74 research outputs found
A coalescence model for freely decaying two-dimensional turbulence
We propose a ballistic coalescence model (punctuated-Hamiltonian approach)
mimicking the fusion of vortices in freely decaying two-dimensional turbulence.
A temporal scaling behaviour is reached where the vortex density evolves like
. A mean-field analytical argument yielding the approximation
is shown to slightly overestimate the decay exponent whereas
Molecular Dynamics simulations give , in agreement with
recent laboratory experiments and simulations of Navier-Stokes equation.Comment: 6 pages, 1 figure, to appear in Europhysics Letter
Closure of two dimensional turbulence: the role of pressure gradients
Inverse energy cascade regime of two dimensional turbulence is investigated
by means of high resolution numerical simulations. Numerical computations of
conditional averages of transverse pressure gradient increments are found to be
compatible with a recently proposed self-consistent Gaussian model. An
analogous low order closure model for the longitudinal pressure gradient is
proposed and its validity is numerically examined. In this case numerical
evidence for the presence of higher order terms in the closure is found. The
fundamental role of conditional statistics between longitudinal and transverse
components is highlighted.Comment: 4 pages, 2 figures, in press on PR
Characteristics of Two-Dimensional Quantum Turbulence in a Compressible Superfluid
Under suitable forcing a fluid exhibits turbulence, with characteristics
strongly affected by the fluid's confining geometry. Here we study
two-dimensional quantum turbulence in a highly oblate Bose-Einstein condensate
in an annular trap. As a compressible quantum fluid, this system affords a rich
phenomenology, allowing coupling between vortex and acoustic energy.
Small-scale stirring generates an experimentally observed disordered vortex
distribution that evolves into large-scale flow in the form of a persistent
current. Numerical simulation of the experiment reveals additional
characteristics of two-dimensional quantum turbulence: spontaneous clustering
of same-circulation vortices, and an incompressible energy spectrum with
dependence for low wavenumbers and dependence for high
.Comment: 7 pages, 7 figures. Reference [29] updated for v
Quasilinear theory of the 2D Euler equation
We develop a quasilinear theory of the 2D Euler equation and derive an
integro-differential equation for the evolution of the coarse-grained
vorticity. This equation respects all the invariance properties of the Euler
equation and conserves angular momentum in a circular domain and linear impulse
in a channel. We show under which hypothesis we can derive a H-theorem for the
Fermi-Dirac entropy and make the connection with statistical theories of 2D
turbulence.Comment: 4 page
Large eddy simulation of two-dimensional isotropic turbulence
Large eddy simulation (LES) of forced, homogeneous, isotropic,
two-dimensional (2D) turbulence in the energy transfer subrange is the subject
of this paper. A difficulty specific to this LES and its subgrid scale (SGS)
representation is in that the energy source resides in high wave number modes
excluded in simulations. Therefore, the SGS scheme in this case should assume
the function of the energy source. In addition, the controversial requirements
to ensure direct enstrophy transfer and inverse energy transfer make the
conventional scheme of positive and dissipative eddy viscosity inapplicable to
2D turbulence. It is shown that these requirements can be reconciled by
utilizing a two-parametric viscosity introduced by Kraichnan (1976) that
accounts for the energy and enstrophy exchange between the resolved and subgrid
scale modes in a way consistent with the dynamics of 2D turbulence; it is
negative on large scales, positive on small scales and complies with the basic
conservation laws for energy and enstrophy. Different implementations of the
two-parametric viscosity for LES of 2D turbulence were considered. It was found
that if kept constant, this viscosity results in unstable numerical scheme.
Therefore, another scheme was advanced in which the two-parametric viscosity
depends on the flow field. In addition, to extend simulations beyond the limits
imposed by the finiteness of computational domain, a large scale drag was
introduced. The resulting LES exhibited remarkable and fast convergence to the
solution obtained in the preceding direct numerical simulations (DNS) by
Chekhlov et al. (1994) while the flow parameters were in good agreement with
their DNS counterparts. Also, good agreement with the Kolmogorov theory was
found. This LES could be continued virtually indefinitely. Then, a simplifiedComment: 34 pages plain tex + 18 postscript figures separately, uses auxilary
djnlx.tex fil
Turbulent jet through porous obstructions under Coriolis effect: an experimental investigation
The present study has the main purpose to experimentally investigate a turbulent momentum jet issued in a basin affected by rotation and in presence of porous obstructions. The experiments were carried out at the Coriolis Platform at LEGI Grenoble (FR). A large and unique set of velocity data was obtained by means of a Particle Image Velocimetry measurement technique while varying the rotation rate of the tank and the density of the canopy. The main differences in jet behavior in various flow configurations were assessed in terms of mean flow, turbulent kinetic energy and jet spreading. The jet trajectory was also detected. The results prove that obstructions with increasing density and increased rotation rates induce a more rapid abatement of both jet velocity and turbulent kinetic energy. The jet trajectories can be scaled by a characteristic length, which is found to be a function of the jet initial momentum, the rotation rate, and the drag exerted by the obstacles. An empirical expression for the latter is also proposed and validated
Impact of dense-water flow over a sloping bottom on open-sea circulation: Laboratory experiments and an Ionian Sea (Mediterranean) example
