Bicoherence Analysis Research Articles

The Bicoherence Analysis of Type-C Quasiperiodic Oscillations in Swift J1727.8−1613

We present the results of bicoherence analysis for Swift J1727.8−1613 during its 2023 outburst, using data from Insight-HXMT. Our analysis focused on observations with quasiperiodic oscillations (QPOs) of frequencies greater than 1 Hz, revealing that all of them belong to type-C QPOs. We found a strong correlation between the QPO frequency and the hardness ratio, as well as a linear relationship between the QPO rms and the hardness ratio. The bicoherence analysis revealed a transition from a “web” pattern to a “hypotenuse” pattern in the low-energy (LE) and high-energy (HE) bands. In the bicoherence patterns, there are correlations between horizontal and vertical bicoherence at f 1 = f 2 = f QPO with count rates. The diagonal structure at f 1 + f 2 = f QPO becomes more prominent with increasing energy. Additionally, we discovered a new bicoherence pattern in the medium energy band from 10 to 20 keV; the diagonal structure at f 1 + f 2 = f har is prominent only in this energy band, which we refer to as the “parallel” pattern. The bicoherence analysis indicates that the source is likely a low-inclination source.

Identifying noise transients in gravitational-wave data arising from nonlinear couplings

Abstract Noise in various interferometer systems can sometimes couple non-linearly to create excess noise in the gravitational wave (GW) strain data. Third-order statistics, such as bicoherence and biphase, can identify these couplings and help discriminate those occurrences from astrophysical GW signals. However, the conventional analysis can yield large bicoherence values even when no phase-coupling is present, thereby, resulting in false identifications. Introducing artificial phase randomization in computing the bicoherence reduces such occurrences with negligible impact on its effectiveness for detecting true phase-coupled disturbances. We demonstrate this property with simulated disturbances – focusing only on short-duration ones (lasting up to a few seconds) in this work. Statistical hypothesis testing is used for distinguishing phase-coupled disturbances from non-phase coupled ones when employing the phase-randomized bicoherence. We also obtain an expression for the bicoherence value that minimizes the sum of the probabilities of false positives and false negatives. This can be chosen as a threshold for shortlisting bicoherence triggers for further scrutiny for the presence of non-linear coupling. Finally, the utility of the phase-randomized bicoherence analysis in GW time-series data is demonstrated for the following three scenarios: (1) Finding third-order statistical similarities within categories of noise transients, such as blips and koi fish. If these non-Gaussian noise transients, or glitches, have a common source, their bicoherence maps can have similarities arising from common bifrequencies related to that source. (2) Differentiating linear or non-linear phase-coupled glitches from compact binary coalescence signals through their bicoherence maps. This is explained with a simulated signal. (3) Identifying repeated bifrequencies in the second and third observation runs (i.e., O2 and O3) of LIGO and Virgo.

The Mobile Phone Electromagnetic Radiation Effects on Heart Rate Variability Function

Background: The proliferation of mobile phone usage has given rise to concerns about the potential health effects of electromagnetic fields (EMF), particularly in relation to heart rate variability (HRV), a key indicator of cardiac health. Previous studies have yielded inconsistent results using lower-order statistical measures, leaving a gap in understanding the nonlinear interactions between EMF exposure and HRV. Objective: This study aimed to investigate the effects of mobile phone EMF on HRV by employing bicoherence analysis of ECG data. It sought to determine whether the position of EMF exposure relative to the heart and the duration of exposure affected HRV parameters. Methods: Twenty subjects were recruited for the study, with ECG and EEG data collected under EMF and non-EMF conditions. ECG data were captured using a 12-lead system, with electrodes placed according to standard guidelines. EEG electrodes were positioned following the 10-20 system. Bicoherence and coherence analyses were conducted to assess nonlinear interactions in HRV activity and the relationship between heart and brain signals. The study also considered the duration of EMF exposure, comparing the effects of 10-minute and 40-minute sessions. Results: The bicoherence values for ECG data during EMF exposure at the left ear showed negligible differences, with values ranging between 0.0 to 0.04. However, chest positions V1 and V2 revealed statistically significant larger bicoherence values during non-EMF trials as opposed to EMF trials. Coherence analysis between ECG and EEG demonstrated significantly higher values across the 16-30Hz frequency band during EMF trials. No significant differences were observed for 10-minute EMF exposure, whereas 40-minute exposure sessions indicated a correlation with changes in HRV. Conclusion: The study's findings suggest that mobile phone EMF can affect HRV parameters, with the effects being more pronounced during longer exposure durations and when the source of EMF is closer to the heart. These results support the need for guidelines on safe mobile phone usage and further research into the effects of EMF on cardiac function.

