Weak Amplitude Research Articles

Statistical Analysis of the Occurrence of Ionospheric Scintillations at the Low-Latitude Sanya Station During 2004–2021

The ionosphere of the Earth often becomes turbulent and develops electron density irregularities that can cause rapid and random changes in the amplitude and phase of radio signals, which is known as ionospheric scintillation. In this study, the statistical behavior of global navigation satellite system (GNSS) ionospheric amplitude scintillation of varying intensities over the Chinese low-latitude station in Sanya (18.34°N, 109.62°E; magnetic latitude: 7.61°N) has been investigated with respect to its dependence on solar activity, seasons, local time (LT), and geomagnetic activity during the period from July 2004 to December 2021. A detailed study on the solar activity dependence of scintillation occurrence shows that the occurrence rates of strong and moderate scintillations significantly increase with enhanced solar activity, but weak amplitude scintillations do not entirely conform to this characteristic. In terms of seasonal dependence, the scintillations in Sanya from 2004 to 2021 mainly occurred during equinoxes and exhibit a distinct equinoctial asymmetry. This asymmetry is characterized by a higher occurrence rate in autumn than in spring during the years 2007, 2011, and from 2017 to 2021, while in other years, the pattern is reversed, with a higher occurrence rate in spring than in autumn. Regarding LT dependence, scintillations are predominantly observed during 19:30–23:30 LT, with a notable persistence beyond midnight during years of high solar activity. Furthermore, geomagnetic disturbances have been observed to promote weak scintillations at 20:00 LT during the autumn and winter of 2014, and from 20:00 LT to 01:00 LT the next day in the latter half of 2013. In contrast, during the spring and autumn of most other years with high solar activity, these disturbances have been found to inhibit weak scintillations from 20:00 LT to midnight. The promoting/inhibiting effect of geomagnetic disturbances on ionospheric scintillation is not solely influenced by electric field disturbances but is to some extent jointly controlled by a variety of factors including solar activity, season, and LT.

Theoretical investigation of the excitation of leaky modes for multilayered models

SUMMARY The dispersion analysis with array-based methods enables us to detect and analyse the multimode dispersive waves with weak amplitudes. Over the past years, there has been widespread extraction of higher normal modes from earthquake records and ambient noise, which have been extensively employed in near-surface and crustal investigations. Notably, the frequent reporting of leaky modes in recent observations has gained significant attention. This is because leaky modes can provide more constraints on subsurface structures. Particularly, a subset of leaky modes is found to be sensitive to P-wave velocities, which has the potential to compensate for the limitations of traditional surface wave inversion. Nevertheless, due to the lack of knowledge of the excitation and practical application of leaky modes, it is urgent to have an effective guide in selecting certain leaky modes for practical inversion combined with other imaging methods. To this end, the theoretical investigation into the excitation of leaky modes for multilayered models is undertaken. By computing theoretical seismograms for various source mechanisms and source depths with the discrete wavenumber and the normal-mode summation methods, respectively, the qualitative evaluation of the leaky-mode contributions to the synthesized seismograms is conducted. Additionally, the impact of the source depth for the same source mechanism is meticulously examined by the dispersion spectra. Furthermore, with the accurate computation of leaky modes, we categorize the leaky modes into PL and OP (organ-pipe) modes according to their distinctive properties, that is, their attenuation and eigen-displacements, which may be used to explain very well the occurrence of certain leaky modes on the dispersion spectrum and be indicative of the reasonable choice of PL modes to put them into practical inversion for P-velocity structures.

Fast and full characterization of large earthquakes from prompt elastogravity signals

Prompt ElastoGravity Signals are light-speed gravity-induced signals recorded before the arrival of seismic waves. They have raised interest for early warning applications but their weak amplitudes close to the background seismic noise have questioned their actual potential for operational use. A deep-learning model has recently demonstrated its ability to mitigate this noise limitation and to provide in near real-time the earthquake magnitude (Mw). However, this approach was efficient only for large earthquakes (Mw ≥ 8.3) of known focal mechanism. Here we show unprecedented performance in full earthquake characterization using the dense broadband seismic network deployed in Alaska and Western Canada. Our deep-learning model provides accurate magnitude and focal mechanism estimates of Mw ≥ 7.8 earthquakes, 2 minutes after origin time (hence the tsunamigenic potential). Our results represent a major step towards the routine use of prompt elastogravity signals in operational warning systems, and demonstrate its potential for tsunami warning in densely-instrumented areas.

