Global Energy Spectra Research Articles

SPECTRAL ANALYSIS IN THE EVALUATION OF THE ELECTROCHEMICAL BEHAVIOR OF HIGH-ENTROPY GdTbDyHoSc AND GdTbDyHoY ALLOYS

The corrosion behavior of disordered systems, such as high-entropy alloys, exhibit a stochastic random process. To accurately predict and analyze the behavior of these systems in service environments, it is necessary to employ new computational and experimental methods alongside classical electrochemical methods. In this study, we highlighted the effectiveness of using fast Fourier transform and wavelet analysis to assess the corrosion behavior of stochastic systems, using the example of equimolar rare-earth alloys GdTbDyHoSc and GdTbDyHoY. To evaluate the corrosion behavior, we measured the time series of potential fluctuations for the studied samples in a 0.01 M NaCl solution over a 12-hour period, at current densities ranging from 0.2 to 0.5 mA/cm2. Applying the fast Fourier transform method to analyze the obtained time series, we observed that the angular coefficient of the slope of the logarithm of the power spectral density logarithm to the logarithm of frequency increased with higher current density. Specifically, for the GdTbDyHoSc alloy, the coefficient increased from –1.46 to –1.35, indicating the prevalence of general corrosion dissolution. In contrast, for the GdTbDyHoY alloy, the coefficient increased from –1.93 to –1.77, suggesting the dominance of localized dissolution. Furthermore, we utilized wavelet analysis to process the time series data for both alloys at current densities ranging from 0.2 to 0.5 mA/cm2. This analysis allowed us to plot time series scalograms, which visually illustrated the intensity of the corrosion process on the surface of the investigated alloys. From the scalograms, we calculated the values of the global energy spectra distributed over frequency ranges, as well as the values of the total energy of the investigated systems. Interestingly, the GdTbDyHoY alloy exhibited higher total energy values compared to the GdTbDyHoSc alloy. Specifically, the total energy for the GdTbDyHoY alloy increased from 0.97 to 2.03 kV2 as the current density increased from 0.2 to 0.5 mA/cm2, respectively. For the GdTbDyHoSc alloy, the total energy increased from 0.50 to 0.84 kV2. In conclusion, the application of fast Fourier transform and wavelet analysis methods proved to be effective tools for gaining a deep understanding of the corrosion behavior of locally disordered chemical systems, such as the high-entropy alloys of GdTbDyHoSc and GdTbDyHoY composition.

Spatio‐Temporal Coarse‐Graining Decomposition of the Global Ocean Geostrophic Kinetic Energy

AbstractWe expand on a recent determination of the first global energy spectrum of the ocean's surface geostrophic circulation (Storer et al., 2022, https://doi.org/10.1038/s41467-022-33031-3) using a coarse‐graining (CG) method. We compare spectra from CG to those from spherical harmonics by treating land in a manner consistent with the boundary conditions. While the two methods yield qualitatively consistent domain‐averaged results, spherical harmonics spectra are too noisy at gyre‐scales (>1,000 km). More importantly, spherical harmonics are inherently global and cannot provide local information connecting scales with currents geographically. CG shows that the extra‐tropics mesoscales (100–500 km) have a root‐mean‐square (rms) velocity of ∼15 cm/s, which increases to ∼30–40 cm/s locally in the Gulf Stream and Kuroshio and to ∼16–28 cm/s in the ACC. There is notable hemispheric asymmetry in mesoscale energy‐per‐area, which is higher in the north due to continental boundaries. We estimate that ≈25%–50% of total geostrophic energy is at scales smaller than 100 km, and is un(der)‐resolved by pre‐SWOT satellite products. Spectra of the time‐mean circulation show that most of its energy (up to 70%) resides in stationary eddies with characteristic scales smaller than (<500 km). This highlights the preponderance of “standing” small‐scale structures in the global ocean due to the temporally coherent forcing by boundaries. By coarse‐graining in space and time, we compute the first spatio‐temporal global spectrum of geostrophic circulation from AVISO and NEMO. These spectra show that every length‐scale evolves over a wide range of time‐scales with a consistent peak at ≈200 km and ≈2–3 weeks.

Energy Spectra and Vorticity Dynamics in a Two-Layer Shallow Water Ocean Model

Abstract The dynamically adaptive WAVETRISK-OCEAN global model is used to solve one- and two-layer shallow water ocean models of wind-driven western boundary current (WBC) turbulence. When the submesoscale is resolved, both the one-layer simulation and the barotropic mode of the two-layer simulations have an energy spectrum with a power law of −3, while the baroclinic mode has a power law of −5/3 to −2 for a Munk boundary layer. This is consistent with the theoretical prediction for the power laws of the barotropic and baroclinic (buoyancy variance) cascades in surface quasigeostrophic turbulence. The baroclinic mode has about 20% of the energy of the barotropic mode in this case. When a Munk–Stommel boundary layer dominates, both the baroclinic and barotropic modes have a power law of −3. Local energy spectrum analysis reveals that the midlatitude and equatorial jets have different energy spectra and contribute differently to the global energy spectrum. We have therefore shown that adding a single baroclinic mode qualitatively changes WBC turbulence, introducing an energy spectrum component typical of what occurs in stratified three-dimensional ocean flows. This suggests that the first baroclinic mode may be primarily responsible for the submesoscale turbulence energy spectrum of the oceans. Adding more vertical layers, and therefore more baroclinic modes, could strengthen the first baroclinic mode, producing a dual cascade spectrum (−5/3, −3) or (−3, −5/3) similar to that predicted by quasigeostrophic and surface quasigeostrophic models, respectively. Significance Statement This research investigates how wind energy is transferred from the largest ocean scales (thousands of kilometers) to the small turbulence scales (a few kilometers or less). We do this by using an idealized model that includes the simplest representation of density stratification. Our main finding is that this simple model captures an essential feature of the energy transfer process. Future work will compare our results to those obtained using ocean models with more realistic stratifications.

