684 research outputs found
Three regularization models of the Navier-Stokes equations
We determine how the differences in the treatment of the subfilter-scale
physics affect the properties of the flow for three closely related
regularizations of Navier-Stokes. The consequences on the applicability of the
regularizations as SGS models are also shown by examining their effects on
superfilter-scale properties. Numerical solutions of the Clark-alpha model are
compared to two previously employed regularizations, LANS-alpha and Leray-alpha
(at Re ~ 3300, Taylor Re ~ 790) and to a DNS. We derive the Karman-Howarth
equation for both the Clark-alpha and Leray-alpha models. We confirm one of two
possible scalings resulting from this equation for Clark as well as its
associated k^(-1) energy spectrum. At sub-filter scales, Clark-alpha possesses
similar total dissipation and characteristic time to reach a statistical
turbulent steady-state as Navier-Stokes, but exhibits greater intermittency. As
a SGS model, Clark reproduces the energy spectrum and intermittency properties
of the DNS. For the Leray model, increasing the filter width decreases the
nonlinearity and the effective Re is substantially decreased. Even for the
smallest value of alpha studied, Leray-alpha was inadequate as a SGS model. The
LANS energy spectrum k^1, consistent with its so-called "rigid bodies,"
precludes a reproduction of the large-scale energy spectrum of the DNS at high
Re while achieving a large reduction in resolution. However, that this same
feature reduces its intermittency compared to Clark-alpha (which shares a
similar Karman-Howarth equation). Clark is found to be the best approximation
for reproducing the total dissipation rate and the energy spectrum at scales
larger than alpha, whereas high-order intermittency properties for larger
values of alpha are best reproduced by LANS-alpha.Comment: 21 pages, 8 figure
Transformation kinetics of alloys under non-isothermal conditions
The overall solid-to-solid phase transformation kinetics under non-isothermal
conditions has been modeled by means of a differential equation method. The
method requires provisions for expressions of the fraction of the transformed
phase in equilibrium condition and the relaxation time for transition as
functions of temperature. The thermal history is an input to the model. We have
used the method to calculate the time/temperature variation of the volume
fraction of the favored phase in the alpha-to-beta transition in a zirconium
alloy under heating and cooling, in agreement with experimental results. We
also present a formulation that accounts for both additive and non-additive
phase transformation processes. Moreover, a method based on the concept of path
integral, which considers all the possible paths in thermal histories to reach
the final state, is suggested.Comment: 16 pages, 7 figures. To appear in Modelling Simul. Mater. Sci. En
Dynamo action at low magnetic Prandtl numbers: mean flow vs. fully turbulent motion
We compute numerically the threshold for dynamo action in Taylor-Green
swirling flows. Kinematic calculations, for which the flow field is fixed to
its time averaged profile, are compared to dynamical runs for which both the
Navier-Stokes and the induction equations are jointly solved. The kinematic
instability is found to have two branches, for all explored Reynolds numbers.
The dynamical dynamo threshold follows these branches: at low Reynolds number
it lies within the low branch while at high kinetic Reynolds number it is close
to the high branch.Comment: 4 pages, 4 figure
Fast Numerical simulations of 2D turbulence using a dynamic model for Subgrid Motions
We present numerical simulation of 2D turbulent flow using a new model for
the subgrid scales which are computed using a dynamic equation linking the
subgrid scales with the resolved velocity. This equation is not postulated, but
derived from the constitutive equations under the assumption that the
non-linear interactions of subgrid scales between themselves are equivalent to
a turbulent viscosity.The performances of our model are compared with Direct
Numerical Simulations of decaying and forced turbulence. For a same resolution,
numerical simulations using our model allow for a significant reduction of the
computational time (of the order of 100 in the case we consider), and allow the
achievement of significantly larger Reynolds number than the direct method.Comment: 35 pages, 9 figure
Vorticity statistics in the two-dimensional enstrophy cascade
We report the first extensive experimental observation of the two-dimensional
enstrophy cascade, along with the determination of the high order vorticity
statistics. The energy spectra we obtain are remarkably close to the Kraichnan
Batchelor expectation. The distributions of the vorticity increments, in the
inertial range, deviate only little from gaussianity and the corresponding
structure functions exponents are indistinguishable from zero. It is thus shown
that there is no sizeable small scale intermittency in the enstrophy cascade,
in agreement with recent theoretical analyses.Comment: 5 pages, 7 Figure
Finite time singularities in a class of hydrodynamic models
Models of inviscid incompressible fluid are considered, with the kinetic
energy (i.e., the Lagrangian functional) taking the form in 3D Fourier representation, where
is a constant, . Unlike the case (the usual Eulerian
hydrodynamics), a finite value of results in a finite energy for a
singular, frozen-in vortex filament. This property allows us to study the
dynamics of such filaments without the necessity of a regularization procedure
for short length scales. The linear analysis of small symmetrical deviations
from a stationary solution is performed for a pair of anti-parallel vortex
filaments and an analog of the Crow instability is found at small wave-numbers.