Dynamics of N-elastically longitudinal coupled rotating pendulums with smooth and discontinuous nonlinearities: Generation of chaotic bursting with many orbits as a solution

The dynamics of a mechanical network, consisting of a certain number (N) of cells, in which each unit cell consists of the irrational coupling of a simple pendulum and inclined mass-spring oscillator, is investigated. The single cell was recently introduced by Ning Han and Qingjie Cao, and it has strong irrational nonlinearity, exhibiting smooth and discontinuous characteristics due to the geometry configuration. The obtained network has a large degree of freedom and consequently has richer dynamics as compared to a single one. The set of discrete equations of this network is found, while the first equation is driven by an external sinusoidal force; the variables here are the angles between the vertical direction and the directions of mass in each unit cell. By using the non-driven version of this set of equations, the equilibrium points are found as well as their stability using the Jacobian matrix. Then, by using the multiple time scale method, the solutions of the set of the network equations are found for weak amplitude oscillations of the system, while the large amplitude solutions are found numerically, showing the ability of the network to transform the shape of some solutions at the input to other forms as the signals evolve in the network. One notices the generation of simple chaotic signals as well as the train of impulse signals. What is important here is the generation of the chaotic bursting with many orbits by the system, which are the simultaneous oscillations around several fixed points. For the case of numerous cells, the system can be used as a waveguide; this is why the set of the equation of the network is reduced to the extended complex Ginzburg Landau (ECGL) equation, with complex nonlinear dispersion and nonlocality terms, using the Tanuiti's reduction perturbation methods. The dissipative dark compacton and peakon as solutions for the ECGL equation are then found. The input-output matching of the network is next investigated via the transfer function of the system near the equilibrium points. The inverse Fourier transform of the transfer function multiplied by the Fourier transform of the input sinusoidal force gives the solution of the network equation for low amplitude oscillations. Finally, the supratransmission condition is studied, leading to the fact that the input sinusoidal signal with frequency nearly inside the forbidden gap zone gradually transforms into the train of chaotic bursting.

Exploring Weak Magnetic Signal Characteristics of Pipeline Welds: Insights into Stress Non-Uniformity Effects.

Weak magnetic detection technology can detect stress concentration areas in ferromagnetic materials. However, the stress non-uniform characteristics of pipeline welds lead to significant differences in stress distribution range and values between inner wall welds and outer wall welds. This discrepancy makes it crucial to further evaluate the impact of stress non-uniformity on magnetic signals. To study the magnetic signal characteristics under the influence of residual stress in weld seams, a magneto-mechanical analytical model was established based on the magnetic charge theory and the distribution characteristics of residual stress in the weld seam. The magneto-mechanical relationship and magnetic signal distribution characteristics at the inner and outer wall welds of the pipeline are calculated. Furthermore, the effects of different excitation intensities on the amplitude growth characteristics of magnetic signals are analyzed and compared. To verify the analysis model, weld detection experiments with different excitation intensities were designed. The results show that both the peak-to-valley values of the normal component and the peak values of the tangential component of the outer wall weld are lower than those of the inner wall weld. Conversely, the peak-to-valley width of the normal component and the peak width of the tangential component are greater than those of the inner wall weld. Additionally, the rate of increase in weak magnetic signal amplitude decreases in a first-order exponential relationship with increasing excitation intensity. The average decay rates of the normal and tangential component amplitude growth rates for the inner wall weld are 34.03% and 27.9%, respectively, while for the outer wall weld, they are 31.75% and 28.01%, respectively. This study contributes to the identification and quantitative assessment of weak magnetic signals in inner and outer wall welds.