Global energy spectrum of the general oceanic circulation

Advent of satellite altimetry brought into focus the pervasiveness of mesoscale eddies {{{{{{{bf{{{{{{{{mathcal{O}}}}}}}}}}}}}}}}({100}) km in size, which are the ocean’s analogue of weather systems and are often regarded as the spectral peak of kinetic energy (KE). Yet, understanding of the ocean’s spatial scales has been derived mostly from Fourier analysis in small "representative” regions that cannot capture the vast dynamic range at planetary scales. Here, we use a coarse-graining method to analyze scales much larger than what had been possible before. Spectra spanning over three decades of length-scales reveal the Antarctic Circumpolar Current as the spectral peak of the global extra-tropical circulation, at ≈ 104 km, and a previously unobserved power-law scaling over scales larger than 103 km. A smaller spectral peak exists at ≈ 300 km associated with mesoscales, which, due to their wider spread in wavenumber space, account for more than 50% of resolved surface KE globally. Seasonal cycles of length-scales exhibit a characteristic lag-time of ≈ 40 days per octave of length-scales such that in both hemispheres, KE at 102 km peaks in spring while KE at 103 km peaks in late summer. These results provide a new window for understanding the multiscale oceanic circulation within Earth’s climate system, including the largest planetary scales.

Atmospheric Energy Spectra in Global Kilometre-Scale Models

Eleven 40-day long integrations of five different global models with horizontal resolutions of less than 9 km are compared in terms of their global energy spectra. The method of normal-mode function decomposition is used to distinguish between balanced (Rossby wave; RW) and unbalanced (inertia-gravity wave; IGW) circulation. The simulations produce the expected canonical shape of the spectra, but their spectral slopes at mesoscales, and the zonal scale at which RW and IGW spectra intersect differ significantly. The partitioning of total wave energies into RWs an IGWs is most sensitive to the turbulence closure scheme and this partitioning is what determines the spectral crossing scale in the simulations, which differs by a factor of up to two. It implies that care must be taken when using simple spatial filtering to compare gravity wave phenomena in storm-resolving simulations, even when the model horizontal resolutions are similar. In contrast to the energy partitioning between the RWs and IGWs, changes in turbulence closure schemes do not seem to strongly affect spectral slopes, which only exhibit major differences at mesoscales. Despite their minor contribution to the global (horizontal kinetic plus potential available) energy, small scales are important for driving the global mean circulation. Our results support the conclusions of previous studies that the strength of convection is a relevant factor for explaining discrepancies in the energies at small scales. The models studied here produce the major large-scale features of tropical precipitation patterns. However, particularly at large horizontal wavenumbers, the spectra of upper tropospheric vertical velocity, which is a good indicator for the strength of deep convection, differ by factors of three or more in energy. High vertical kinetic energies at small scales are mostly found in those models that do not use any convective parameterisation.

Energy Power Spectra Measured at an Interplanetary Shock by the New Horizon's SWAP Experiment: 1D Full Particle Simulations versus Observations

Abstract One-dimensional particle-in-cell (PIC) simulations are used to analyze the energy spectra measured by the New Horizons’ Solar Wind Around Pluto (SWAP) instrument in the upstream region of an interplanetary shock observed at a distance of ∼34 au from the Sun. The use of individual populations simulating the different solar wind ion and pick-up ion (PUI) populations allows us to clearly identify the contribution of each population to the global energy spectra. The important role of shock front obliquity is stressed in the formation of PUIs streaming back along the magnetic field into the upstream region far from the front. Energy spectra measured by the SWAP experiment are well reproduced in the present simulations. A detailed analysis shows that (1) the highest-energy part of the spectrum is formed primarily by both backstreaming PUI–H+ and PUI–He+; (2) the middle-energy part of the energy spectrum is composed of both solar wind SW–H+ and SW–He2+ incoming ions that are superimposed on the PUI–H+ population; and (3) the low-energy range is composed of incoming PUI–H+. The agreement between experimental and simulation results is improved by using an initially filled-shell distribution for the PUI–H+ population (instead of a zero-thickness shell), as this affects the low-energy part of the spectrum strongly. This means that PUI–H+ ions have sufficient time to diffuse onto and fill out a shell distribution after their initial pick-up in the heliosphere, indicating that the subsequent cooling has an important impact on the global energy spectrum.

