Energetic Scales Research Articles

Rydberg Composites

We introduce the Rydberg Composite, a new class of Rydberg matter where a single Rydberg atom is interfaced with a dense environment of neutral ground state atoms. The properties of the Composite depend on both the Rydberg excitation, which provides the gross energetic and spatial scales, and on the distribution of ground state atoms within the volume of the Rydberg wave function, which sculpt the electronic states. The latter range from the "trilobites", for small numbers of scatterers, to delocalized and chaotic eigenstates for disordered scatterer arrays, culminating in the dense scatterer limit in symmetry-dominated wave functions which promise good control in future experiments. We characterize these scenarios with different theoretical methods, enabling us to obtain scaling behavior for the regular spectrum and measures of chaos and delocalization in the disordered regime. Thus, we obtain a systematic description of the Composite states. The 2D monolayer Composite possesses the richest spectrum with an intricate band structure in the limit of homogeneous scatterers.

A statistical analysis of developing knock intensity in a mixture with temperature inhomogeneities

Knock formation and its intensity for a stoichiometric ethanol/air mixture under a representative end-gas auto-ignition condition in IC engines with temperature inhomogeneities are investigated using multi-dimensional direct numerical simulations (DNS) with a 40-species skeletal mechanism of ethanol. Two- and three-dimensional simulations are performed by systematically varying temperature fluctuations and its most energetic length scale, lT. The volumetric fraction of the mixture regions that have the propensity to detonation development, FD, is proposed as a metric to predict the amplitude of knock intensity. It is found that with increasing lT, FD shows a good agreement with the heat release fraction of the mixture regions with pressure greater than equilibrium pressure, FH. The detonation peninsula is well captured by FD and FH when plotting them as a function of the volume-averaged ξ, ξ¯, (ξ=a/Ssp is the ratio of the acoustic speed, a to the ignition front speed, Ssp). Decreasing lT is found to significantly reduce the super-knock intensity. The results suggest that decreasing lT, as in engines with tumble designs resulting in a smaller turbulence scale, will be effective in mitigating the the super-knock development.

Direct numerical simulation of supersonic flow and acoustics over a compression ramp

We present direct numerical simulations of the shock wave boundary layer interaction (SBLI) at Mach number 2.9 over a 24° ramp. We study both the numerical accuracy and flow physics. Two classes of spatial reconstruction schemes are employed: the monotonic upstream-centered scheme for conservation laws and the Weighted Essentially Non-Oscillatory (WENO) scheme, of accuracy ranging from 2nd- to 11th-order. Using the canonical Taylor–Green vortex test-case, a simple and computationally inexpensive rescaling of the candidate stencil values—within the context of the high-order WENO scheme—is proposed for reducing the numerical dissipation, particularly in under-resolved simulations. For the compression ramp case, higher-order schemes are shown to capture the size of the SBLI separation zone more accurately, a consequence of resolving much finer turbulence structures. For second- and fifth-order schemes, the energy of the unresolved small scale turbulence shifts the cascade of the turbulence kinetic energy (TKE) spectrum, thus resulting in more energetic large scale turbulent structures. Consequently, the λ-shock foot shifts further downstream, leading to a smaller separation bubble size. Nonetheless, other statistical quantities, such as the turbulence anisotropy invariant map and the turbulence kinetic energy budget terms, show little dependence on the type and order of the spatial reconstruction scheme. Finally, using the more accurate ninth-order WENO results, it is reasoned that the interaction of the λ-shock with the post-shock relaxation region drives the low-frequency oscillation of the λ-shock.