Application of Fractional-Order Multi-Wing Chaotic System to Weak Signal Detection

This work investigates a fractional-order multi-wing chaotic system for detecting weak signals. The influence of the order of fractional calculus on chaotic systems’ dynamical behavior is examined using phase diagrams, bifurcation diagrams, and SE complexity diagrams. Then, the principles and methods for determining the frequencies and amplitudes of weak signals are examined utilizing fractional-order multi-wing chaotic systems. The findings indicate that the lowest order at which this kind of fractional-order multi-wing chaotic system appears chaotic is 2.625 at a=4, b=8, and c=1, and that this value decreases as the driving force increases. The four-wing and double-wing change dynamics phenomenon will manifest in a fractional-order chaotic system when the order exceeds the lowest order. This phenomenon can be utilized to detect weak signal amplitudes and frequencies because the system parameters control it. A detection array is built to determine the amplitude using the noise-resistant properties of both four-wing and double-wing chaotic states. Deep learning images are then used to identify the change in the array’s wing count, which can be used to determine the test signal’s amplitude. When frequencies detection is required, the MUSIC method estimates the frequencies using chaotic synchronization to transform the weak signal’s frequencies to the synchronization error’s frequencies. This solution adds to the contact between fractional-order calculus and chaos theory. It offers suggestions for practically implementing the chaotic weak signal detection theory in conjunction with deep learning.

Spatial difference of salt dynamics within burrows in high salinity zone (high intertidal zone & supratidal zone) of mudflat

Surface evaporation and seawater concentration in the tidal flat have been demonstrated as sources of salt for phreatic brine layers. However, the mechanisms of salt replenishment in such layers remain unclear. Here, the transport processes and factors influencing surface salt in mudflat under the influence of bioturbation were examined in the high salinity zone (high intertidal zone & supratidal zone) along the southern coast of Laizhou Bay, China. In this study, the laboratory model and numerical model of salt transport in the mudflat brine distribution area under the influence of crab burrows were constructed through in-situ investigation to simulate the salt transport process in the mudflat brine distribution area under different tidal amplitudes and different beach salinity, and the influence of the diameter and density of crab burrows on the water-salt exchange process was analyzed. The results indicate that in the salt-crust-free region, the salinity change in burrow-dense area (BDA) lags behind that of independent burrow (IB). At the same time, the salinity increase of IB is at most 17 ppt higher than that of BDA, and the salinity decrease of IB is at most 9 ppt lower than that of BDA, which made BDA promoting more salt accumulation and facilitating the salt transport to deeper layers. In the salt-crust-bearing region, due to the high salt content on the beach surface and the weak tidal amplitude, salt is continuously released and accumulated in the surface during multiple tidal cycles, but the ability to transport to the deep layer is weak. In this case, burrows characterized by larger diameters become the preferential paths for salt transport. In addition, crab burrows affect the evaporation of sediments. In this study, the surface salinity of sediments under the influence of burrows is around 10–45 ppt higher than that without burrows.

Volcanic-controlled basin architecture variation and dynamic sediment filling in the South Lufeng Sag, South China Sea

Volcanic-controlled changes of basin architectures and sediments have given rise to diverse and rapidly evolving “dynamic geomorphology,” which poses challenges to successful petroleum development. Nonetheless, the accompanying volcanic deposits and landforms often produce rich and distinct seismic responses within conventional sedimentary layers, offering vital support in addressing this critical issue. Based on this, we compared the volcanic activity stages, evolution of geomorphology, and sediment dispersal processes to determine the process of basinal evolution by analyzing the episodes and distribution of volcanic-related deposits, sub-stages, seismic facies, and attributes of deposits of the South Lufeng Sag in the Pearl River Mouth Basin, South China Sea. The widespread development of strong amplitude attributes and chaotic reflection variance cube attribute spatial perspectives reveal the evolution of both intrusive and effusive facies in the lower Wenchang Formation across three stages of volcanic activity. The seismic amplitude difference of the andesite and andesitic tuff unveils the transition of the depositional pathway from north to south in the west depression with change of depocenters, lays the foundation for the dynamic geomorphic evolution of the “transitional basin” in the region. In the middle Huizhou-Lufeng uplift, the chaotic reflection with weak amplitude and obvious diapir structures revealed by andesite constrain the distribution of sedimentary space and the transformation of sedimentary pathways within the basin, and the evolution process of the “restricted basin” is summarised in terms of sedimentary filling processes. The seismic amplitude differences of basalt and andesitic tuff - related sediments in the east depression record the process of transformation from a single sedimentary channel to multi-pathway transport, which is summarised as the evolutionary model of the “diffusive basin”. This study offers a meticulous exploration into the evolutionary trajectory of dynamic geomorphology and sedimentary accumulation in a basin regulated by volcanic activity. The findings pave the way for the extensive application of this methodology in petroleum development across various geographic regions.

