Taylor's (1935) dissipation surrogate reinterpreted

New results from direct numerical simulation of decaying isotropic turbulence show that Taylor’s expression for the viscous dissipation rate ε = CεU3/L is more appropriately interpreted as a surrogate for the inertial energy flux. As a consequence, the well known dependence of the Taylor prefactor Cε on Reynolds number Cε(RL)→Cε,∞ can be understood as corresponding to the onset of an inertial range

Research in nonlinear structural and solid mechanics

Recent and projected advances in applied mechanics, numerical analysis, computer hardware and engineering software, and their impact on modeling and solution techniques in nonlinear structural and solid mechanics are discussed. The fields covered are rapidly changing and are strongly impacted by current and projected advances in computer hardware. To foster effective development of the technology perceptions on computing systems and nonlinear analysis software systems are presented

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

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

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

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 $d$-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

Magnetic resonance imaging of myocardial strain after acute ST-segment-elevation myocardial infarction: a systematic review

The purpose of this systematic review is to provide a clinically relevant, disease-based perspective on myocardial strain imaging in patients with acute myocardial infarction or stable ischemic heart disease. Cardiac magnetic resonance imaging uniquely integrates myocardial function with pathology. Therefore, this review focuses on strain imaging with cardiac magnetic resonance. We have specifically considered the relationships between left ventricular (LV) strain, infarct pathologies, and their associations with prognosis. A comprehensive literature review was conducted in accordance with the PRISMA guidelines. Publications were identified that (1) described the relationship between strain and infarct pathologies, (2) assessed the relationship between strain and subsequent LV outcomes, and (3) assessed the relationship between strain and health outcomes. In patients with acute myocardial infarction, circumferential strain predicts the recovery of LV systolic function in the longer term. The prognostic value of longitudinal strain is less certain. Strain differentiates between infarcted versus noninfarcted myocardium, even in patients with stable ischemic heart disease with preserved LV ejection fraction. Strain recovery is impaired in infarcted segments with intramyocardial hemorrhage or microvascular obstruction. There are practical limitations to measuring strain with cardiac magnetic resonance in the acute setting, and knowledge gaps, including the lack of data showing incremental value in clinical practice. Critically, studies of cardiac magnetic resonance strain imaging in patients with ischemic heart disease have been limited by sample size and design. Strain imaging has potential as a tool to assess for early or subclinical changes in LV function, and strain is now being included as a surrogate measure of outcome in therapeutic trials

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

Texture, twinning and metastable "tetragonal" phase in ultrathin films of HfO₂ on a Si substrate

Thin HfO<sub>2</sub> films grown on the lightly oxidised surface of (100) Si wafers have been examined using dark-field transmission electron microscopy and selected area electron diffraction in plan view. The polycrystalline film has a grain size of the order of 100 nm and many of the grains show evidence of twinning on (110) and (001) planes. Diffraction studies showed that the film had a strong [110] out-of-plane texture, and that a tiny volume fraction of a metastable (possibly tetragonal) phase was retained. The reasons for the texture, twinning and the retention of the metastable phase are discussed