Effects of Turbulence and Temperature Fluctuations on Knock Development in an Ethanol/Air Mixture

The effects of turbulence on knock development and intensity for a thermally inhomogeneous stoichiometric ethanol/air mixture at a representative end-gas autoignition condition in internal combustion engines are investigated using direct numerical simulations with a skeletal reaction mechanism. Two- and three-dimensional simulations are performed by varying the most energetic length scale of temperature, $$l_T$$ , and its relative ratio with the most energetic length scale of turbulence, $$l_T/l_e$$ , together with two different levels of the turbulent velocity fluctuation, $$u'$$ . It is found that $$l_T$$ / $$l_e$$ and the ratio of ignition delay time to eddy-turnover time, $$\tau _{ig}/\tau _t$$ , are the key parameters that control the detonation development. An increase in either $$l_T$$ or $$l_e$$ enhances the detonation propensity by allowing a longer run-up distance for the detonation development. The characteristic length scale of the temperature field, $$l_T$$ , is significantly modified by high turbulence intensity achieved by a large $$l_e$$ and $$u'$$ . The intense turbulence mixing effectively distributes the initial temperature field to broader scales to support the developing detonation waves, thereby increasing the likelihood of the detonation formation. On the contrary, high turbulence intensity with a short mixing time scale, achieved by a small $$l_e$$ and a large $$u'$$ , reduces the super-knock intensity attributed to the finer broken-up structures of detonation waves. Either $$\tau _{ig}/\tau _t$$ less than unity or $$l_e = l_T$$ even with a large $$u'$$ is found to have no significant effect on super-knock mitigation. Finally, high turbulent intensity may induce high-pressure spikes comparable to the von Neumann spike. Increased temperature and pressure by combustion heating, noticeably after the peak of heat release rate, significantly enhance the collision and interaction of multiple emerging autoignition fronts near the ending combustion process, resulting in localized high-pressure spikes.

Destabilization of beta-induced Alfvén eigenmodes by energetic trapped electrons in tokamak

The stability of high torodial mode number (n) beta-induced Alfvén eigenmodes excited by precessional resonance of magnetically trapped energetic electrons in low magnetic-shear tokamak plasma is investigated. The dispersion relation of the energetic-electron beta-induced Alfvén eigenmodes (e-BAE) is derived and solved analytically and numerically. It is found that the contribution of the trapped energetic electrons to the e-BAE dispersion relation is limited to the ideal MHD structure of the BAE. Numerical results show that, for typical equilibrium parameters, the e-BAE can be destabilized by the energetic electrons, and the mode frequency is consistent with the experimental observation. Varying the background plasma parameters can lead to transitions between e-BAEs and energetic particle modes. Moreover, the dependence of the e-BAE frequencies and growth rates on energetic electron parameters shows that the growth rates monotonically increase(decrease) with the energetic electron density(the normalized energetic electron density scale length), and the frequencies are not much affected. The frequency and growth rate are sensitive to the energetic electron temperature, and there exists a maximum growth rate.

Recovering the Eulerian energy spectrum from noisy Lagrangian tracers

We consider the time-sequential state estimation of a flow field given a stream of noisy measurements that are provided by instruments advected by the flow, known as Lagrangian tracers or drifters. Lagrangian drifters collect real-time data as they move through the velocity field and are an important data collection method for atmospheric and oceanic measurements. We quantify the recovery of the Eulerian energy spectra from observations of Lagrangian drifters. This is performed by utilizing special Lagrangian data assimilation algorithms, known as conditionally Gaussian nonlinear filters. We address the following questions: how much of the turbulent Eulerian energy spectra can be recovered from assimilation of Lagrangian trajectory data and how accurately are the various energetic scales recovered relative to the truth. These issues are primarily studied in the perfect model scenario, but we quantify recovery due to model error by reduced order models via spectral truncation of the forecast model. We demonstrate high recovery skill of the two-dimensional turbulent energy spectra for both an exact filter and an imperfect filter, based on extreme localization of the covariance matrix, which is vastly cheaper than the exact filter, for both an inverse cascade spectrum with slope k−5∕3 and a direct cascade spectrum with slope k−3. The dependence of the spectral energy recovery skill on the number of tracers and the spectral truncation grid size is also studied.

Toward Rational Understandings of α-C-H Functionalization: Energetic Studies of Representative Tertiary Amines.