Research on the processing and interpretation methods of distributed fiber optic vibration signal logging injection profiles

The oil and gas industry currently faces the dual challenges of improving extraction efficiency and reducing environmental impacts. Traditional well monitoring technologies are increasingly unable to meet the demands of modern oil and gas extraction due to technological limitations and environmental concerns. Distributed Acoustic Sensing (DAS) technology, which utilizes optical fibers as sensing elements, enables real-time and accurate monitoring of the CO2 injection process in wells. However, DAS technology encounters issues such as weak amplitude signals and noise interference in practical applications. In response, a comprehensive method for processing and interpreting DAS logging data for CO2 injection wells has been proposed. This method involves restoring amplitude signals through wavefront energy compensation and applying Gaussian filtering and wavelet threshold denoising algorithms for noise reduction. The processed results are classified using the K-Medoids clustering algorithm and the CO2 absorption volume in the injection layer is calculated using the integral area method. The accuracy and practicality of this method have been validated through comparative analysis with pulse neutron oxygen activation logging results. This approach aims to address the challenges faced by DAS technology in the oil and gas industry, thereby providing technical support for the efficient, environmentally friendly, and intelligent management of oil and gas fields.

Two-dimensional shielded vortices in a shear current

The interaction of shielded vortices, with a continuous vorticity distribution, and a shear current of weak vorticity amplitude but similar velocity compared to the vortex amplitude is numerically investigated in two-dimensional isochoric flows. Different types of axisymmetric shielded vortices, namely, a neutral unstable vortex, a neutral robust vortex, and a non-neutral vortex are considered. The vortices are linear combinations of vorticity layer-modes, which consist of conveniently normalized cylindrical Bessel functions of order 0, truncated by a zero of the Bessel function of order 1. The vortex–current interaction is investigated by superposing initially the vortices at different initial locations along the cross-flow axis in the shear current. The numerical results show that some shielded vortices, as well as the shear current, remain robust while the vortices cross the shear current and reach a stable equilibrium location, which is of the same sign vorticity as its amount of circulation. There exist two unstable equilibrium locations where most of the vortices persist during a relatively short time interval before heading to their stable equilibrium region in the shear current.

Two chironomid-inferred mean July air temperature reconstructions in the South Carpathian Mountains over the last 2000 years

