Nonlinear Energy Transfer Research Articles

Nearly Perfect Raman Self-Cleaning in Graded-Index Multimode Fibers Using Pearcey-Gaussian Pulses

We propose a temporal manipulation scheme for the inner-mode interactions in graded-index multimode fibers (GRIN-MMF). In this scheme, a so-called Pearcey-Gaussian (PeG) wave packet is constructed for the pulse profile, which allows the manipulation of the self-compressing control by the second- and third-order dispersions. Our simulations show that such linear compressing cooperates with the nonlinear compressing of the Kerr effect when the wavelength is close to the zero-dispersion point of the fiber, which enables the manipulation of the nonlinear energy transfer from the higher modes to the fundamental one. Such cooperation of the linear and nonlinear effects triggers a Stokes soliton in the fundamental mode while the Raman red-shifts in the higher modes are negligible. After the proper filter in the spectrum, a nearly perfect Raman self-cleaning with the energy of the fundamental mode reaching 97.2 % is observed.

Strong increase in the effective two-photon absorption cross-section of excitons in quantum dots due to the nonlinear interaction with localized plasmons in gold nanorods.

Excitons in semiconductor quantum dots (QDs) feature high values of the two-photon absorption cross-sections (TPACSs), enabling applications of two-photon-excited photoluminescence (TPE PL) of QDs in biosensing and nonlinear optoelectronics. However, efficient TPE PL of QDs requires high-intensity laser fields, which limits these applications. There are two possible ways to increase the TPE PL of QDs: by increasing their photoluminescence quantum yield (PLQY) or by further increasing the TPACS. Plasmonic nanoparticles (PNPs) may act as open nanocavities for increasing the PLQY via the Purcell effect, but this enhancement is strictly limited by the maximum possible PLQY value of 100%. Here we directly investigated the effect of PNPs on the effective TPACS of excitons in QDs. We have found that effective TPACS of excitons in a QD-PMMA thin film can be increased by a factor of up to 12 near the linearly excited gold nanorods (GNRs). Using gold nanospheres (GNSs), in which plasmons cannot be excited in the infrared range, as a control system, we have shown that, although both GNSs and GNRs increase the recombination rate of excitons, the TPACS is increased only in the case of GNRs. We believe that the observed effect of TPACS enhancement is a result of the nonlinear interaction of the plasmons in GNRs with excitons in QDs, which we have supported by numerical simulations. The results show the way to the rational design of the spectral features of plasmon-exciton hybrids for using them in biosensing and nonlinear optoelectronics.

Energy-flux vector in anisotropic turbulence: application to rotating turbulence

Abstract

Nonlinear Performance of MEMS Vibratory Ring Gyroscope

Micro-electro-mechanical system (MEMS) gyroscopes are an important sort of inertial sensor for identifying parameters of spinning structures, such as the spinning speed and angular deviation, based on the Coriolis effect. In this paper, the nonlinear mechanism of MEMS vibratory ring gyroscopes is analyzed by applying a fully coupled nonlinear model, in which the gyroscopic coupling and geometrically and structurally nonlinear couplings are all taken into account. The coupled differential equations governing the drive and sense motions are established via the Lagrangian equations. Numerical simulation is conducted, and the key nonlinear components and energy transfer behaviors between the drive and sense modes are elucidated. It is revealed that the cubic rigidity nonlinearity is another significant factor leading to the coupling between the drive and sense modes other than the gyroscopic coupling. Perturbation analysis is also carried out by using the method of multiple scales. The nonlinear frequency–amplitude responses of the drive and sense vibrations are obtained, and comprehensive parametric studies are performed. The significant effects of system damping, excitation amplitude, drive amplitude and spinning speed on the responses are discussed, which will facilitate to improve the nonlinear performance and sensitivity of the gyroscope.

Evolution of wave spectra during sea breeze and tropical cyclone

Wave spectral components change with time and through space by receiving energy from wind, through non-linear energy transfer among the spectral components and dissipation due to white-capping and friction. Changes in wave spectra are high during local events like sea-land breeze and extreme events like tropical cyclones (TC). The wave spectral evolution during a sea-land breeze cycle and TC are studied using both measured and modelled data. During a sea-land breeze cycle, the winds are simulated using Weather Research and Forecasting model and waves using the Simulating Waves Nearshore model. Simulated source terms vary according to the intensification and weakening of sea breeze, with energy from wind input having a maximum influence on wave spectra and white-capping having the least. The evolution of wave spectra during the TC using the European Centre for Medium-Range Weather Forecasts ERA-5 reanalysis data shows large spatial and temporal variations. During the TC, large waves are found in the right quadrant to the TC heading direction. TC generated waves are mostly young wind-seas with the youngest of waves found in the left quadrants and the wave-field does not exactly follow the wind field but depends on the velocity of forward motion of TC.