Laboratory observation of nonlinear wave shapes due to spatial varying opposing currents

Physical experiments were conducted to examine the influence of adverse currents on the propagation of shallower water waves and their impact on the evolution of nonlinear wave shapes. Irregular waves, characterized by varying initial peak periods and amplitudes, were generated in a physical wave flume equipped with a bottom slope of 1/20. Three groups of spatially varying opposing currents were generated in the flume and interacted with the aforementioned wave trains. Experimental results confirm that strong opposing currents can significantly intensify local wave nonlinearity, thereby further influencing the deformation characteristics of waves. In contrast, a weak opposing current (without wave-blocking) has a negligible effect. Bicoherence analysis revealed that the degree of phase coupling among triads of waves increased with an elevated current velocity before wave-blocking. Nevertheless, during partial wave-blocking, the degree of phase coupling was seemingly weakened by an increase in opposing current. Moreover, the influence of a co-existing current in the formation of extreme waves was recognized. The study confirms that adverse currents notably affect extreme wave steepness and extreme wave skewness, with a negligible impact on extreme wave asymmetry. As a result, empirical formulas modified by current effects are presented, describing certain key nonlinear wave shapes as functions of the local Ursell number.

Observations of Parametric Subharmonic Instability of Diurnal Internal Tides in the Northwest Pacific

Abstract Based on yearlong observations from three moorings at 12°, 14°, and 16°N in the northwest Pacific, this study presents observational evidence for the occurrence and behavior of parametric subharmonic instability (PSI) of diurnal internal tides (ITs) both in the upper and abyssal ocean around the critical latitudes (O1 IT: 13.44°N; K1 IT: 14.52°N), which is relatively less explored in comparison with PSI of M2 ITs. At 14°N, near-inertial waves (NIWs) feature a “checkerboard” pattern with comparable upward- and downward-propagating components, while the diurnal ITs mainly feature a low-mode structure. The near-inertial kinetic energy at 14°N, correlated fairly well with the diurnal KE, is the largest among three moorings. The bicoherence analysis, and a causality analysis method newly introduced here, both show statistically significant phase locking between PSI triads at 14°N, while no significant signals emerge at 12° and 16°N. The estimated PSI energy transfer rate shows a net energy transfer from diurnal ITs to NIWs with an annual-mean value of 1.5 × 10−10 W kg−1. The highly sheared NIWs generated by PSI result in a 2–6 times larger probability of shear instability events at 14°N than 12° and 16°N. Through swinging the local effective inertial frequency close to either O1 or K1 subharmonic frequencies, the passages of anticyclonic and cyclonic eddies both result in elevated NIWs and shear instability events by enhancing PSI efficiency. Particularly, different from the general understanding that cyclonic eddies usually expel NIWs, enhanced NIWs and instability are observed within cyclonic eddies whose relative vorticity can modify PSI efficiency. Significance Statement Parametric subharmonic instability (PSI) effectively transfers energy from low-mode internal tides (ITs) to high-mode near-inertial waves (NIWs), triggering elevated mixing around critical latitudes. This study provides observational evidence for the occurrence of PSI of diurnal ITs in the northwest Pacific and its role in enhancing shear instability. Generally, anticyclonic eddies act to trap NIWs while cyclonic eddies tend to expel NIWs. Here we document elevated NIWs and shear instability within both anticyclonic and cyclonic eddies, which shift the local effective inertial frequency close to either O1 or K1 subharmonic frequencies, thereby enhancing PSI efficiency. Processes associated with PSI and the modulation of PSI efficiency by mesoscale eddies have significant implications for improving mixing parameterizations in ocean circulation and climate models.