Kolmogorov’s hypotheses and global energy spectrum of turbulence

We relate the justification of Kolmogorov’s hypotheses on the local isotropy and small-scale universality in real turbulent flows to an observed universality of basis independence for the global energy spectrum and energy flux of small-scale turbulence. To readily examine the small-scale universality, an approach is suggested that investigates the global energy spectrum in a general spectral space for which the nonlinear interscale interaction may not be Fourier-triadic. Specific verifications are performed based on direct numerical simulations of turbulence in a spherical geometry and reexaminations of several existing results for turbulent channel flows.

Investigation of a clinical PET detector module design that employs large-area avalanche photodetectors

We investigated the feasibility of designing an Anger-logic PET detector module using large-area high-gain avalanche photodiodes (APDs) for a brain-dedicated PET/MRI system. Using Monte Carlo simulations, we systematically optimized the detector design with regard to the scintillation crystal, optical diffuser, surface treatment, layout of large-area APDs, and signal-to-noise ratio (SNR, defined as the 511 keV photopeak position divided by the standard deviation of noise floor in an energy spectrum) of the APD devices. A detector prototype was built comprising an 8 × 8 array of 2.75 × 3.00 × 20.0 mm3 LYSO (lutetium-yttrium-oxyorthosilicate) crystals and a 22.0 × 24.0 × 9.0 mm3 optical diffuser. From the four designs of the optical diffuser tested, two designs employing a slotted diffuser are able to resolve all 64 crystals within the block with good uniformity and peak-to-valley ratio. Good agreement was found between the simulation and experimental results. For the detector employing a slotted optical diffuser, the energy resolution of the global energy spectrum after normalization is 13.4 ± 0.4%. The energy resolution of individual crystals varies between 11.3 ± 0.3% and 17.3 ± 0.4%. The time resolution varies between 4.85 ± 0.04 (center crystal), 5.17 ± 0.06 (edge crystal), and 5.18 ± 0.07 ns (corner crystal). The generalized framework proposed in this work helps to guide the design of detector modules for selected PET system configurations, including scaling the design down to a preclinical PET system, scaling up to a whole-body clinical scanner, as well as replacing APDs with other novel photodetectors that have higher gain or SNR such as silicon photomultipliers.

Application of an Inverse Method to Coastal Modeling

Abstract Free surface coastal models currently suffer from the difficulty of having to specify the global circulation during the initialization process and along the open boundaries. As an alternative to the long spinup periods, an original explicit approach based on inverse techniques has been developed. Data originating from in situ observations and/or ocean general circulation models are optimally interpolated over the small-scale grid in such a way that the tendency terms are reduced to physically consistent values. The errors on the “true” tendencies and the truncated nonlinear term are evaluated to compute the model covariance. The observation covariance matrix is divided into two parts: the homogeneous, isotropic matrix calculated with a global energy spectrum; and a parameterized nonhomogeneous, nonisotropic matrix. The inverse method is applied to the study of the interaction of a barotropic alongshore current over a narrow canyon. The transient processes following the initialization are drastica...

Global energy spectra of bands and density of states in a class of two-tile systems

Electronic properties of a general class of one-dimensional two-tile systems are calculated exactly. The systems containing periodic crystals, generalized Fibonacci quasicrystals, generalized Thue-Morse aperiodic lattices and even other two-tile aperiodic lattices, can be divided into two different families which are constructed by the inflation rules: {A, B} --> {A(m11) B(m12) A(m21) (B(m22)} and {A, B} --> {A(n11) B(n12), B(n21) A(n22}, respectively. As typical examples, global spectra of bands and density of states in some two-tile aperiodic systems are numerically calculated. Some interesting properties are obtained.

Experiments on the structure and dynamics of forced, quasi-two-dimensional turbulence

Simulated upwelling fronts have been generated around the outer edge of a cylindrical tank filled with a two-layer fluid system and driven by a surface stress. Initially, an axisymmetric front was observed which subsequently became unstable to small baroclinic eddies. These eddies continued to grow until they reached an equilibrium size. Under some circumstances, cyclonic eddies pinched-off from the fully developed front and moved away from the mean position of the front into the fluid interior. Streak photographs of the fully developed flow field were digitized to generate a velocity field interpolated on to a regular grid. A direct two-dimensional Fourier transform was performed on the turbulent kinetic energy field deduced from such images and one-dimensional energy E(k) spectra were extracted. Consistent spectrum would correspond to an inverse energy cascade range; this yielded a Kolmogorov constant (C) that varied within the limits 2.8 [les ] C [les ] 3.8. The approximately k−5.5 range, which is much steeper than that predicted by the original statistical theories, is nevertheless consistent with those found frequently in numerical experiments.The spectral slopes inferred from particle dispersion methods and from one-dimensional Fourier transforms of the longitudinal velocity correlations were compared with the results obtained above and in previous laboratory experiments. In general, the global energy spectra are consistent with an interpretation of the fluid dynamics as being that of two-dimensional turbulence. This in turn implies that known properties of such flows may be invoked to explain the appearance of a number of naturally occurring phenomena in coastal upwelling fronts.