We present chironomid-based reconstructions of mean July air temperature changes over the last 2000 years from Lake Latoriței (1530 m a.s.l.) in the Southern Carpathians. A multi-proxy analysis was performed along a 58 cm long sediment core and two training sets were used for quantitative July air temperature reconstructions: the Eastern-European (EE, 212 lakes) and the Finnish-Polish-Carpathian (FPC, 273 lakes). The transfer functions had a coefficient of determination ( r2) 0.88 and 0.91 with a root mean squared error of prediction (RMSEP) 0.88°C and 1.02°C. Despite possible biases resulting from methodological problems and the ecological complexity of the chironomid response to both climatic and environmental changes, the agreement of the temperature reconstruction of Lake Latoriței with other alpine records suggests that the transfer function successfully reconstructed past summer temperatures between 750 and 1830 CE. Biases in the temperature reconstruction in the period before 750 and after 1830 CE were likely caused by increased abundance of rheophilic and semi-terrestrial chironomid species related to increased inflow activity before 750 CE and local land use changes after 1830 CE, which was also indicated by increasing deforestation and increasing lake productivity in the pollen and diatom records. Our results suggest that the region experienced a warm period between 750 and 1360 CE, and a cold period between 1360 and 1600 CE followed by fluctuating summer temperatures until 1830 CE. These events were associated with the so-called ‘Mediaeval Warm Period’ (MWP) and the ‘Little Ice Age’ (LIA), respectively. The inference models reconstructed a decrease in July air temperatures by 0.7°C–1.1°C during the LIA relative to the warmer MWP. We also demonstrated that the FPC training set gives better results, supporting that local/continental training sets are efficient to detect weak amplitude summer temperature changes in the Late-Holocene.

A moderately chocked estuary: Influence of a constriction on the water level variations of the Wouri estuary (Cameroon)

We study the water-level (WL) evolution in the Douala basin (DB), a sub-basin of the Wouri estuary, separated from the ocean by a natural constriction and influenced by tides and river inflow. Our objective is to assess whether floods in Douala city could result from water overflow from the Douala basin due to Wouri river floods. We first evaluate the constriction’s damping effect by analyzing tide amplitude variations from the ocean to the basin. A simplified model for basin WL variation is developed, incorporating a dissipation parameter (Г) that is evaluated using weak tidal amplitude modulation from the ocean to the basin over the dry season of 2023. Results in the DB reveal nondimensional choking-parameter (P) values of 12–19, indicating moderate dissipation. The basin's relatively small area results in a nondimensional river discharge parameter (S) of 0–12, indicating high river discharge regimes. Subsequently, the model is used to evaluate the mean and maximum WL, as well as tide amplitude variations of the DB, as functions of river flow and ocean tides. The mean WL increases, but the maximum tide amplitude decreases as river input increases. The maximum WL in the basin always exceeds the maximum amplitude of ocean tides but is only significantly higher when river input is above 1000 m3/s. In current conditions, where maximum observed river input is around 1800 m3/s, it is unlikely that flooding will extend beyond the basin borders into the city of Douala. For a moderate increase (20%) in future maximum river fluxes, it is also unlikely that the DB will overflow into Douala city. Only a drastic increase in mean ocean level and river fluxes (which are possible scenarios associated with climate change) could potentially lead to a significant rise in basin WL, resulting in severe flooding.

Research on Acoustic Emission Characteristics and Crack Evolution during Rock Failure under Tensile and Tensile- and Compressive-Shear Stress States

Tensile, compressive-shear, and tensile-shear failure are three typical failure modes of rock- and lining-support structural materials in underground engineering. Comparative studies of the acoustic emission (AE) evolution characteristics of specimens of the same shape and size under different stress states are of great significance in determining universal disaster warning guidelines. Based on a self-developed multi-functional test system, direct tensile, compressive-shear, and tensile-shear tests were conducted on intact and jointed rock-like specimens, comparing AE amplitude and peak frequency parameters under different failure modes from the perspectives of crack scale and crack type evolution. All failure tests were monitored with microcrack propagation at an early stage until ultimate rupture occurred at the peak-load moment. As a result, the “quiet-period” could only be observed from the compressive-shear test. The AE signals distributed in three bands can be used as an indicator of failure identifications. Tensile and shear cracks can be identified by strong and weak amplitudes of low- and high-frequency signals. These results enhance the knowledge of the failure modes of rock mechanics for more applications in monitoring disasters in rock engineering.