A local approximate Hamiltonian is obtained for the nonlinear long-scale
dynamics of this system. Self-similar solutions of the corresponding equations
are found analytically. They describe the formation of a finite time
singularity, with all length scales decreasing like ,
where is the singularity time.Comment: LaTeX, 17 pages, 3 eps figures. This version is close to the journal
pape
Statistics of Dissipation and Enstrophy Induced by a Set of Burgers Vortices
Dissipation and enstropy statistics are calculated for an ensemble of
modified Burgers vortices in equilibrium under uniform straining. Different
best-fit, finite-range scaling exponents are found for locally-averaged
dissipation and enstrophy, in agreement with existing numerical simulations and
experiments. However, the ratios of dissipation and enstropy moments supported
by axisymmetric vortices of any profile are finite. Therefore the asymptotic
scaling exponents for dissipation and enstrophy induced by such vortices are
equal in the limit of infinite Reynolds number.Comment: Revtex (4 pages) with 4 postscript figures included via psfi
Crab Cavity and Cryomodule Development for HL-LHC
The HL-LHC project aims at increasing the LHC luminosity by a factor 10 beyond the design value. The installation of a set of RF Crab Cavities to increase bunch crossing angle is one of the key upgrades of the program. Two concepts, Double Quarter Wave (DQW) and RF Dipole (RFD) have been proposed and are being produced in parallel for test in the SPS beam before the next long shutdown of CERN accelerator’s complex. In the retained concept, two cavities are hosted in one single cryomodule, providing thermal insulation and interfacing with RF coupling, tuning, cryogenics and beam vacuum. This paper overviews the main design choices for the cryomodule and its different components, which have the goal of optimizing the structural, thermal and electro-magnetic behavior of the system, while respecting the existing constraints in terms of integration in the accelerator environment. Prototyping and testing of the most critical components, manufacturing, preparation and installation strategies are also described
Entire solutions of hydrodynamical equations with exponential dissipation
We consider a modification of the three-dimensional Navier--Stokes equations
and other hydrodynamical evolution equations with space-periodic initial
conditions in which the usual Laplacian of the dissipation operator is replaced
by an operator whose Fourier symbol grows exponentially as \ue ^{|k|/\kd} at
high wavenumbers . Using estimates in suitable classes of analytic
functions, we show that the solutions with initially finite energy become
immediately entire in the space variables and that the Fourier coefficients
decay faster than \ue ^{-C(k/\kd) \ln (|k|/\kd)} for any . The
same result holds for the one-dimensional Burgers equation with exponential
dissipation but can be improved: heuristic arguments and very precise
simulations, analyzed by the method of asymptotic extrapolation of van der
Hoeven, indicate that the leading-order asymptotics is precisely of the above
form with . The same behavior with a universal constant
is conjectured for the Navier--Stokes equations with exponential
dissipation in any space dimension. This universality prevents the strong
growth of intermittency in the far dissipation range which is obtained for
ordinary Navier--Stokes turbulence. Possible applications to improved spectral
simulations are briefly discussed.Comment: 29 pages, 3 figures, Comm. Math. Phys., in pres
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