SummaryFunctionalization of α-C–H bonds of tertiary amines to build various α-C–X bonds has become a mainstream in synthetic chemistry nowadays. However, due to lack of fundamental knowledge on α-C–H bond strength as an energetic guideline, rational exploration of new synthetic methodologies remains a far-reaching anticipation. Herein, we report a unique hydricity-based approach to establish the first integrated energetic scale covering both the homolytic and heterolytic energies of α-C–H bonds for 45 representative tertiary amines and their radical cations. As showcased from the studies on tetrahydroisoquinolines (THIQs) by virtue of their thermodynamic criteria, the feasibility and mechanisms of THIQ oxidation were deduced, which, indeed, were found to correspond well with experimental observations. This integrated scale provides a good example to relate bond energetics with mechanisms and thermodynamic reactivity of amine α-C–H functionalization and hence, may be referenced for analyzing similar structure-property problems for various substrates.

Wide-Swath Altimetric Satellite Data Assimilation With Correlated-Error Reduction

For decades now, satellite altimetric observations have been successfully integrated in numerical oceanographic models using data assimilation (DA). So far, sea surface height (SSH) data were provided by one-dimensional nadir altimeters. The next generation Surface Water and Ocean Topography (SWOT) satellite altimeter will provide two-dimensional wide-swath altimetric information with an unprecedented high resolution. This new type of SSH data is expected to strongly improve altimetric assimilation. However, the SWOT data is also expected to be affected by spatially correlated errors and, hence, can not be assimilated as easily as nadir altimeters. The present paper proposes to embed a state-of-the-art correlated-error reduction (CER) method for the SWOT data into an ensemble-based DA scheme. The DA with the new correlated-error reduced-data (CER-data) is implemented and tested in a simple SSH reconstruction problem using artificial SWOT data and a quasi-geostrophic model. The results show that, in an energetic large scale region, the DA with CER-data—in comparison to the classical DA—reduces the root-mean-square-error (RMSE) of the reconstruction in SSH by approximately 10%, in relative vorticity by 5% and in surface currents by 5–10%, and also slightly improves the noise-to-signal ratio and spectral coherence of the SSH signal at mesoscale (100–200 km) but with a small degradation on the large scales (>300 km). In a less energetic region, the DA with CER-data cuts down the RMSE in SSH by more than 50% on average therefore allowing a significantly more accurate reconstruction of SSH at mesoscale in terms of noise-to-signal ratio, spectral coherence, and power spectral density.

Large-eddy simulations of idealized atmospheric boundary layers using Nalu-Wind

Accurate prediction of wind-plant performance relies, in part, on properly characterizing the turbulent atmospheric boundary layer (ABL) flow in which wind turbines operate. Large-eddy simulation (LES) is a powerful tool for simulating ABLs because it resolves the largest, most energetic scales of three-dimensional turbulent motions. Yet LES predictions are well known to depend on modeling choices such as grid resolution, numerical discretization schemes, and closures for unresolved scales of turbulence. Here, we evaluate how these choices influence predictions of ABL winds using Nalu-Wind, a wind-specific fork of the open-source, generalized, unstructured, massively parallel flow solver NaluCFD/Nalu.

Effect of adverse pressure gradients on turbulent wing boundary layers

The characteristics of turbulent boundary layers (TBLs) subjected to adverse pressure gradients are analysed through well-resolved large-eddy simulations. The geometries under study are the NACA0012 and NACA4412 wing sections, at and angle of attack, respectively, both of them at a Reynolds number based on inflow velocity and chord length of . The turbulence statistics show that adverse pressure gradients (APGs) have a significant effect on the mean velocity, velocity fluctuations and turbulent kinetic energy budget, and this effect is more prominent on the outer region of the boundary layer. Furthermore, the effect of flow history is assessed by means of an integrated Clauser pressure-gradient parameter (Vinuesa et al., Flow Turbul. Combust., vol. 99, 2017, pp. 565–587), through the study of cases with matching local values of and the friction Reynolds number to isolate this effect. Our results show a noticeable effect of the flow history on the outer region, however the differences in the near-wall peak of the tangential velocity fluctuations appear to be mostly produced by the local APG magnitude. The one-dimensional power-spectral density shows energetic small scales in the outer region of APG TBLs, whereas these energetic scales do not appear in zero-pressure-gradient (ZPG) TBLs, suggesting that small scales near the wall are advected towards the outer layer by the APG. Moreover, the linear coherence spectra show that the spectral outer peak of high-Reynolds-number ZPG TBLs is highly correlated with the near-wall region (Baars et al., J. Fluid Mech., vol. 823, 2017, R2), unlike APG TBLs which do not show such a correlation. This result, together with the different two-dimensional spectra of APG and high-Reynolds-number ZPG TBLs, suggests different energisation mechanisms due to APG and increase in Reynolds number. To the authors’ knowledge, this is the first in-depth analysis of the TBL characteristics over wings, including detailed single-point statistics, spectra and coherence.

