262 research outputs found
Finite Volume Streaming-based Lattice Boltzmann algorithm for fluid-dynamics simulations: a one-to-one accuracy and performance study
A new finite volume (FV) discretisation method for the Lattice Boltzmann (LB)
equation which combines high accuracy with limited computational cost is
presented. In order to assess the performance of the FV method we carry out a
systematic comparison, focused on accuracy and computational performances, with
the standard (ST) Lattice Boltzmann equation algorithm. To our
knowledge such a systematic comparison has never been previously reported. In
particular we aim at clarifying whether and in which conditions the proposed
algorithm, and more generally any FV algorithm, can be taken as the method of
choice in fluid-dynamics LB simulations. For this reason the comparative
analysis is further extended to the case of realistic flows, in particular
thermally driven flows in turbulent conditions. We report the first successful
simulation of high-Rayleigh number convective flow performed by a Lattice
Boltzmann FV based algorithm with wall grid refinement.Comment: 15 pages, 14 figures (discussion changes, improved figure
readability
Theories of convection and the spectrum of turbulence in the solar photosphere
Classical theories of turbulence do not describe accurately inertial range
scaling laws in turbulent convection and notably fail to model the shape of the
turbulent spectrum of solar photospheric convection. To understand these
discrepancies, a detailed study of scale-by-scale budgets in turbulent
Rayleigh-B\'enard convection is presented, with particular emphasis placed on
anisotropy and inhomogeneity. A generalized Kolmogorov equation applying to
convection is derived and its various terms are computed using numerical
simulations of turbulent Boussinesq convection. The analysis of the isotropic
part of the equation shows that the third-order velocity structure function is
significantly affected by buoyancy forcing and large-scale inhomogeneities.
Anisotropic contributions to this equation are also shown to be comparable to
their isotropic counterpart at moderate to large scales. Implications of these
results for convection in the solar photosphere, mesogranulation and
supergranulation are discussed.Comment: 6 pages, 3 figures -- To appear in the Proceedings of Symposium no.
239 "Convection in Astrophysics", International Astronomical Union., held
21-25 August, 2006 in Prague, Czech Republi
Velocity gradients statistics along particle trajectories in turbulent flows: the refined similarity hypothesis in the Lagrangian frame
We present an investigation of the statistics of velocity gradient related
quantities, in particluar energy dissipation rate and enstrophy, along the
trajectories of fluid tracers and of heavy/light particles advected by a
homogeneous and isotropic turbulent flow. The Refined Similarity Hypothesis
(RSH) proposed by Kolmogorov and Oboukhov in 1962 is rephrased in the
Lagrangian context and then tested along the particle trajectories. The study
is performed on state-of-the-art numerical data resulting from numerical
simulations up to Re~400 with 2048^3 collocation points. When particles have
small inertia, we show that the Lagrangian formulation of the RSH is well
verified for time lags larger than the typical response time of the particle.
In contrast, in the large inertia limit when the particle response time
approaches the integral-time-scale of the flow, particles behave nearly
ballistic, and the Eulerian formulation of RSH holds in the inertial-range.Comment: 7 pages, 7 figures; Physical Review E (accepted Dec 7, 2009
Rayleigh and Prandtl number scaling in the bulk of Rayleigh-Benard turbulence
The Rayleigh (Ra) and Prandtl (Pr) number scaling of the Nusselt number Nu,
the Reynolds number Re, the temperature fluctuations, and the kinetic and
thermal dissipation rates is studied for (numerical) homogeneous
Rayleigh-Benard turbulence, i.e., Rayleigh-Benard turbulence with periodic
boundary conditions in all directions and a volume forcing of the temperature
field by a mean gradient. This system serves as model system for the bulk of
Rayleigh-Benard flow and therefore as model for the so called ``ultimate regime
of thermal convection''. With respect to the Ra dependence of Nu and Re we
confirm our earlier results \cite{loh03} which are consistent with the
Kraichnan theory \cite{kra62} and the Grossmann-Lohse (GL) theory
\cite{gro00,gro01,gro02,gro04}, which both predict and . However the Pr dependence within these two theories is
different. Here we show that the numerical data are consistent with the GL
theory , . For the thermal and kinetic
dissipation rates we find \eps_\theta/(\kappa \Delta^{2}L^{-2}) \sim (Re
Pr)^{0.87} and \eps_u/(\nu^3 L^{-4}) \sim Re^{2.77}, also both consistent
with the GL theory, whereas the temperature fluctuations do not depend on Ra
and Pr. Finally, the dynamics of the heat transport is studied and put into the
context of a recent theoretical finding by Doering et al. \cite{doe05}.Comment: 8 pages, 9 figure
Universality of anisotropic fluctuations from numerical simulations of turbulent flows
We present new results from a direct numerical simulation of a three
dimensional homogeneous Rayleigh-Benard system (HRB), i.e. a convective cell
with an imposed linear mean temperature profile along the vertical direction.