Nonlinear energy transfer from low frequency electromagnetic fluctuations to broadband turbulence during edge localized mode crashes

Long ELMy H-mode KSTAR discharges are used to show that low frequencies () of the ion-scale density fluctuations contain electromagnetic components that transfer energy from to higher frequency () fluctuations during ELM crashes via three-wave non-linear interactions. Such non-linear interactions are not observed during the inter-ELM phases. These observations suggest that investigations on the enhanced fluctuation and transport levels during ELM crashes require a careful analysis of the non-linear couplings between low frequency electromagnetic and broadband fluctuations in addition to other causes such as open (stochastic) magnetic fields and advective transport. Our results are based on conditionally ensemble-averaged second-order and third-order spectral analyses applied to 2, 660 ELMs obtained from three different KSTAR discharges to ensure statistical validity.

Experimental Study on Spatial Variation of Mass Transport Induced by Surface Waves Generated in a Finite-Depth Laboratory Flume

AbstractThe aim of laboratory experiments conducted in a wave flume is to confirm that wave-induced mass transport varies along the way of propagation of regular mechanically generated waves in water of finite depth. This effect is attributed to the interactions between primary waves generated in the flume and associated free waves. Measurements of wave kinematics in several locations along the flume are performed to evaluate mass transport. Wave gauges and the particle image velocimetry technique are employed, respectively, to provide information on the evolution of the oscillating water surface and the wave velocity field under regular waves. Laboratory data are compared with numerical predictions of the derived nonlinear wavemaker model based on a pseudospectral approach. The experimental data exhibit good agreement with the numerical results with respect to particle trajectories and mass transport for nonlinear transitional and shallow water waves. Numerical and experimental investigations confirm that free-surface oscillatory motion and particle kinematics are affected by second-order free waves, which modify the characteristics of laboratory waves, especially in a strongly nonlinear shallow water regime. Moreover, the present study gives valuable insight into the effects of the interaction between two independent waves on wave-induced mass transport, which highlights the need of including nonlinear energy transfers between higher harmonics for the reliable estimation of wave processes in ocean circulation models.

Scale-by-scale energy transfer in a dual-plane jet flow

We numerically investigate the scale-by-scale energy transfer along all three directions (i.e., streamwise, vertical, and spanwise directions) at three specifically selected centerline locations (i.e., X/L0 = 7, 12, and 20) in a dual-plane jet flow by using the Karman–Howarth–Monin–Hill (KHMH) equation, where X and L0 are the streamwise distance from the inlet and the initial jet width, respectively. Unlike the well-known Karman–Howarth equation, the fully generalized KHMH equation allows us to study the scale-by-scale energy balance without any assumptions (i.e., homogeneity and isotropy). We calculate each term in the KHMH equation by using the data from a direct numerical simulation [Zhou et al., “Dual-plane turbulent jets and their non-Gaussian velocity fluctuations,” Phys. Rev. Fluids 3, 124604 (2018)]. At X/L0 = 7, where the flow is inhomogeneous and anisotropic, the scale-by-scale energy transfer is quite different in the streamwise, vertical, and spanwise directions. One interesting finding is that a negative production term in the vertical direction can be found in the reversal flow region. Unlike most flows previously investigated, the linear energy cascade plays an important role in the energy cascade. The linear energy transfer is heavily dependent on the direction: in the streamwise direction, it is forward (from the large scale to the small scale), but in the vertical direction, it is backward (from the small scale to the large scale). A physical model is proposed and also verified, which suggests that the forward linear energy cascade corresponds to fluid compression, and the backward linear energy cascade corresponds to the fluid stretching. At X/L0 = 12, where the energy spectrum exhibits a well-defined −5/3 scaling, there is no equilibrium energy cascade. The linear energy cascade is still dominant and shows a backward cascade in the streamwise direction and a forward cascade in the vertical direction, while the non-linear energy cascade remains forward. At X/L0 = 20, where the flow becomes much more homogeneous and isotropic, within a short scale-range around the Taylor microscale, the dissipation term can be balanced by the combination of the non-linear energy transfer term and advection term. This observation to some extent echoes Kolmogorov’s hypothesis, but limited only to length scales around the Taylor microscale, and the persistence of the advection term can find its root in the low local Reynolds number at that length scale.