Towards Rational Understandings of α-C–H Functionalization: Energetic Studies of Representative Tertiary Amines

Functionalization of α-C–H bonds of tertiary amines to build various α-C–X bonds has become a mainstream in synthetic chemistry. However, due to lack of fundamental knowledge on α-C–H bond strength, rational exploration of new synthetic methodologies remains a far-reaching anticipation. Herein, we report a unique hydricity-based approach to establish the first integrated energetic scale covering both the homolytic and heterolytic energies of α-C–H bonds for 45 representative tertiary amines and their radical cations. As showcased from the studies on tetrahydroisoquinolines by virtue of the thermodynamic criteria, the feasibility and mechanisms of their oxidation were deduced, and indeed, were found to correspond well with experimental observations. This energetic scale actually provides a good example among the α-C–H categories to relate the bond thermodynamics with mechanisms/reactivity of their α-C–H transformation, and hence, may be referenced for analyzing similar structure-property problems for a wide variety of substrates.

Strain gradient crystal plasticity model based on generalized non-quadratic defect energy and uncoupled dissipation

The present paper proposes a flexible Gurtin-type strain gradient crystal plasticity (SGCP) model based on generalized non-quadratic defect energy and uncoupled constitutive assumption for dissipative processes. A power-law defect energy, with adjustable order-controlling index n, is proposed to provide a comprehensive investigation into the energetic length scale effects under proportional and non-proportional loading conditions. Results of this investigation reveal quite different effects of the energetic length scale, depending on the value of n and the type of loading. For n ≥ 2, regardless of the loading type, the energetic length scale has only influence on the rate of the classical kinematic hardening, as reported in several SGCP works. However, in the range of n < 2, this parameter leads to unusual nonlinear kinematic hardening effects with inflection points in the macroscopic mechanical response, resulting in an apparent increase of the yield strength under monotonic loading. More complex effects, with additional inflection points, are obtained under non-proportional loading conditions, revealing new loading history memory-like effects of the energetic length scale. Concerning dissipation, to make the dissipative effects more easily controllable, dissipative processes due to plastic strains and their gradients are assumed to be uncoupled. Separate formulations, expressed using different effective plastic strain measures, are proposed to describe such processes. Results obtained using these formulations show the great flexibility of the proposed model in controlling some major dissipative effects, such as elastic gaps. A simple way to remove these gaps under certain non-proportional loading conditions is provided. Application of the proposed uncoupled formulations to simulate the mechanical response of a sheared strip has led to accurate prediction of the plastic strain distributions, which compare very favorably with those predicted using discrete dislocation mechanics.

Energetics of optimal undulatory swimming organisms.

Energy consumption is one of the primary considerations in animal locomotion. In swimming locomotion, a number of questions related to swimming energetics of an organism and how the energetic quantities scale with body size remain open, largely due to the difficulties with modeling and measuring the power production and consumption. Based on a comprehensive theoretical framework that incorporates cyclic muscle behavior, structural dynamics and swimming hydrodynamics, we perform extensive computational simulations and show that many of the outstanding problems in swimming energetics can be explained by considering the coupling between hydrodynamics and muscle contraction characteristics, as well as the trade-offs between the conflicting performance goals of sustained swimming speed U and cost of transport COT. Our results lead to three main conclusions: (1) in contrast to previous hypotheses, achieving optimal values of U and COT is independent of producing maximal power or efficiency; (2) muscle efficiency in swimming, in contrast to that in flying or running, decreases with increasing body size, consistent with muscle contraction characteristics; (3) the long-standing problem of two disparate patterns of longitudinal power output distributions in swimming fish can be reconciled by relating the two patterns to U-optimal or COT-optimal swimmers, respectively. We also provide further evidence that the use of tendons in caudal regions is beneficial from an energetic perspective. Our conclusions explain and unify many existing observations and are supported by computational data covering nine orders of magnitude in body size.

