533 research outputs found
Coriolis force in Geophysics: an elementary introduction and examples
We show how Geophysics may illustrate and thus improve classical Mechanics
lectures concerning the study of Coriolis force effects. We are then interested
in atmospheric as well as oceanic phenomena we are familiar with, and are for
that reason of pedagogical and practical interest. Our aim is to model them in
a very simple way to bring out the physical phenomena that are involved.Comment: Accepted for publication in European Journal of Physic
Field theory of the inverse cascade in two-dimensional turbulence
A two-dimensional fluid, stirred at high wavenumbers and damped by both
viscosity and linear friction, is modeled by a statistical field theory. The
fluid's long-distance behavior is studied using renormalization-group (RG)
methods, as begun by Forster, Nelson, and Stephen [Phys. Rev. A 16, 732
(1977)]. With friction, which dissipates energy at low wavenumbers, one expects
a stationary inverse energy cascade for strong enough stirring. While such
developed turbulence is beyond the quantitative reach of perturbation theory, a
combination of exact and perturbative results suggests a coherent picture of
the inverse cascade. The zero-friction fluctuation-dissipation theorem (FDT) is
derived from a generalized time-reversal symmetry and implies zero anomalous
dimension for the velocity even when friction is present. Thus the Kolmogorov
scaling of the inverse cascade cannot be explained by any RG fixed point. The
beta function for the dimensionless coupling ghat is computed through two
loops; the ghat^3 term is positive, as already known, but the ghat^5 term is
negative. An ideal cascade requires a linear beta function for large ghat,
consistent with a Pad\'e approximant to the Borel transform. The conjecture
that the Kolmogorov spectrum arises from an RG flow through large ghat is
compatible with other results, but the accurate k^{-5/3} scaling is not
explained and the Kolmogorov constant is not estimated. The lack of scale
invariance should produce intermittency in high-order structure functions, as
observed in some but not all numerical simulations of the inverse cascade. When
analogous RG methods are applied to the one-dimensional Burgers equation using
an FDT-preserving dimensional continuation, equipartition is obtained instead
of a cascade--in agreement with simulations.Comment: 16 pages, 3 figures, REVTeX 4. Material added on energy flux,
intermittency, and comparison with Burgers equatio
Helicity cascades in rotating turbulence
The effect of helicity (velocity-vorticity correlations) is studied in direct
numerical simulations of rotating turbulence down to Rossby numbers of 0.02.
The results suggest that the presence of net helicity plays an important role
in the dynamics of the flow. In particular, at small Rossby number, the energy
cascades to large scales, as expected, but helicity then can dominate the
cascade to small scales. A phenomenological interpretation in terms of a direct
cascade of helicity slowed down by wave-eddy interactions leads to the
prediction of new inertial indices for the small-scale energy and helicity
spectra.Comment: 7 pages, 8 figure
The imprint of large-scale flows on turbulence
We investigate the locality of interactions in hydrodynamic turbulence using
data from a direct numerical simulation on a grid of 1024^3 points; the flow is
forced with the Taylor-Green vortex. An inertial range for the energy is
obtained in which the flux is constant and the spectrum follows an approximate
Kolmogorov law. Nonlinear triadic interactions are dominated by their non-local
components, involving widely separated scales. The resulting nonlinear transfer
itself is local at each scale but the step in the energy cascade is independent
of that scale and directly related to the integral scale of the flow.
Interactions with large scales represent 20% of the total energy flux. Possible
explanations for the deviation from self-similar models, the link between these
findings and intermittency, and their consequences for modeling of turbulent
flows are briefly discussed
Intermittency in the Joint Cascade of Energy and Helicity
The statistics of the energy and helicity fluxes in isotropic turbulence are
studied using high resolution direct numerical simulation. The scaling
exponents of the energy flux agree with those of the transverse velocity
structure functions through refined similarity hypothesis, consistent with
Kraichnan's prediction \cite{Kr74}. The helicity flux is even more intermittent
than the energy flux and its scaling exponents are closer to those of the
passive scalar. Using Waleffe's helical decomposition, we demonstrate that the
existence of positive mean helicity flux inhibits the energy transfer in the
negative helical modes, a non-passive effect
Decay of scalar variance in isotropic turbulence in a bounded domain
The decay of scalar variance in isotropic turbulence in a bounded domain is
investigated. Extending the study of Touil, Bertoglio and Shao (2002; Journal
of Turbulence, 03, 49) to the case of a passive scalar, the effect of the
finite size of the domain on the lengthscales of turbulent eddies and scalar
structures is studied by truncating the infrared range of the wavenumber
spectra. Analytical arguments based on a simple model for the spectral
distributions show that the decay exponent for the variance of scalar
fluctuations is proportional to the ratio of the Kolmogorov constant to the
Corrsin-Obukhov constant. This result is verified by closure calculations in
which the Corrsin-Obukhov constant is artificially varied. Large-eddy
simulations provide support to the results and give an estimation of the value
of the decay exponent and of the scalar to velocity time scale ratio
Classical and quantum regimes of two-dimensional turbulence in trapped Bose-Einstein condensates
We investigate two-dimensional turbulence in finite-temperature trapped
Bose-Einstein condensates within damped Gross-Pitaevskii theory. Turbulence is
produced via circular motion of a Gaussian potential barrier stirring the
condensate. We systematically explore a range of stirring parameters and
identify three regimes, characterized by the injection of distinct quantum
vortex structures into the condensate: (A) periodic vortex dipole injection,
(B) irregular injection of a mixture of vortex dipoles and co-rotating vortex
clusters, and (C) continuous injection of oblique solitons that decay into
vortex dipoles. Spectral analysis of the kinetic energy associated with
vortices reveals that regime (B) can intermittently exhibit a Kolmogorov
power law over almost a decade of length or wavenumber () scales.