Evolution of Infragravity Waves Over a Shoal Under Nonbreaking Conditions

AbstractThe present paper aims to clarify the mechanism of infragravity wave (IGW) energy amplification over nearshore shoals reported in recent studies. Wave transformation and energy transfer between short waves (SWs) and IGWs were investigated using SWASH model for nonbreaking random waves propagating over trapezoid shoals with different bottom slopes. It was found that the time lag of IGWs relative to SW groups is the major mechanism for energy transfer from SWs to IGWs and the amplification of IGW energy over all segments of the shoal. The time lag is generated on the front slope and enlarged on the plateau of the shoal, decreases on the rear slope with higher decreasing rates on milder slopes. Over the rear slope, the evolution of IGWs depends on the relative importance of deshoaling and nonlinear energy transfer. It was found that nonlinear energy transfer dominates over the rear slope gentler than 1/60, causing the IGW energy to increase over the first half of the deshoaling process and decrease over the second half whereas deshoaling dominates for steeper rear slope and the IGW energy decay over the whole slope. It is demonstrated numerically and theoretically that the shoals with gentler bottom slopes amplify the IGW energy more effectively by providing longer distance for nonlinear energy transfer to build up. The persistent nonlinear energy transfer on the plateau indicates the important role of wave spatial evolution history in the subsequent IGWs evolution. Strong free IGWs were detected on leeward of the shoal, possibly due to release of topography‐induced additional bound IGWs.

Field Evidence of Inverse Energy Cascades in the Surfzone

AbstractLow-frequency currents and eddies transport sediment, pathogens, larvae, and heat along the coast and between the shoreline and deeper water. Here, low-frequency currents (between 0.1 and 4.0 mHz) observed in shallow surfzone waters for 120 days during a wide range of wave conditions are compared with theories for generation by instabilities of alongshore currents, by ocean-wave-induced sea surface modulations, and by a nonlinear transfer of energy from breaking waves to low-frequency motions via a two-dimensional inverse energy cascade. For these data, the low-frequency currents are not strongly correlated with shear of the alongshore current, with the strength of the alongshore current, or with wave-group statistics. In contrast, on many occasions, the low-frequency currents are consistent with an inverse energy cascade from breaking waves. The energy of the low-frequency surfzone currents increases with the directional spread of the wave field, consistent with vorticity injection by short-crested breaking waves, and structure functions increase with spatial lags, consistent with a cascade of energy from few-meter-scale vortices to larger-scale motions. These results include the first field evidence for the inverse energy cascade in the surfzone and suggest that breaking waves and nonlinear energy transfers should be considered when estimating nearshore transport processes across and along the coast.

Identification of a network of nonlinear interactions as a mechanism triggering the onset of edge localized modes

Edge localized modes (ELMs) remain a critical issue for the lifetime of in-vessel components of fusion reactors such as ITER. We study ELMs triggered when the pedestal parameters are below the peeling-ballooning limit. These ELMs occur while the pedestal recovers after an ELM crash. We identify a mechanism by which a non-linear perturbation involving many active triads—a network of non-linear interactions – leads to the triggering of these ELMs. Each active triad leads to the non-linear transfer of energy between three waves, such that the network of non-linear interactions lead to a transfer of energy between many waves. The triggering of this non-linear perturbation systematically coincides with a pedestal perturbation induced by the neutral beam injection beams and localized near the magnetic surface of safety factor q = 5. Among the non-linear interactions detected during the ELM by a bi-coherence analysis, the most active triad involves a slow frequency that is qualitatively consistent with a geodesic acoustic mode located at the same location, i.e., near the q = 5 surface.