We measure the SO(3)-decomposition of both velocity structure functions and
buoyancy terms. We give a dimensional prediction for the values of the
anisotropic scaling exponents in this Rayleigh-Benard systems. Measured scaling
does not follow dimensional estimate, while a better agreement can be found
with the anisotropic scaling of a different system, the random-Kolmogorov-flow
(RKF). Our findings support the conclusion that scaling properties of
anisotropic fluctuations are universal, i.e. independent of the forcing
mechanism sustaining the turbulent flow.Comment: 4 pages, 3 figure
Particle-laden two-dimensional elastic turbulence
The aggregation properties of heavy inertial particles in the elastic
turbulence regime of an Oldroyd-B fluid with periodic Kolmogorov mean flow are
investigated by means of extensive numerical simulations in two dimensions.
Both the small and large scale features of the resulting inhomogeneous particle
distribution are examined, focusing on their connection with the properties of
the advecting viscoelastic flow. We find that particles preferentially
accumulate on thin highly elastic propagating waves and that this effect is
largest for intermediate values of particle inertia. We provide a quantitative
characterization of this phenomenon that allows to relate it to the
accumulation of particles in filamentary highly strained flow regions producing
clusters of correlation dimension close to 1. At larger scales, particles are
found to undergo turbophoretic-like segregation. Indeed, our results indicate a
close relationship between the profiles of particle density and fluid velocity
fluctuations. The large-scale inhomogeneity of the particle distribution is
interpreted in the framework of a model derived in the limit of small, but
finite, particle inertia. The qualitative characteristics of different
observables are, to a good extent, independent of the flow elasticity. When
increased, the latter is found, however, to slightly reduce the globally
averaged degree of turbophoretic unmixing.Comment: 12 pages, 9 figures. Submitted to EPJ
Non-Oberbeck-Boussinesq effects in two-dimensional Rayleigh-Benard convection in glycerol
We numerically analyze Non-Oberbeck-Boussinesq (NOB) effects in
two-dimensional Rayleigh-Benard flow in glycerol, which shows a dramatic change
in the viscosity with temperature. The results are presented both as functions
of the Rayleigh number (Ra) up to (for fixed temperature difference
between the top and bottom plates) and as functions of
"non-Oberbeck-Boussinesqness'' or "NOBness'' () up to 50 K (for fixed
Ra). For this large NOBness the center temperature is more than 5 K
larger than the arithmetic mean temperature between top and bottom plate
and only weakly depends on Ra. To physically account for the NOB deviations of
the Nusselt numbers from its Oberbeck-Boussinesq values, we apply the
decomposition of into the product of two effects, namely
first the change in the sum of the top and bottom thermal BL thicknesses, and
second the shift of the center temperature as compared to . While
for water the origin of the deviation is totally dominated by the second
effect (cf. Ahlers et al., J. Fluid Mech. 569, pp. 409 (2006)) for glycerol the
first effect is dominating, in spite of the large increase of as compared
to .Comment: 6 pages, 7 figure
Lagrangian single particle turbulent statistics through the Hilbert-Huang Transform
The Hilbert-Huang transform is applied to analyze single particle Lagrangian
velocity data from numerical simulations of hydrodynamic turbulence. The
velocity trajectory is described in terms of a set of intrinsic mode functions,
C_{i}(t), and of their instantaneous frequency, \omega_{i}(t). On the basis of
this decomposition we define the \omega-conditioned statistical moments of the
C_{i} modes, named q-order Hilbert Spectra (HS). We show that such new
quantities have enhanced scaling properties as compared to traditional Fourier
transform- or correlation-based (Structure Functions) statistical indicators,
thus providing better insights into the turbulent energy transfer process. We
present a clear empirical evidence that the energy-like quantity, i.e. the
second-order HS, displays a linear scaling in time in the inertial range, as
expected from dimensional analysis and never observed before. We also measure
high order moment scaling exponents in a direct way, without resorting the
Extended Self Similarity (ESS) procedure. This leads to a new estimate of the
Lagrangian structure functions exponents which are consistent with the
multifractal prediction in the Lagrangian frame as proposed in [Biferale et
al., Phys. Rev. Lett. vol. 93, 064502 (2004)].Comment: 5 pages, 5 figure
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