Bicoherence Analysis of Oxygen Ion Cyclotron Harmonic Waves Observed by Van Allen Probes

AbstractBicoherence analysis is statistically performed for the oxygen ion cyclotron harmonic (OCH) waves observed by Van Allen Probes. While OCH waves and so‐called electromagnetic ion cyclotron harmonics have indistinguishable spectral characteristics in observation, they are believed to be excited by different mechanisms with the latter being suggested to arise from nonlinear wave‐wave coupling. Our result reveals that most of the OCH wave events have small bicoherence indices, so they are unlikely excited by wave‐wave coupling. The result is not much affected by the parameter choice in the bicoherence analysis, although increasing the subinterval length and/or reducing the subinterval overlap increases the chance of getting large bicoherence index values. Furthermore, the examination of two special events with large bicoherence indices shows that the observed phase relationship among different wave components does not align with the expectation from wave‐wave coupling. The events cannot be convincingly confirmed to be generated through wave‐wave coupling.

Experimental characterization of the quasi-coherent mode in EDA H-Mode and QCE scenarios at ASDEX Upgrade

The quasi-coherent mode (QCM), appearing in enhanced D α high confinement mode (EDA H-mode) and quasi-continuous exhaust (QCE) plasmas has been analysed in detail at ASDEX Upgrade via thermal helium beam spectroscopy under various discharge parameters. In both scenarios the QCM appears to be localized close to the separatrix and to propagate in ion diamagnetic direction in the plasma frame. The poloidal wavenumber of the QCM is about 0.025<kθρs<0.075 and the radial wavenumber is kr≈0 cm−1 . It was found that the plasmas are generally below the ideal MHD limit at the separatrix. All the properties are consistent with ideal, resistive or kinetic ballooning modes. Simultaneous to the appearance of the QCM, higher harmonic modes can be observed in EDA H-modes, which are exclusively visible in magnetic pick-up coils and have toroidal mode numbers of up to n = 10. By performing a bicoherence analysis it was found that the higher harmonic modes and the QCM are coupling, but are disjoint phenomena. Qualitatively, the bandwidth of the QCM serves as a promising distinctive feature between QCE plasmas and EDA H-modes.

Investigation of a low frequency coherent mode in Wendelstein 7-X with island divertor

During the island divertor operation of W7-X, especially in standard magnetic configuration (with 5/5 island chain in the scrape-off-layer (SOL)), quasi-periodic electromagnetic oscillation is observed. It appears in the frequency range of 1 kHz–2 kHz, therefore it is called the low frequency mode (LFM) within this paper. It is observed by multiple diagnostics, amongst them, a poloidal correlation reflectometer allowing radial localization of the LFM. The LFM is localized in the SOL and shows an obvious modulation effect on the plasma perpendicular velocity ( V⊥ ). Furthermore, broadband turbulence is observed in the fluctuation spectra of the electron density and the magnetic field and the perpendicular correlation length of turbulence eddies are modulated. The calculation of the poloidal flow velocity and its oscillation allows us to study the effect of the LFM on the flow. Cross correlation analysis shows that the perpendicular flow oscillation and the turbulence modulation are closely correlated. The application of external control coils to adjust the island size and position result in a strong modification of the magnetic topology at the plasma edge which affects the appearance, amplitude and frequency of the LFM. Bi-coherence analysis indicates that nonlinear interactions among turbulence components is a possible mechanism for the generation of the LFM.

Observed oceanic response to Tropical Cyclone Amphan (2020) from a subsurface mooring in the Bay of Bengal

Upper ocean responses to the super Tropical Cyclone (TC) Amphan and modulation of energy dissipation by internal tides were investigated using in situ observations from a subsurface mooring in Bay of Bengal (BoB). The observations showed that the entire observed water column (150–800 m) cooled significantly, up to a maximum of 2 ℃, and salinity increased significantly at 150–200 m within one week after the TC, mainly due to the TC-induced upwelling. Dynamic response was characterized by strong near-inertial oscillation above 120 m. The near inertial waves (NIWs) had a maximum velocity and kinetic energy at 112.6 m, about 0.34 m/s and 59.5 J/m3, respectively. The energy spectrum and bicoherence analysis indicated that, the nonlinear wave-wave interaction between NIWs (f) and semi-diurnal tide (D2), as well as the self-interaction of NIWs were enhanced after the passage of TC. The nonlinear wave-wave interaction processes were able to transfer energy to higher mode internal waves, thus accelerating energy attenuation. Hence, the observed e-folding time for near-inertial kinetic energy (6.2 days) was only 41 % of the theoretical e-folding time. This study provided a new evidence for the mechanism of energy dissipation of NIWs and semi-diurnal tide during a TC condition in the southern BoB.