Effects of Nonlinear Stores on the Dynamics of a Computational Model Airplane

It has been shown experimentally that local nonlinear stores attached to the wings of a model airplane enhance overall energy dissipation through global nonlinear modal energy exchanges. Here, a computational model is developed to investigate this effect. The dynamics of the airplane–store system is studied under impulse loading with both stores locked (L-L configuration), left-wing store unlocked (U-L), or both stores unlocked (U-U). Each store acts as a rigid mass when locked, or as a strongly nonlinear element otherwise. The results are in agreement with the experimental ones at different impulse levels. The simulated responses for the U-L and U-U configurations are then projected onto the normal modes of the underlying L-L system to study modal energy redistributions caused by the nonlinear stores. The U-L and U-U configurations exhibit irreversible nonlinear energy transfers from the airplane modes to the stores, with faster decay of total energy compared with the L-L configuration, corroborating the experimental results. The stores also drastically affect the distribution of energy among airplane modes, also contributing to enhanced energy dissipation. Finally, harmonic excitation is considered, and the nonlinear effects are confined to a specific frequency band. This work confirms the drastic dynamic effects that local nonlinear attachments can have on the dynamics of the (linear) structures to which they are attached. Whether such local strong nonlinearities are to be purposely designed to enhance energy dissipation or need to be accounted for to mitigate their possibly detrimental effects is of great practical significance in different applications.

The Seasonality of Submesoscale Energy Production, Content, and Cascade

AbstractSubmesoscale processes in the upper ocean vary seasonally, in tight correspondence with mixed layer thickness variability. Based on a global high‐resolution MITgcm simulation, seasonal evaluation of strong vorticity and spectral analysis of the kinetic energy in the Kuroshio Extension System show the strongest submesoscales occur in March, implying a lag of about a month behind mixed layer thickness maximum in February. An analysis of spectral energy sources and transfers indicates that the seasonality of the submesoscale energy content is a result of the competition between the conversion of available potential energy into submesoscale kinetic energy via a buoyancy production/vertical buoyancy flux associated with mixed layer instability and nonlinear energy transfers to other scales associated with an energy cascade. The buoyancy production is seasonally in phase with the mixed layer depth, but the transfers of energy across scales makes energizing the reservoir of submesoscale kinetic energy lag behind by a month.

Bound and free infragravity wave energy over a bar

The propagation of bound and free infragravity wave energy under short-wave breaking conditions induced by a longshore bar is investigated through field observations. Near-bottom pressure records deployed in a cross-shore array at S. Jacinto barred beach (Portugal) were analysed. In these observations, short-wave breaking induced by the longshore bar occurred mainly in intermediate water depths.The ratio between bound and total (bound plus free) infragravity wave energy was estimated with the methodology of Herbers et al. (1994). This ratio had a maximum value of 0.6 at the breaking onset, which is consistent with values presented elsewhere.A decrease of the bound infragravity wave energy was observed after short-wave breaking near the bar crest. This is in part due to nonlinear energy transfers from infragravity to short-wave frequencies as detected on the imaginary part of the bispectrum, in a weakly dispersive Boussinesq approximation. The other part is due to the process of release/transform bound into free infragravity wave energy that was assessed with a simplified energy balance equation.A conceptual model for the exchange of bound infragravity wave energy during short-wave breaking in intermediate water depths is proposed. This conceptual model involves both the kh and the ga/C2 generalized nonlinearity parameter.

Investigating Spectral Distortion of Local Volcano Infrasound by Nonlinear Propagation at Sakurajima Volcano, Japan

AbstractSound waves generated by erupting volcanoes can be used to infer important source dynamics, yet acoustic source‐time functions may be distorted during propagation, even at local recording distances ( 15 km). The resulting uncertainty in source estimates can be reduced by improving constraints on propagation effects. We aim to quantify potential distortions caused by wave steepening during nonlinear propagation, with the aim of improving the accuracy of volcano‐acoustic source predictions. We hypothesize that wave steepening causes spectral energy transfer away from the dominant source frequency. To test this, we apply a previously developed single‐point, frequency domain, quadspectral density‐based nonlinearity indicator to 30 acoustic signals from Vulcanian explosion events at Sakurajima Volcano, Japan, in an 8‐day data set collected by five infrasound stations in 2013 with 2.3‐ to 6.2‐km range. We model these results with a 2‐D axisymmetric finite‐difference method that includes rigid topography, wind, and nonlinear propagation. Simulation results with flat ground indicate that wave steepening causes up to 2 dB (1% of source level) of cumulative upward spectral energy transfer for Sakurajima amplitudes. Correction for nonlinear propagation may therefore provide a valuable second‐order improvement in accuracy for source parameter estimates. However, simulations with wind and topography introduce variations in the indicator spectra on order of a few decibels. Nonrandom phase relationships generated during propagation or at the source may be misinterpreted as nonlinear spectral energy transfer. The nonlinearity indicator is therefore best suited to small source‐receiver distances (e.g., 2 km) and volcanoes with simple sources (e.g., gas‐rich strombolian explosions) and topography.

