper
a scaling argument for the velocity and temperature fluctuations in the bulk is
developeVarious recent experiments hint at a geometry dependence of scaling
relations in Rayleigh-Benard convection. Aspect ratio and shape dependences
have been found. In this paper a mechanism is offered which can account for
such dependences. It is based on Prandtl's theory for laminar boundary layers
and on the conservation of volume flux of the large scale wind. The mechanism
implies the possibility of different thicknesses of the kinetic boundary layers
at the sidewalls and the top/bottom plates, just as experimentally found by Qiu
and Xia (Phys. Rev. E58, 486 (1998)), and also different -scaling of the
wind measured over the plates and at the sidewalls. In the second part of the
paper a scaling argument for the velocity and temperature fluctuations in the
bulk is developeComment: 4 pages, 1 figur
Scale resolved intermittency in turbulence
The deviations ("intermittency corrections") from classical
("K41") scaling of the moments of the velocity
differences in high Reynolds number turbulence are calculated, extending a
method to approximately solve the Navier-Stokes equation described earlier. We
suggest to introduce the notion of scale resolved intermittency corrections
, because we find that these are large in
the viscous subrange, moderate in the nonuniversal stirring subrange but,
surprisingly, extremely small if not zero in the inertial subrange. If ISR
intermittency corrections persisted in experiment up to the large Reynolds
number limit, our calculation would show, that this could be due to the opening
of phase space for larger wave vectors. In the higher order velocity moment
the crossover between inertial and viscous subrange is
, thus the inertial subrange is {\it smaller} for higher
moments.Comment: 12 pages, Latex, 2 tables, 7 figure
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