Transition between continuous and discrete spectra of high-wavenumber turbulence in neutral gas pressure scan experiments on a linear magnetized plasma

Spectral transition between continuous and discrete spectra has been observed in high-wavenumber turbulence excitation experiments. The transition appeared in neutral gas scanning, which shows that continuous spectra dominate at low gas pressures and discrete spectra dominate at high gas pressures. Both spectra have well smaller spatial scale than the ion effective Larmor radius. The discrete spectra have 6–11 peaks and maximum peak values at 4th or 5th peak. Correlation length analysis reveals that the continuous component is turbulent and the discrete component is coherent. The bicoherence analysis shows that the turbulent spectra have finite nonlinear coupling, whereas the discrete spectra have no corresponding coupling.

Millennial-scale variability of the Antarctic ice sheet during the early Miocene

Millennial-scale ice sheet variability (1-15 kyr periods) is well documented in the Quaternary, providing insight into critical atmosphere-ocean-cryosphere interactions that can inform the mechanism and pace of future climate change. Ice sheet variability at similar frequencies is comparatively less known and understood prior to the Quaternary during times, where higher atmospheric pCO2 and warmer climates prevailed, and continental-scale ice sheets were largely restricted to Antarctica. In this study, we evaluate a high-resolution clast abundance dataset (ice-rafted debris) that captures East Antarctic ice sheet variability in the western Ross Sea during the early Miocene. This dataset is derived from a 100 m-thick mudstone interval in the ANtarctic DRILLing (ANDRILL or AND) core 2A, which preserves a record of precession and eccentricity variability. The sedimentation rates are of appropriate resolution to also characterize the signature of robust, subprecession cyclicity. Strong sub-precession (~10 kyr) cyclicity is observed, with an amplitude modulation in lockstep with eccentricity, indicating a relationship between high-frequency Antarctic ice sheet dynamics and astronomical forcing. Bicoherence analysis indicates that many of the observed millennial-scale cycles (as short as 1.2 kyr) are associated with nonlinear interactions (combination or difference tones) between each other and the Milankovitch cycles. The presence of these cycles during the Miocene reveals the ubiquity of millennial-scale ice sheet variability and sheds light on the interactions between Earth's atmosphere, ocean, and ice in climates warmer than the Quaternary.

Instability and transition onset downstream of a laminar separation bubble at Mach 6

Instability measurements of an axisymmetric, laminar separation bubble were made over a sharp cone-cylinder-flare with a$12^{\circ }$flare angle under hypersonic quiet flow. Two distinct instabilities were identified: Mack's second mode (which peaked between 190 and 290 kHz) and the shear-layer instability in the same frequency band as Mack's first mode (observed between 50 and 150 kHz). Both instabilities were measured with surface pressure sensors and were captured with high-speed schlieren. Linear stability analysis results agreed well with these measured instabilities in terms of both peak frequencies and amplification rates. Lower-frequency fluctuations were also noted in the schlieren data. Bicoherence analysis revealed nonlinear phase-locking between the shear-layer and second-mode instabilities. For the first time in axisymmetric, low-disturbance flow, naturally generated intermittent turbulent spots were observed in the reattached boundary layer. These spots appeared to evolve from shear-layer-instability wave packets convecting downstream. This work presents novel experimental evidence of the hypersonic shear-layer instability contributing directly to transition onset for an axisymmetric model.

Visual cortical LFP in relation to the hippocampal theta rhythm in track running rats.

Theta oscillations in the primary visual cortex (VC) have been observed during running tasks, but the mechanism behind their generation is not well understood. Some studies have suggested that theta in the VC is locally generated, while others have proposed that it is volume conducted from the hippocampus. The present study aimed to investigate the relationship between hippocampal and VC LFP dynamics. Analysis of power spectral density revealed that LFP in the VC was similar to that in the hippocampus, but with lower overall magnitude. As running velocity increased, both the power and frequency of theta and its harmonics increased in the VC, similarly to what is observed in the hippocampus. Current source density analysis triggered to theta did not identify distinct current sources and sinks in the VC, supporting the idea that theta in the VC is conducted from the adjacent hippocampus. Phase coupling between theta, its harmonics, and gamma is a notable feature in the hippocampus, particularly in the lacunosum moleculare. While some evidence of coupling between theta and its harmonics in the VC was found, bicoherence estimates did not reveal significant phase coupling between theta and gamma. Similar results were seen in the cross-region bicoherence analysis, where theta showed strong coupling with its harmonics with increasing velocity. Thus, theta oscillations observed in the VC during running tasks are likely due to volume conduction from the hippocampus.