Adaptation of the Parameterization of the Nonlinear Energy Transfer for Short Fetch Conditions in the WAVEWATCH III Wave Prediction Model

The parameterization of the nonlinear energy transfer called Discrete Interaction Approximation (DIA) is optimized in the WAVEWATCH III wave model by the criterion of minimizing deviations of model predictions from the data of field measurements. Short fetches are considered for which the wind-input source function had been previously adjusted. The results of the numerical simulation and field experiment for the DIA built-in version and for the DIA with the proposed parameters are compared. The improvement of the reproduction of the main parameters of the wave spectra, significant wave height, and their mean period by the model is shown.

On energy exchanges between eddies and the mean flow in quasigeostrophic turbulence

We study the term in the eddy energy budget of continuously stratified quasigeostrophic turbulence that is responsible for energy extraction by eddies from the background mean flow. This term is a quadratic form, and we derive Euler–Lagrange equations describing its eigenfunctions and eigenvalues, the former being orthogonal in the energy inner product and the latter being real. The eigenvalues correspond to the instantaneous energy growth rate of the associated eigenfunction. We find analytical solutions in the Eady problem. We formulate a spectral method for computing eigenfunctions and eigenvalues, and compute solutions in Phillips-type and Charney-type problems. In all problems, instantaneous growth is possible at all horizontal scales in both inviscid problems and in problems with linear Ekman friction. We conjecture that transient growth at small scales is matched by linear transfer to decaying modes with the same horizontal structure, and we provide simulations supporting the plausibility of this hypothesis. In Charney-type problems, where the linear problem has exponentially growing modes at small scales, we expect net energy extraction from the mean flow to be unavoidable, with an associated nonlinear transfer of energy to dissipation.

Growth of Au Hollow Stars and Harmonic Excitation Energy Transfer.

Optical excitation, subsequent energy transfer, and emission are fundamental to many physical problems. Optical antennas are ideal candidates for manipulating these processes. We extend energy transfer to second- and third-harmonic (SH and TH) fields through the collaborative susceptibility χ(n) (n = 1, 2, 3) resonances of nonlinear optical antennas. Hollow gold stars, with a broadband response covering the fundamental, SH, and TH frequencies, are synthesized as nonlinear antennas. Harmonic resonance energy transfer through a χ(3) → χ(1) collaboration is revealed. A χ(3) → χ(2) collaboration is uncovered, with largely enhanced SH radiation demonstrated by exciting the three resonances at the fundamental, SH, and TH frequencies. A theoretical model of the effective nonlinear susceptibilities is proposed to calculate the efficiencies of the two nonlinear energy transfer processes.

L-mode to H-mode transition triggered by sawtooth-induced heat flux in EAST

H-modes induced by sawtooth events can be often observed in discharges with marginal auxiliary power injection in EAST. Poloidal flow shear at the very plasma edge, increasing ∼25% up to the threshold value, is observed just before the L-H transition by means of a fast reciprocating probe array in EAST. This suddenly risen poloidal flow shear, caused by the increased turbulent driven Reynolds force, is motived by the heat pulse originally released by a sawtooth crash at the plasma core. Associated with the critical poloidal flow shear, the local turbulent decorrelation rate increases significantly. The increased turbulent decorrelation rate compensated by nonlinear energy transfer rate from the turbulence to the low-frequency shear flows, exceeding the turbulence energy input rate, is sustained for several hundred microseconds till the turbulence quench happening.

Experimental and numerical study of the propagation of focused wave groups in the nearshore zone

The propagation of focused wave groups in intermediate water depth and the shoaling zone is experimentally and numerically considered in this paper. The experiments are carried out in a two-dimensional wave flume and wave trains derived from Pierson-Moskowitz and JONSWAP spectrum are generated. The peak frequency does not change during the wave train propagation for Pierson-Moskowitz waves; however, a downshift of this peak is observed for JONSWAP waves. An energy partitioning is performed in order to track the spatial evolution of energy. Four energy regions are defined for each spectrum type. A nonlinear energy transfer between different spectral regions as the wave train propagates is demonstrated and quantified. Numerical simulations are conducted using a modified Boussinesq model for long waves in shallow waters of varying depth. Experimental results are in satisfactory agreement with numerical predictions, especially in the case of wave trains derived from JONSWAP spectrum.