Energy transfer and dissipation in forced isotropic turbulence

A model for the Reynolds number dependence of the dimensionless dissipation rate $C_{\varepsilon}$ was derived from the dimensionless K\'{a}rm\'{a}n-Howarth equation, resulting in $C_{\varepsilon}=C_{\varepsilon, \infty} + C/R_L + O(1/R_L^2)$, where $R_L$ is the integral scale Reynolds number. The coefficients $C$ and $C_{\varepsilon,\infty}$ 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 $R_L=5875$ ($R_\lambda=435$), which were used to establish that the decay of dimensionless dissipation with increasing Reynolds number took the form of a power law $R_L^n$ with exponent value $n = -1.000\pm 0.009$, and that this decay of $C_{\varepsilon}$ was actually due to the increase in the Taylor surrogate $U^3/L$. The model equation was fitted to data from the DNS which resulted in the value $C=18.9\pm 1.3$ and in an asymptotic value for $C_\varepsilon$ in the infinite Reynolds number limit of $C_{\varepsilon,\infty} = 0.468 \pm 0.006$.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 $\zeta_n$ from the structure functions $S_n(r)$, is presented as an alternative to the extended self-similarity (ESS) method and the use of generalized structure functions. We propose plotting the ratio $|S_n(r)/S_3(r)|$ against the separation $r$ in accordance with a standard technique for analysing experimental data. This method differs from the ESS technique, which plots $S_n(r)$ against $S_3(r)$, with the assumption $S_3(r) \sim r$. Using our method for the particular case of $S_2(r)$ we obtain the new result that the exponent $\zeta_2$ decreases as the Taylor-Reynolds number increases, with $\zeta_2 \to 0.679 \pm 0.013$ as $R_{\lambda} \to \infty$. This supports the idea of finite-viscosity corrections to the K41 prediction for $S_2$, 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

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 $d$-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 ${\mathcal O}(k^2)$ 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

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

Effects of grass competition upon the establishment of hardwood plantations in Iowa

Third-year results are reported for a test of the effects of removing sod competition, mulching with sod, and root pruning on the survival and growth of black locust, green ash and American elm seedlings planted in both medium and heavy sod covers. Four sizes of sod scalps, 6 (check), 12. 24 and 48 inches in diameter were used. Half of all the plots were mulched with inverted sod, and root-pruned seedlings were used on half of the plots. Two supplementary studies. designed to help explain some of the results of the planting study, also are reported. One of these tested the effects of 12- and 48-inch scalps with and without inverted sod mulch. and those of a check. upon soil moisture during the growing season. This study was located on the heavily sodded area used in the planting study. The other supplementary experiment was designed to determine the permanent wilting point and the relative rates of soil moisture depletion by hardwood tree seedlings and bromegrass over a range of soil moisture values from field capacity to permanent wilting

Optical control of internal electric fields in band-gap graded InGaN nanowires

InGaN nanowires are suitable building blocks for many future optoelectronic devices. We show that a linear grading of the indium content along the nanowire axis from GaN to InN introduces an internal electric field evoking a photocurrent. Consistent with quantitative band structure simulations we observe a sign change in the measured photocurrent as a function of photon flux. This negative differential photocurrent opens the path to a new type of nanowire-based photodetector. We demonstrate that the photocurrent response of the nanowires is as fast as 1.5 ps

Fiber-optic three axis magnetometer prototype development

The goal of this research program was to develop a high sensitivity, fiber optic, interferometric, three-axis magnetometer for interplanetary spacecraft applications. Dynamics Technology, Inc. (DTI) has successfully integrated a low noise, high bandwidth interferometer with high sensitivity metallic glass transducers. Also, DTI has developed sophisticated signal processing electronics and complete data acquisition, filtering, and display software. The sensor was packaged in a compact, low power and weight unit which facilitates deployment. The magnetic field sensor had subgamma sensitivity and a dynamic range of 10(exp 5) gamma in a 10 Hz bandwidth. Furthermore, the vector instrument exhibited the lowest noise level when only one axis was in operation. A system noise level of 1 gamma rms was observed in a 1 Hz bandwidth. However, with the other two channels operating, the noise level increased by about one order of magnitude. Higher system noise was attributed to cross-channel interference among the dither fields

Trajectory structures and transport

The special problem of transport in 2-dimensional divergence-free stochastic velocity fields is studied by developing a statistical approach, the nested subensemble method. The nonlinear process of trapping determined by such fields generates trajectory structures whose statistical characteristics are determined. These structures strongly influence the transport.Comment: Latex file 19 pages, includes 12 EPS figures. Extended version of the invited talk at the ITCPP, Santorini, 200

Radiation-induced root surface caries restored with glass-ionomer cement placed in conventional and ART cavity preparations: Results at two years

The document attached has been archived with permission from the Australian Dental Association (8th Jan 2008). An external link to the publisher’s copy is included.Background: There are no published studies comparing the clinical performances of more-viscous glass-ionomer cement (GIC) restorations when placed using conventional and atraumatic restorative treatment (ART) cavity preparation methods to restore root surface caries. Methods: One dentist used encapsulated Fuji IX GP and Ketac-Molar to restore 72 conventional and 74 ART cavity preparations for 15 patients who had received cervicofacial radiation therapy. Two assessors evaluated the restorations at six, 12, and 24 months for retention, marginal defects and surface wear, and recurrent caries. Results: After two years, the cumulative restoration successes were 65.2 per cent for the conventional and 66.2 per cent for the ART cavity preparations, without statistical or clinical significance (P>0.50). Restoration dislodgement accounted for 82.8 per cent and marginal defects for 17.2 per cent of all failures. There were no instances of unsatisfactory restoration wear or recurrent caries observed. Teeth with three or more restored cervical surfaces accounted for 79.3 per cent of all failures (P<0.0001). Conclusions: For root surface caries restored with GIC, the use of hand instruments only with the ART method was an equally effective alternative to conventional rotary instrumentation for cavity preparation. Larger restorations had higher failures, usually from dislodgement.JY Hu, XC Chen, YQ Li, RJ Smales and KH Yi