1,006 research outputs found
Eulerian spectral closures for isotropic turbulence using a time-ordered fluctuation-dissipation relation
Procedures for time-ordering the covariance function, as given in a previous
paper (K. Kiyani and W.D. McComb Phys. Rev. E 70, 066303 (2004)), are extended
and used to show that the response function associated at second order with the
Kraichnan-Wyld perturbation series can be determined by a local (in wavenumber)
energy balance. These time-ordering procedures also allow the two-time
formulation to be reduced to time-independent form by means of exponential
approximations and it is verified that the response equation does not have an
infra-red divergence at infinite Reynolds number. Lastly, single-time
Markovianised closure equations (stated in the previous paper above) are
derived and shown to be compatible with the Kolmogorov distribution without the
need to introduce an ad hoc constant.Comment: 12 page
Upper critical dimension of the KPZ equation
Numerical results for the Directed Polymer model in 1+4 dimensions in various
types of disorder are presented. The results are obtained for system size
considerably larger than that considered previously. For the extreme strong
disorder case (Min-Max system), associated with the Directed Percolation model,
the expected value of the meandering exponent, zeta = 0.5 is clearly revealed,
with very week finite size effects. For the week disorder case, associated with
the KPZ equation, finite size effects are stronger, but the value of seta is
clearly seen in the vicinity of 0.57. In systems with "strong disorder" it is
expected that the system will cross over sharply from Min-Max behavior at short
chains to weak disorder behavior at long chains. This is indeed what we find.
These results indicate that 1+4 is not the Upper Critical Dimension (UCD) in
the week disorder case, and thus 4+1 does not seem to be the upper critical
dimension for the KPZ equation
Energy transfer and dissipation in forced isotropic turbulence
A model for the Reynolds number dependence of the dimensionless dissipation
rate was derived from the dimensionless
K\'{a}rm\'{a}n-Howarth equation, resulting in , where is the integral scale Reynolds
number. The coefficients and arise from asymptotic
expansions of the dimensionless second- and third-order structure functions.
This theoretical work was supplemented by direct numerical simulations (DNSs)
of forced isotropic turbulence for integral scale Reynolds numbers up to
(), which were used to establish that the decay of
dimensionless dissipation with increasing Reynolds number took the form of a
power law with exponent value , and that this
decay of was actually due to the increase in the Taylor
surrogate . The model equation was fitted to data from the DNS which
resulted in the value and in an asymptotic value for
in the infinite Reynolds number limit of
.Comment: 26 pages including references and 6 figures. arXiv admin note: text
overlap with arXiv:1307.457
Spectral analysis of structure functions and their scaling exponents in forced isotropic turbulence
The pseudospectral method, in conjunction with a new technique for obtaining
scaling exponents from the structure functions , is presented
as an alternative to the extended self-similarity (ESS) method and the use of
generalized structure functions. We propose plotting the ratio
against the separation in accordance with a standard
technique for analysing experimental data. This method differs from the ESS
technique, which plots against , with the assumption . Using our method for the particular case of we obtain the new
result that the exponent decreases as the Taylor-Reynolds number
increases, with as . This
supports the idea of finite-viscosity corrections to the K41 prediction for
, and is the opposite of the result obtained by ESS. The pseudospectral
method also permits the forcing to be taken into account exactly through the
calculation of the energy input in real space from the work spectrum of the
stirring forces.Comment: 31 pages including appendices, 10 figure
Non-local modulation of the energy cascade in broad-band forced turbulence
Classically, large-scale forced turbulence is characterized by a transfer of
energy from large to small scales via nonlinear interactions. We have
investigated the changes in this energy transfer process in broad-band forced
turbulence where an additional perturbation of flow at smaller scales is
introduced. The modulation of the energy dynamics via the introduction of
forcing at smaller scales occurs not only in the forced region but also in a
broad range of length-scales outside the forced bands due to non-local triad
interactions. Broad-band forcing changes the energy distribution and energy
transfer function in a characteristic manner leading to a significant
modulation of the turbulence. We studied the changes in this transfer of energy
when changing the strength and location of the small-scale forcing support. The
energy content in the larger scales was observed to decrease, while the energy
transport power for scales in between the large and small scale forcing regions
was enhanced. This was investigated further in terms of the detailed transfer
function between the triad contributions and observing the long-time statistics
of the flow. The energy is transferred toward smaller scales not only by
wavenumbers of similar size as in the case of large-scale forced turbulence,
but by a much wider extent of scales that can be externally controlled.Comment: submitted to Phys. Rev. E, 15 pages, 18 figures, uses revtex4.cl
Re-examination of the infra-red properties of randomly stirred hydrodynamics
Dynamic renormalization group (RG) methods were originally used by Forster,
Nelson and Stephen (FNS) to study the large-scale behaviour of
randomly-stirred, incompressible fluids governed by the Navier-Stokes
equations. Similar calculations using a variety of methods have been performed
since, but have led to a discrepancy in results. In this paper, we carefully
re-examine in -dimensions the approaches used to calculate the renormalized
viscosity increment and, by including an additional constraint which is
neglected in many procedures, conclude that the original result of FNS is
correct. By explicitly using step functions to control the domain of
integration, we calculate a non-zero correction caused by boundary terms which
cannot be ignored. We then go on to analyze how the noise renormalization,
absent in many approaches, contributes an correction to the
force autocorrelation and show conditions for this to be taken as a
renormalization of the noise coefficient. Following this, we discuss the
applicability of this RG procedure to the calculation of the inertial range
properties of fluid turbulence.Comment: 16 pages, 6 figure
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