Observation of Plasma Turbulence in a Hall Thruster Using Microwave Interferometry

To understand anomalous electron transport in a Hall thruster, plasma turbulence inside the acceleration channel was observed using a 76 GHz microwave interferometer. The dependence of the amplitude of the 100–500 kHz turbulence on magnetic flux density, and the relationships between the turbulence and other plasma instabilities and between the turbulence and the discharge current were investigated through spectral density and bicoherence analysis. The amplitude of electron number density fluctuations of the turbulence, integrating the spectral density from 100 to 500 kHz, is , or almost 10% of the time-averaged electron number density. The amplitude of the turbulence decreases with increase in weak magnetic field strength (coil current less than 0.6 A) and then increases with increase in magnetic field strength. The amplitude of the turbulence has a positive relation to the discharge current, leads to anomalous electron transport inside the acceleration channel, and is coupled with ionization instability. In addition, low-frequency perturbations of several hundred hertz were observed, with a positive relation to the turbulence and coupled with both ionization instability and turbulence.

Rossby wave second harmonic generation observed in the middle atmosphere

Second harmonic generation is the lowest-order wave-wave nonlinear interaction occurring in, e.g., optical, radio, and magnetohydrodynamic systems. As a prototype behavior of waves, second harmonic generation is used broadly, e.g., for doubling Laser frequency. Second harmonic generation of Rossby waves has long been believed to be a mechanism of high-frequency Rossby wave generation via cascade from low-frequency waves. Here, we report the observation of a Rossby wave second harmonic generation event in the atmosphere. We diagnose signatures of two transient waves at periods of 16 and 8 days in the terrestrial middle atmosphere, using meteor-radar wind observations over the European and Asian sectors during winter 2018–2019. Their temporal evolution, frequency and wavenumber relations, and phase couplings revealed by bicoherence and biphase analyses demonstrate that the 16-day signature is an atmospheric manifestation of a Rossby wave normal mode, and its second harmonic generation gives rise to the 8-day signature. Our finding confirms the theoretically-anticipated Rossby wave nonlinearity.

Nonlinear Interaction Between H+ Band and He+ Band EMIC Waves: Van Allen Probe Observations and Hybrid Simulations

AbstractNonlinear theory has predicted that wave‐wave coupling from different band electromagnetic ion cyclotron (EMIC) waves can occur in multiple‐ion plasmas. However, no direct observational evidence has been reported yet. Here we present multiple substructures on the frequency spectrum of EMIC waves with observations of Van Allen Probes. Some substructures are demonstrated to be excited by nonlinear interactions between preexisting H+ band and He+ band EMIC waves through the bicoherence analysis. Additionally, hybrid simulation displays that a new wave is motivated at sum frequencies after two independent pump waves of different band EMIC waves are injected, implying that the nonlinear wave‐wave interactions could drive EMIC waves with higher wavenumbers. Therefore, this letter provides the first observational evidence of wave‐wave coupling between H+ band and He+ band EMIC waves.

Using the bispectrum to probe radio X-ray correlations in GRS 1915+105

ABSTRACT We present the results of bicoherence analysis on observations of GRS 1915+105 that exhibit quasi-periodic oscillations (QPOs). The bicoherence is a higher order statistic that can be used to probe the relation between the phases of a triplet of Fourier frequencies. Despite showing very similar power spectra, the observations exhibit different patterns in their bicoherence, indicating that the QPOs are phase coupled to the noise in different ways. We show that the bicoherence pattern exhibited correlates with the frequency of the QPO, the hardness ratio, as well as the radio properties of the source. In particular, we find that the nature of phase coupling between the QPO and the high and low frequency broad-band components is different between radio quiet, radio plateau, and radio steep conditions. We also investigate the phase lag behaviour of observations with QPO frequency above 2 Hz that show different bicoherence patterns and find statistically significant differences between them, indicating a change in the underlying physical mechanism. Finally, we present a scenario whereby the cooling of the jet electrons by soft photons from the accretion disc could explain the observed correlations between the bicoherence and radio properties.