Multi-tier dynamic sampling weak RF signal estimation theory

This paper presents a theoretical analysis in discrete time for a multi-tier weak radiofrequency (RF) signal estimation process with N simultaneous signals. Discrete time dynamic sampling is introduced and is shown to provide the capability to extract signal parameter values with increased accuracy compared with accuracy of estimates obtained in prior work. This paper advances phase measurement approaches by proposing discrete time dynamic sampling which our paper shows offers the desirable capability for more accurate weak signal parameter estimates. For N=2 simultaneous signals with a strong signal at 850 MHz and a weak signal at 855 MHz, the results show that dynamically sampling the instantaneous frequency at 24 times the Nyquist rate provides weak signal frequency estimates that are within 1.7 times 10^{-5} of the actual weak signal frequency and weak signal amplitude estimates that are within 428 PPM of the actual weak signal amplitude. Results are also presented for situations with N=2 simultaneous 5G signals. In one case, the strong signal is 3950 MHz, and the weak signal is 3955 MHz; in the other case the strong case is 5950 MHz, and the weak signal is 5955 MHz. The results for these cases show that estimates obtained with dynamic sampling are more accurate than estimates provided using a single sample rate of 65 MSPS. This work has promising applications for weak signal parameters estimation using instantaneous frequency measurements.

Introduction of new attributes: Scaling Exponent and its double derivatives for better land seismic volume interpretation

For the first time, we propose to study the behavior of the correlation (scaling) exponent and its second order with prestack seismic data. For our research, we have chosen Dibrugarh prestack 3D seismic data from the Assam-Arakan Basin, India. We have improved the calculation process so that it is possible to read amplitude values directly from SEG-Y file and collect data from the entire chosen in- or cross-line. As a result, we can now study significant amount of data within less amount of time. After completing the analysis, we could identify the main stratigraphic layers, basement, and the zones of weak and prominent amplitudes from the survey. Strong amplitude zones correlate with low scaling exponent values. Weak amplitudes reflect as high scaling exponent zones. New attributes introduced give a scope to automatize the interpretation of 3D seismic data without learning.

A novel scheme based on angular dispersion-induced microbunching mechanism for harmonic generation in storage ring

Angular dispersion-induced microbunching (ADM) scheme was proposed to generate high harmonic coherent radiation in the storage ring with weak energy modulation amplitude. However, it is still difficult to convert the external UV seed laser into the sub-nanometer wavelength. In this paper, we proposed a novel scheme based on ADM mechanism. By properly choosing the parameters, theory and one order simulation demonstrate that it is possible to produce ultrahigh harmonic coherent radiation in the storage ring. The high harmonic conversion efficiency of the proposed scheme may open up a new opportunity to produce sub-nanometer X-ray coherent radiation in the storage ring.

Personal thermoregulation by mid-infrared engineered materials

Regulation of human thermal radiation plays a vital role in personal heat management. Conventional textiles cannot satisfy the demands for dynamic heat dissipation because of their high emissivities. Recent studies on the regulation of textile emissivity through electricity, heat, sweat, and force have made significant progress in resolving this conundrum. However, this technology is still plagued by weak wearability, low stability, and limited dynamic regulation amplitude of heating/cooling. In this review, we first explain the heat transfer model of adjustable heat radiation smart textiles to comprehend the boundary conditions of heat management in this technology. The regulatory principles and recent developments related to electricity, heat, sweat, and force regulation are then systematically summarized. Finally, the difficulties encountered and future development directions are discussed. Therefore, it is necessary to rapidly promote the practical application of adjustable heat-radiating smart textiles.

Multi-scale dynamics of the interaction between waves and mean flows: From nonlinear WKB theory to gravity-wave parameterizations in weather and climate models

The interaction between small-scale waves and a larger-scale flow can be described by a multi-scale theory that forms the basis for a new class of parameterizations of subgrid-scale gravity waves (GW) in weather and climate models. The development of this theory is reviewed here. It applies to all interesting regimes of atmospheric stratification, i.e., also to moderately strong stratification as occurring in the middle atmosphere, and thereby extends classic assumption for the derivation of quasi-geostrophic theory. At strong wave amplitudes a fully nonlinear theory arises that is complemented by a quasilinear theory for weak GW amplitude. The latter allows the extension to a spectral description that forms the basis of numerical implementations that avoid instabilities due to caustics, e.g., from GW reflection. Conservation properties are discussed, for energy and potential vorticity, as well as conditions under which a GW impact on the larger-scale flow is possible. The numerical implementation of the theory for GW parameterizations in atmospheric models is described, and the consequences of the approach are discussed, as compared to classic GW parameterizations. Although more costly than the latter, it exhibits significantly enhanced realism, while being considerably more efficient than an approach where all relevant GWs are to be resolved. The reported theory and its implementation might be of interest also for the efficient and conceptually insightful description of other wave-mean interactions, including those where the formation of caustics presents a special challenge.

