497 research outputs found
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
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
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
A formal derivation of the local energy transfer (LET) theory of homogeneous turbulence
A statistical closure of the Navier-Stokes hierarchy which leads to equations for the two-point, two-time covariance of the velocity field for stationary, homogeneous isotropic turbulence is presented. It is a generalisation of the self-consistent field method due to Edwards (1964) for the stationary, single-time velocity covariance. The probability distribution functional P [u, t] is obtained, in the form of a series, from the Liouville equation by means of a perturbation expansion about a Gaussian distribution, which is chosen to give the exact two-point, two-time covariance. The triple moment is calculated in terms of an ensemble-averaged infinitesimal velocity-field propagator, and shown to yield the Edwards result as a special case. The use of a Gaussian zero-order distribution has been found to justify the introduction of a fluctuation-response relation, which is in accord with modern dynamical theories. In a sense this work completes the analogy drawn by Edwards between turbulence and Brownian motion. Originally Edwards had shown that the noise input was determined by the correlation of the velocity field with the externally applied stirring forces but was unable to determine the system response. Now we find that the system response is determined by the correlation of the velocity field with internal quasi-entropic forces. This analysis is valid to all orders of perturbation theory, and allows the recovery of the Local Energy Transfer (LET) theory, which had previously been derived by more heuristical methods. The LET theory is known to be in good agreement with experimental results. It is also unique among two-point statistical closures in displaying an acceptable (i.e. non-Markovian) relationship between the transfer spectrum and the system response, in accordance with experimental results. As a result of the latter property, it is compatible with the Kolmogorov (K41) spectral phenomenology
Experimental analysis of lateral impact on planar brittle material: spatial properties of the cracks
The breakup of glass and alumina plates due to planar impacts on one of their
lateral sides is studied. Particular attention is given to investigating the
spatial location of the cracks within the plates. Analysis based on a
phenomenological model suggests that bifurcations along the cracks' paths are
more likely to take place closer to the impact region than far away from it, i.
e., the bifurcation probability seems to lower as the perpendicular distance
from the impacted lateral in- creases. It is also found that many observables
are not sensitive to the plate material used in this work, as long as the
fragment multiplicities corresponding to the fragmentation of the plates are
similar. This gives support to the universal properties of the fragmentation
process reported in for- mer experiments. However, even under the just
mentioned circumstances, some spatial observables are capable of distinguishing
the material of which the plates are made and, therefore, it suggests that this
universality should be carefully investigated
Cooling of relativistic electron beams in intense laser pulses : chirps and radiation
Next-generation high-power laser facilities (such as the Extreme Light Infrastructure) will provide unprecedented field intensities, and will allow us to probe qualitatively new physical regimes for the first time. One of the important fundamental questions which will be addressed is particle dynamics when radiation reaction and quantum effects play a significant role. Classical theories of radiation reaction predict beam cooling in the interaction of a relativistic electron bunch and a high-intensity laser pulse, with final-state properties only dependent on the laser fluence. The observed quantum suppression of this cooling instead exhibits a dependence on the laser intensity directly. This offers the potential for final-state properties to be modified or even controlled by tailoring the intensity profile of the laser pulse. In addition to beam properties, quantum effects will be manifest in the emitted radiation spectra, which could be manipulated for use as radiation sources. We compare predictions made by classical, quasi-classical and stochastic theories of radiation reaction, and investigate the influence of chirped laser pulses on the observed radiation spectra
Reconstruction of plasma density profiles by measuring spectra of radiation emitted from oscillating plasma dipoles
We suggest a new method for characterising non-uniform density distributions of plasma by measuring the spectra of radiation emitted from a localised plasma dipole oscillator excited by colliding electromagnetic pulses. The density distribution can be determined by scanning the collision point in space. Two-dimensional particle-in-cell simulations demonstrate the reconstruction of linear and nonlinear density profiles corresponding to laser-produced plasma. The method can be applied to a wide range of plasma, including fusion and low temperature plasmas. It overcomes many of the disadvantages of existing methods that only yield average densities along the path of probe pulses, such as interferometry and spectroscopy
Experimental analysis of lateral impact on planar brittle material
The fragmentation of alumina and glass plates due to lateral impact is
studied. A few hundred plates have been fragmented at different impact
velocities and the produced fragments are analyzed. The method employed in this
work allows one to investigate some geometrical properties of the fragments,
besides the traditional size distribution usually studied in former
experiments. We found that, although both materials exhibit qualitative similar
fragment size distribution function, their geometrical properties appear to be
quite different. A schematic model for two-dimensional fragmentation is also
presented and its predictions are compared to our experimental results. The
comparison suggests that the analysis of the fragments' geometrical properties
constitutes a more stringent test of the theoretical models' assumptions than
the size distribution
Onset criteria for freely decaying isotropic turbulence
From direct numerical simulation (DNS) of turbulence decaying from specified initial conditions for the range of initial Taylor-Reynolds numbers 2.58 ≤ Rλ(0) ≤ 358.6, it was found that the shape of the iconic curve of dimensionless dissipation versus Reynolds number depended strongly on the choice of measurement time. For our preferred time, a composite based on peak values in the dissipation and inertial transfer curves, the result was virtually identical to the forced, stationary case. In order to try varying the initial conditions, an additional run was performed, using the data from a stationary, forced simulation with Rλ = 335 for the initial condition. The results of this suggested that the time taken for energy to pass through the cascade was about one half of an initial eddy turnover time. In the course of studying onset criteria, we found that the exponent for the power-law decay of the energy decreased with increasing Reynolds number and lay in the range 1.35 ≤ n ≤ 2.60
Raman backscattering saturation due to coupling between ωp and 2ωp modes in plasma
Raman backscattering (RBS) in plasma is the basis of plasma-based amplifiers and is important in laser-driven fusion experiments. We show that saturation can arise from nonlinearities due to coupling between the fundamental and harmonic plasma wave modes for sufficiently intense pump and seed pulses. We present a time-dependent analysis that shows that plasma wave phase shifts reach a maximum close to wavebreaking. The study contributes to a new understanding of RBS saturation for counter-propagating laser pulses
- …