Modelling the effect of surface passivation within higher-order strain gradient plasticity: The case of wire torsion

The effect of surface passivation on the torsional behavior of thin metallic wires is studied within two frameworks of higher-order strain gradient plasticity, i.e. the simplified version of Gudmundson theory and the Polizzotto theory. The elastoplastic solution to the wire torsion problem is obtained. The flexibility of the higher-order theories is emphasized by solving the torsion problem for two boundary conditions, i.e. with and without surface passivation. The two types of models predict similar trends related to the size effect and the passivation effect in the wire torsion. By accounting for a free energy involving one energetic length scale, a formula relating the normalized torque to the wire radius is derived. The formula confirms a standardized increase in strain hardening with diminishing wire diameter. The distributions of plastic shear strain and its gradient along the radial coordinate for the unpassivated and passivated wires are given. It is found that the plastic flow would be strongly suppressed at the passivated wire surface. Numerical results also show that the energetic length scale plays an important role in modelling the elevation of strain hardening due to passivation.

Wind turbine wake intermittency dependence on turbulence intensity and pitch motion

Turbulence intermittency characteristics of the flow behind pitching and fixed wind turbines are assessed via hot-wire anemometry in a wind tunnel experiment. The pitching wind turbine model is free to oscillate in the streamwise direction to simulate pitch motion. Two inflow conditions are considered: 15% and 1.8% turbulent intensities. Empirical mode decomposition and Hilbert Huang transform are employed and validated by comparing the Hilbert energy spectrum with the Fourier energy spectrum. The extended self-similarity model indicates that pitching effects are more pronounced at locations where the flow is less turbulent due to its effect of being overshadowed by intermittency caused by tip vortex shedding. This agrees with arbitrary order Hilbert spectrum analysis (HSA) results. HSA is proven to be more accurate for scaling exponent estimation than structure functions as the latter results are significantly affected by the energetic scales. Premultiplied energy spectra show that pitch motion affects preferably large scales 0.1D−0.5D and the same amount of energy is contained on smaller scales compared to the fixed turbine, suggesting potential of higher power production. This work considers offshore wind turbine wakes by examining the pitch motion effects on the flow. Hence, results have direct implications on power production and quantification of fatigue loads due to pitch cyclic motion.

Wavelet Coherency Structure in Open Channel Flow

Many studies based on single-point measurement data have demonstrated the impressive ability of wavelet coherency analysis to catch the coherent structures in the wall-bounded flows; however, the question of how the events found by the wavelet coherency analysis relate to the features of the coherent structures remains open. Time series of velocity fields in x–y plane of the steady open channel flow was obtained from a time-resolved particle imaging velocimetry system. The local wavelet spectrum found shows that one of the main energetic scales in open channel flows is 3h motions. The wavelet coherent coefficients of u and v series from the same measurement points successfully detected the occurrence and the scale of these 3h motions, and the phase angle indicates their inside velocity structure is organized by the Q2 and Q4 events. The wavelet coherency analysis between different measurement points further reveals the incline feature of the 3h scale motions. All the features of this 3h motion found by the wavelet coherency analysis coincide well with the flow field that is created by the passing of hairpin packets.

Analysis of energetic intensity of Cern neutrino conversion types using the theory of covariance functions

In this paper, the changes of energetic intensity of Cern neutrinos during an experiment are analysed. For the analysis of energetic intensity of neutrinos, the theory of covariance functions was applied. The estimates of cross-covariance functions of digital data of energetic intensity of neutrinos or autocovariance functions of single data are calculated according to the random functions formed in the energetic intensity measuring data arrays in the form of vectors. The covariance functions have been calculated by varying the quantisation interval on the energetic scale and applying the computer program developed using MATLAB 7 package of procedures.