The impact of freshening over the Antarctic Ocean on Pacific Decadal Oscillation

<p>The profound influence of the Antarctic Ocean freshening on the Pacific Decadal Oscillation (PDO) is investigated in this study by utilizing a series of fully coupled ocean-atmosphere 400-year-modeling experiments. The simulated results derived from the Fast Ocean-Atmosphere Model (FOAM) can reasonably identify the spatial pattern and time period (10–20 years and 20–50 years) of the observed PDO with slightly weak amplitudes. In the sensitivity experiment (Southern Ocean Water Hosing), 1.0 Sv (Sverdrup, 1Sv = 1.0 × 106 m<sup>3</sup>/s) freshwater flux is uniformly imposed over the Antarctic Ocean for 400 years. As a response to this Antarctic Ocean freshening, the Tropical Pacific Ocean displays a normal “La Niña pattern”, while the low-frequency variability within the North Pacific Ocean is much weakened. Preserving the PDO’s spatial pattern, the multidecadal (20–50 years) magnitude becomes weak and shifts toward higher frequency. In contrast, the decadal magnitude of the PDO (10–20 years) is slightly reinforced and also shifts towards higher frequency. Dynamical analysis indicates that the shortening of the PDO multidecadal variability is mainly caused by the acceleration of the first-baroclinic-mode Rossby waves. The spreading of the fresh anomalies and associated increasing stratification in the North Pacific Ocean result in the shortening of the long Rossby wave propagation to cross the subtropical North Pacific basin. A heat budget analysis further shows that the upper-ocean thermodynamic variability in relationship to the stratification oscillation in the North Pacific Ocean is mainly associated with the anomalous behaviors of the meridional advection, heat flux and ocean mixing.</p>

Reflection of internal gravity waves in the form of quasi-axisymmetric beams

Preservation of the angle of reflection when an internal gravity wave hits a sloping boundary generates a focusing mechanism if the angle between the direction of propagation of the incident wave and the horizontal is close to the slope inclination (near-critical reflection). This paper provides an explicit description of the leading approximation of the unique Leray solution to the near-critical reflection of internal waves from a slope in the form of a beam wave. More precisely, our beam wave approach allows to construct a fully consistent and Lyapunov stable approximate solution, L2-close to the Leray solution, in the form of a beam wave, within a certain (nonlinear) time-scale. To the best of our knowledge, this is the first result where a mathematical study of internal waves in terms of spatially localized beam waves is performed.A beam wave is a linear superposition of rapidly oscillating plane waves, where the high frequency of oscillation is proportional to the inverse of a power of the small parameter measuring the weak amplitude of waves.Being localized in the physical space thanks to rapid oscillations (and high variations of the modulus of the wavenumber), beams are physically more relevant than plane waves/packets of waves, whose wavenumber is nearly fixed (microlocalized). At the mathematical level, this marks a strong difference between the previous plane waves/packets of waves analysis and our approach.The main novelty of this work is to exploit the spatial localization of beam waves to exhibit a spatially localized, physically relevant solution and to improve the previous mathematical results from a twofold perspective: 1) our beam wave approximate solution is the sum of a finite number of terms, each of them is a consistent solution to the system and there is no artificial/non-physical corrector; 2) thanks to the absence of artificial correctors (used in the previous results) and to the special structure of the nonlinear term, we can push the expansion of our solution to next orders, so improving the accuracy and enlarging the consistency time-scale.Finally, our results provide a set of initial conditions localized on rays, for which the Leray solution maintains approximately in L2 the same localization.