655 research outputs found
Enstrophy dissipation in two-dimensional turbulence
Insight into the problem of two-dimensional turbulence can be obtained by an
analogy with a heat conduction network. It allows the identification of an
entropy function associated to the enstrophy dissipation and that fluctuates
around a positive (mean) value. While the corresponding enstrophy network is
highly nonlocal, the direction of the enstrophy current follows from the Second
Law of Thermodynamics. An essential parameter is the ratio of the intensity of driving as a function of
wavenumber , to the dissipation strength , where is the
viscosity. The enstrophy current flows from higher to lower values of ,
similar to a heat current from higher to lower temperature. Our probabilistic
analysis of the enstrophy dissipation and the analogy with heat conduction thus
complements and visualizes the more traditional spectral arguments for the
direct enstrophy cascade. We also show a fluctuation symmetry in the
distribution of the total entropy production which relates the probabilities of
direct and inverse enstrophy cascades.Comment: 8 pages, revtex
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
Magnetic Fields and Passive Scalars in Polyakov's Conformal Turbulence
Polyakov has suggested that two dimensional turbulence might be described by
a minimal model of conformal field theory. However, there are many minimal
models satisfying the same physical inputs as Polyakov's solution (p,q)=(2,21).
Dynamical magnetic fields and passive scalars pose different physical
requirements. For large magnetic Reynolds number other minimal models arise.
The simplest one, (p,q)=(2,13) makes reasonable predictions that may be tested
in the astrophysical context. In particular, the equipartition theorem between
magnetic and kinetic energies does not hold: the magnetic one dominates at
larger distances.Comment: 12 pages, UR-1296, ER-745-4068
On the stationarity of linearly forced turbulence in finite domains
A simple scheme of forcing turbulence away from decay was introduced by
Lundgren some time ago, the `linear forcing', which amounts to a force term
linear in the velocity field with a constant coefficient. The evolution of
linearly forced turbulence towards a stationary final state, as indicated by
direct numerical simulations (DNS), is examined from a theoretical point of
view based on symmetry arguments. In order to follow closely the DNS the flow
is assumed to live in a cubic domain with periodic boundary conditions. The
simplicity of the linear forcing scheme allows one to re-write the problem as
one of decaying turbulence with a decreasing viscosity. Scaling symmetry
considerations suggest that the system evolves to a stationary state, evolution
that may be understood as the gradual breaking of a larger approximate symmetry
to a smaller exact symmetry. The same arguments show that the finiteness of the
domain is intimately related to the evolution of the system to a stationary
state at late times, as well as the consistency of this state with a high
degree of isotropy imposed by the symmetries of the domain itself. The
fluctuations observed in the DNS for all quantities in the stationary state can
be associated with deviations from isotropy. Indeed, self-preserving isotropic
turbulence models are used to study evolution from a direct dynamical point of
view, emphasizing the naturalness of the Taylor microscale as a self-similarity
scale in this system. In this context the stationary state emerges as a stable
fixed point. Self-preservation seems to be the reason behind a noted similarity
of the third order structure function between the linearly forced and freely
decaying turbulence, where again the finiteness of the domain plays an
significant role.Comment: 15 pages, 7 figures, changes in the discussion at the end of section
VI, formula (60) correcte
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Spectral nonlocality, absolute equilibria and Kraichnan-Leith-Batchelor phenomenology in two-dimensional turbulent energy cascades
We study the degree to which Kraichnan–Leith–Batchelor (KLB) phenomenology describes two-dimensional energy cascades in α turbulence, governed by ∂θ/∂t+J(ψ,θ)=ν∇2θ+f, where θ=(−Δ)α/2ψ is generalized vorticity, and ψ^(k)=k−αθ^(k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (α=1), regular two-dimensional flow (α=2) and rotating shallow flow (α=3), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar inertial range for 2.52.5 leads us to predict that any inverse cascade for α≥2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α≥2.5 is significantly steeper than the KLB prediction, while for α<2.5 we obtain the KLB spectrum
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
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
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
Predictability in Systems with Many Characteristic Times: The Case of Turbulence
In chaotic dynamical systems, an infinitesimal perturbation is exponentially
amplified at a time-rate given by the inverse of the maximum Lyapunov exponent
. In fully developed turbulence, grows as a power of the
Reynolds number. This result could seem in contrast with phenomenological
arguments suggesting that, as a consequence of `physical' perturbations, the
predictability time is roughly given by the characteristic life-time of the
large scale structures, and hence independent of the Reynolds number. We show
that such a situation is present in generic systems with many degrees of
freedom, since the growth of a non-infinitesimal perturbation is determined by
cumulative effects of many different characteristic times and is unrelated to
the maximum Lyapunov exponent. Our results are illustrated in a chain of
coupled maps and in a shell model for the energy cascade in turbulence.Comment: 24 pages, 10 Postscript figures (included), RevTeX 3.0, files packed
with uufile
Anisotropy and non-universality in scaling laws of the large scale energy spectrum in rotating turbulence
Rapidly rotating turbulent flow is characterized by the emergence of columnar
structures that are representative of quasi-two dimensional behavior of the
flow. It is known that when energy is injected into the fluid at an
intermediate scale , it cascades towards smaller as well as larger scales.
In this paper we analyze the flow in the \textit{inverse cascade} range at a
small but fixed Rossby number, {}. Several
{numerical simulations with} helical and non-helical forcing functions are
considered in periodic boxes with unit aspect ratio. In order to resolve the
inverse cascade range with {reasonably} large Reynolds number, the analysis is
based on large eddy simulations which include the effect of helicity on eddy
viscosity and eddy noise. Thus, we model the small scales and resolve
explicitly the large scales. We show that the large-scale energy spectrum has
at least two solutions: one that is consistent with
Kolmogorov-Kraichnan-Batchelor-Leith phenomenology for the inverse cascade of
energy in two-dimensional (2D) turbulence with a {}
scaling, and the other that corresponds to a steeper {}
spectrum in which the three-dimensional (3D) modes release a substantial
fraction of their energy per unit time to 2D modes. {The spectrum that} emerges
{depends on} the anisotropy of the forcing function{,} the former solution
prevailing for forcings in which more energy is injected into 2D modes while
the latter prevails for isotropic forcing. {In the case of anisotropic forcing,
whence the energy} goes from the 2D to the 3D modes at low wavenumbers,
large-scale shear is created resulting in another time scale ,
associated with shear, {thereby producing} a spectrum for the
{total energy} with the 2D modes still following a {}
scaling
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