The North Ionian Gyre (NIG) displays prominent inversions on decadal scales. We investigate the role of internal forcing induced by changes in the horizontal pressure gradient due to the varying density of Adriatic Deep Water (AdDW), which spreads into the deep layers of the northern Ionian Sea. In turn, the AdDW density fluctuates according to the circulation of the NIG through a feedback mechanism known as the bimodal oscillating system. We set up laboratory experiments with a two-layer ambient fluid in a circular rotating tank, where densities of 1000 and 1015ÄâŹÂŻkgÄâŹÂŻm-3 characterize the upper and lower layers, respectively. From the potential vorticity evolution during the dense-water outflow from a marginal sea, we analyze the response of the open-sea circulation to the along-slope dense-water flow. In addition, we show some features of the cyclonic and anticyclonic eddies that form in the upper layer over the slope area. We illustrate the outcome of the experiments of varying density and varying discharge rates associated with dense-water injection. When the density is high (1020ÄâŹÂŻkgÄâŹÂŻm-3) and the discharge is large, the kinetic energy of the mean flow is stronger than the eddy kinetic energy. Conversely, when the density is lower (1010ÄâŹÂŻkgÄâŹÂŻm-3) and the discharge is reduced, vortices are more energetic than the mean flow - that is, the eddy kinetic energy is larger than the kinetic energy of the mean flow. In general, over the slope, following the onset of dense-water injection, the cyclonic vorticity associated with current shear develops in the upper layer. The vorticity behaves in a two-layer fashion, thereby becoming anticyclonic in the lower layer of the slope area. Concurrently, over the deep flat-bottom portion of the basin, a large-scale anticyclonic gyre forms in the upper layer extending partly toward a sloping rim. The density record shows the rise of the pycnocline due to the dense-water sinking toward the flat-bottom portion of the tank. We show that the rate of increase in the anticyclonic potential vorticity is proportional to the rate of the rise of the interface, namely to the rate of decrease in the upper-layer thickness (i.e., the upper-layer squeezing). The comparison of laboratory experiments with the Ionian Sea is made for a situation when the sudden switch from cyclonic to anticyclonic basin-wide circulation took place following extremely dense Adriatic water overflow after the harsh winter in 2012. We show how similar the temporal evolution and the vertical structure are in both laboratory and oceanic conditions. The demonstrated similarity further supports the assertion that the wind-stress curl over the Ionian Sea is not of paramount importance in generating basin-wide circulation inversions compared with the internal forcing
Slow relaxation in the two dimensional electron plasma under the strong magnetic field
We study slow relaxation processes in the point vortex model for the
two-dimensional pure electron plasma under the strong magnetic field. By
numerical simulations, it is shown that, from an initial state, the system
undergoes the fast relaxation to a quasi-stationary state, and then goes
through the slow relaxation to reach a final state. From analysis of simulation
data, we find (i) the time scale of the slow relaxation increases linearly to
the number of electrons if it is measured by the unit of the bulk rotation
time, (ii) during the slow relaxation process, each electron undergoes an
superdiffusive motion, and (iii) the superdiffusive motion can be regarded as
the Levy flight, whose step size distribution is of the power law. The time
scale that each electron diffuses over the system size turns out to be much
shorter than that of the slow relaxation, which suggests that the correlation
among the superdiffusive trajectories is important in the slow relaxation
process.Comment: 11pages, 19 figures. Submitted to J. Phys. Soc. Jp
Generalized thermodynamics and Fokker-Planck equations. Applications to stellar dynamics, two-dimensional turbulence and Jupiter's great red spot
We introduce a new set of generalized Fokker-Planck equations that conserve
energy and mass and increase a generalized entropy until a maximum entropy
state is reached. The concept of generalized entropies is rigorously justified
for continuous Hamiltonian systems undergoing violent relaxation. Tsallis
entropies are just a special case of this generalized thermodynamics.
Application of these results to stellar dynamics, vortex dynamics and Jupiter's
great red spot are proposed. Our prime result is a novel relaxation equation
that should offer an easily implementable parametrization of geophysical
turbulence. This relaxation equation depends on a single key parameter related
to the skewness of the fine-grained vorticity distribution. Usual
parametrizations (including a single turbulent viscosity) correspond to the
infinite temperature limit of our model. They forget a fundamental systematic
drift that acts against diffusion as in Brownian theory. Our generalized
Fokker-Planck equations may have applications in other fields of physics such
as chemotaxis for bacterial populations. We propose the idea of a
classification of generalized entropies in classes of equivalence and provide
an aesthetic connexion between topics (vortices, stars, bacteries,...) which
were previously disconnected.Comment: Submitted to Phys. Rev.
Relaxation equations for two-dimensional turbulent flows with a prior vorticity distribution
Using a Maximum Entropy Production Principle (MEPP), we derive a new type of
relaxation equations for two-dimensional turbulent flows in the case where a
prior vorticity distribution is prescribed instead of the Casimir constraints
[Ellis, Haven, Turkington, Nonlin., 15, 239 (2002)]. The particular case of a
Gaussian prior is specifically treated in connection to minimum enstrophy
states and Fofonoff flows. These relaxation equations are compared with other
relaxation equations proposed by Robert and Sommeria [Phys. Rev. Lett. 69, 2776
(1992)] and Chavanis [Physica D, 237, 1998 (2008)]. They can provide a
small-scale parametrization of 2D turbulence or serve as numerical algorithms
to compute maximum entropy states with appropriate constraints. We perform
numerical simulations of these relaxation equations in order to illustrate
geometry induced phase transitions in geophysical flows.Comment: 21 pages, 9 figure
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