Recovery of wall-shear stress to equilibrium flow conditions after a rough-to-smooth step change in turbulent boundary layers

This paper examines the recovery of the wall-shear stress of a turbulent boundary layer that has undergone a sudden transition from a rough to a smooth surface. Early work of Antonia &amp; Luxton (J. Fluid Mech., vol. 53, 1972, pp. 737–757) questioned the reliability of standard smooth-wall methods for measuring wall-shear stress in such conditions, and subsequent studies show significant disagreement depending on the approach used to determine the wall-shear stress downstream. Here we address this by utilising a collection of experimental databases at $Re_{\unicode[STIX]{x1D70F}}\approx 4100$ that have access to both ‘direct’ and ‘indirect’ measures of the wall-shear stress to understand the recovery to equilibrium conditions of the new surface. Our results reveal that the viscous region ($z^{+}\lesssim 4$) recovers almost immediately to an equilibrium state with the new wall conditions; however, the buffer region and beyond takes several boundary layer thicknesses before recovering to equilibrium conditions, which is longer than previously thought. A unique direct numerical simulation database of a wall-bounded flow with a rough-to-smooth wall transition is employed to confirm these findings. In doing so, we present evidence that any estimate of the wall-shear stress from the mean velocity profile in the buffer region or further away from the wall tends to underestimate its magnitude in the near vicinity of the rough-to-smooth transition, and this is likely to be partly responsible for the large scatter of recovery lengths to equilibrium conditions reported in the literature. Our results also reveal that smaller energetic scales in the near-wall region recover to an equilibrium state associated with the new wall conditions within one boundary layer thickness downstream of the transition, while larger energetic scales exhibit an over-energised state for several boundary layer thicknesses downstream of the transition. Based on these observations, an alternative approach to estimating the wall-shear stress from the premultiplied energy spectrum is proposed.

Ocean‐Scale Interactions From Space

Satellite observations of the last two decades have led to a major breakthrough emphasizing the existence of a strongly energetic mesoscale turbulent eddy field in all the oceans. This ocean mesoscale turbulence is characterized by cyclonic and anticyclonic eddies (with a 100‐ to 300‐km size and depth scales of ∼500–1,000 m) that capture approximatively 80% of the total kinetic energy and is now known to significantly impact the large‐scale ocean circulation, the ocean's carbon storage, the air‐sea interactions, and therefore the Earth climate as a whole. However, ocean mesoscale turbulence revealed by satellite observations has properties that differ from those related to classical geostrophic turbulence theories. In the last decade, a large number of theoretical and numerical studies has pointed to submesoscale surface fronts (1–50 km), not resolved by satellite altimeters, as the key suspect explaining these discrepancies. Submesoscale surface fronts have been shown to impact mesoscale eddies and the large‐scale ocean circulation in counterintuitive ways, leading in particular to up‐gradient fluxes. The ocean engine is now known to involve energetic scale interactions, over a much broader range of scales than expected one decade ago, from 1 to 5,000 km. New space observations with higher spatial resolution are however needed to validate and improve these recent theoretical and numerical results.

Instrumentation for solar spectropolarimetry: state of the art and prospects

Given its unchallenged capabilities in terms of sensitivity and spatial resolution, the combination of imaging spectropolarimetry and numeric Stokes inversion represents the dominant technique currently used to remotely sense the physical properties of the solar atmosphere and, in particular, its important driving magnetic field. Solar magnetism manifests itself in a wide range of spatial, temporal, and energetic scales. The ubiquitous but relatively small and weak fields of the so-called quiet Sun are believed today to be crucial for answering many open questions in solar physics, some of which have substantial practical relevance due to the strong Sun-Earth connection. However, such fields are very challenging to detect because they require spectropolarimetric measurements with high spatial (sub-arcsec), spectral (<100 mA), and temporal (<10 s) resolution along with high polarimetric sensitivity (<0.001 of the intensity). We collect and discuss both well-established and upcoming instrumental solutions developed during the last decades to push solar observations toward the above-mentioned parameter regime. This typically involves design trade-offs due to the high dimensionality of the data and signal-to-noise-ratio considerations, among others. We focus on the main three components that form a spectro-polarimeter, namely, wavelength discriminators, the devices employed to encode the incoming polarization state into intensity images (polarization modulators), and the sensor technologies used to register them. We consider the instrumental solutions introduced to perform this kind of measurements at different optical wavelengths and from various observing locations, i.e., ground-based, from the stratosphere or near space.