Beta-induced Alfvén eigenmodes and geodesic acoustic modes in the presence of strong tearing activity during the current ramp-down on JET

The analysis of the current ramp-down phase of JET plasmas has revealed the occurrence of additional magnetic oscillations in pulses characterized by large magnetic islands. The frequencies of these oscillations range from 5 to , being well below the toroidal gap in the Alfvén continuum and of the same order as the low-frequency gap opened by plasma compressibility. The additional oscillations only appear when the magnetic island width exceeds a critical threshold, suggesting that the oscillations could tap their energy from the tearing mode (TM) by a non-linear coupling mechanism. A possible role of fast ions in the excitation process can be excluded, being the pulse phase considered in the observations characterized by very low additional heating. The calculation of the coupled Alfvén–acoustic continuum in toroidal geometry suggests the possibility of beta-induced Alfvén eigenmodes (BAEs) rather than beta-induced Alfvén–acoustic eigenmodes. As a main novelty compared to previous work, the analysis of the electron temperature profiles from electron cyclotron emission has shown the simultaneous presence of magnetic islands on different rational surfaces in pulses with multiple magnetic oscillations in the low-frequency gap of the Alfvén continuum. This observation supports the hypothesis of different BAE with toroidal mode number n = 1 associated with different magnetic islands. As another novelty, the observation of magnetic oscillations with n = 2 in the BAE range is reported for the first time in this work. Some pulses, characterized by slowly rotating magnetic islands, exhibit additional oscillations with n = 0, likely associated with geodesic acoustic modes (GAMs), and a cross-spectral bicoherence analysis has confirmed a non-linear interaction between TM, BAE and GAM, with the novelty of the observation of multiple triplets (twin BAEs plus GAM), due to the simultaneous presence of several magnetic islands in the plasma.

Electromagnetic Ion Cyclotron Harmonic Waves Generated via Nonlinear Wave‐Wave Couplings

AbstractIn this letter, we report an electromagnetic ion cyclotron (EMIC) harmonic event observed by the Van Allen Probe B, whose generation is demonstrated to result from nonlinear wave‐wave resonances through the bicoherence analysis. Hybrid simulation shows that the second to sixth harmonics could be excited in sequence after a pump EMIC wave is initially injected, which is in consistent with the observations of EMIC harmonic. It indicates the important role of the second harmonic in the generation of higher harmonics. Finally, the statistical distribution for the amplitude of EMIC second harmonic waves indicates that the energy transfer rate from the fundamental wave to the second harmonic is mainly less than 2%, which might be too low to result in third and other higher harmonics above the observational level. Our results will give some new insights into the excitation of EMIC harmonic waves in the inner magnetosphere.

Observation of Near-Inertial Waves Induced by Typhoon Mitag (2019) on the Southwestern East China Sea Continental Slope

Based on horizontal velocity data recorded by a moored acoustic Doppler current profiler (ADCP) deployed on the southwestern continental slope of the East China Sea (ECS), this study investigates the characteristics of near-inertial waves (NIWs) induced by typhoon Mitag in October 2019. The results indicated that Mitag-induced near-inertial kinetic energy (NIKE) was mainly concentrated above 290 m and was subsurface-intensified; both the maximum velocity and kinetic energy of the NIWs occurred at a depth of 100 m and were 0.21 m/s and 23.01 J/m3, respectively. The rotary vertical wavenumber spectra suggested that both downward and upward energy propagation existed. However, upward energy propagation was much smaller than downward energy propagation, mainly in the 0.007–0.014 cpm wavenumber band. The NIWs had an e-folding timescale of 9.5 days and were red-shifted as a result of the Doppler shift of the Kuroshio. Normal mode analysis suggested that the NIWs were dominated by the first and fourth baroclinic modes, which together accounted for 76.7% of the total NIKE. Spectral analysis showed that although the spectral density of the semidiurnal internal tide (M2) peak overwhelmed that of the NIWs by a factor of approximately 30, the shear strength generated by the NIWs was comparable to that of the semidiurnal internal tide (M2), which plays an important role in upper ocean mixing on the southwestern continental slope of the ECS. In addition, the bicoherence analysis suggested that a harmonic wave (M2–f) was generated via the nonlinear interaction between the NIWs and semidiurnal internal tide (M2), which reflects the energy dissipation mechanism of semidiurnal tides and NIWs on the southwestern continental slope of the ECS.