The kinetic energy spectrum of regime (C) exhibits a clear power law
associated with an inertial range for weak-wave turbulence, and a
power law for high wavenumbers. We thus identify distinct regimes of forcing
for generating either two-dimensional quantum turbulence or classical weak-wave
turbulence that may be realizable experimentally.Comment: 11 pages, 10 figures. Minor updates to text and figures 1, 2 and
Lattice Boltzmann study on Kelvin-Helmholtz instability: the roles of velocity and density gradients
A two-dimensional lattice Boltzmann model with 19 discrete velocities for
compressible Euler equations is proposed (D2V19-LBM). The fifth-order Weighted
Essentially Non-Oscillatory (5th-WENO) finite difference scheme is employed to
calculate the convection term of the lattice Boltzmann equation. The validity
of the model is verified by comparing simulation results of the Sod shock tube
with its corresponding analytical solutions. The velocity and density gradient
effects on the Kelvin-Helmholtz instability (KHI) are investigated using the
proposed model. Sharp density contours are obtained in our simulations. It is
found that, the linear growth rate for the KHI decreases with
increasing the width of velocity transition layer but increases with
increasing the width of density transition layer . After the
initial transient period and before the vortex has been well formed, the linear
growth rates, and , vary with and
approximately in the following way, and
, where , ,
and are fitting parameters and is the effective
interaction width of density transition layer. When
the linear growth rate does not vary significantly any more.
One can use the hybrid effects of velocity and density transition layers to
stabilize the KHI. Our numerical simulation results are in general agreement
with the analytical results [L. F. Wang, \emph{et al.}, Phys. Plasma
\textbf{17}, 042103 (2010)].Comment: Accepted for publication in PR
The Evolution of Cosmic Magnetic Fields: From the Very Early Universe, to Recombination, to the Present
(abridged) A detailed examination of the evolution of stochastic magnetic
fields between high cosmic temperatures and the present epoch is presented. A
simple analytical model matching the results of the 3D MHD simulations allows
for the prediction of present day magnetic field correlation lengths and
energy. Our conclusions are multi fold. (a) Initial primordial fields with only
a small amount of helicity are evolving into maximally helical fields. (b)
There exists a correlation between the strength of the magnetic field, B, at
the peak of it's spectrum and the location of the peak, given at the present
epoch by: B ~ 5x10^{-12} (L/kpc) Gauss, where L is the correlation length
determined by the initial magnetic field. (c) Concerning studies of generation
of cosmic microwave background (CMBR) anisotropies due to primordial magnetic
fields of B~10^{-9} Gauss on ~ 10 Mpc scales, such fields are not only
impossible to generate in early causal magnetogenesis scenarios but also
seemingly ruled out by distortions of the CMBR spectrum due to magnetic field
dissipation on smaller scales and the overproduction of cluster magnetic
fields. (d) The most promising detection possibility of CMBR distortions due to
primordial magnetic fields may be on much smaller scales at higher multipoles
l~10^6 where the signal is predicted to be the strongest. (e) It seems possible
that magnetic fields in clusters of galaxies are entirely of primordial origin,
without invoking dynamo amplification. Such fields would be of (pre-collapse)
strength 10^{-12} - 10^{-11} Gauss with correlation lengths in the kpc range,
and would also exist in voids of galaxies.Comment: 35 pages, 22 figures, revtex style, submitted to PR
'Put Your Money Where Your Mouth Is!': Effects of Streaks on Confidence and Betting in a Binary Choice Task.
This is the final published version. It first appeared at http://onlinelibrary.wiley.com/doi/10.1002/bdm.1844/abstract.Human choice under uncertainty is influenced by erroneous beliefs about randomness. In simple binary choice tasks, such as red/black predictions in roulette, long outcome runs (e.g. red, red, red) typically increase the tendency to predict the other outcome (i.e. black), an effect labeled the "gambler's fallacy." In these settings, participants may also attend to streaks in their predictive performance. Winning and losing streaks are thought to affect decision confidence, although prior work indicates conflicting directions. Over three laboratory experiments involving red/black predictions in a sequential roulette task, we sought to identify the effects of outcome runs and winning/losing streaks upon color predictions, decision confidence and betting behavior. Experiments 1 (n = 40) and 3 (n = 40) obtained trial-by-trial confidence ratings, with a win/no win payoff and a no loss/loss payoff, respectively. Experiment 2 (n = 39) obtained a trial-by-trial bet amount on an equivalent scale. In each experiment, the gambler's fallacy was observed on choice behavior after color runs and, in experiment 2, on betting behavior after color runs. Feedback streaks exerted no reliable influence on confidence ratings, in either payoff condition. Betting behavior, on the other hand, increased as a function of losing streaks. The increase in betting on losing streaks is interpreted as a manifestation of loss chasing; these data help clarify the psychological mechanisms underlying loss chasing and caution against the use of betting measures ("post-decision wagering") as a straightforward index of decision confidence. © 2014 The Authors. Journal of Behavioral Decision Making published by John Wiley & Sons Ltd
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