Estimation Of Energy Fluxes Research Articles

Regionalized ensemble estimation of wave periods for assessing wave energy resources across Canada. Part II: Wave-period and wave-energy analyses

The cornerstone for harnessing and utilizing wave energy resources lies in the precise and thorough estimation and assessment of wave energy fluxes through advanced modeling of wave periods. This study implements the developed macroscale regionalized ensemble wave-period modeling (MREWPM) method to accomplish the initial integrated estimation and analysis of wave periods and wave energy fluxes across Canada, complemented by advanced estimations of wave heights and wind speeds. The results indicate that Canadian wave periods lengthen in shallow, low-backscatter, southern, remote, or eastern waters, and exhibit temporal variability in breezy, low-backscatter, southern, remote, or eastern regions. The trend of wave periods exhibited fluctuations, decreasing before and increasing after the trough (9.06 s in 2004) during cool seasons. Temporal variabilities and trends of wave periods were more fragmented and heterogeneous compared to averages. Canadian wave energy fluxes generally exhibit an increase southward with latitudes. The wave energy typically diminishes from offshore (deep waters) to nearshore areas (shallow waters), with this attenuation being more pronounced in winter months. There is a rough decrease from winter, autumn, and spring to summer months, mirroring the seasonal variations of wave periods. This seasonality tends to be more pronounced in highly energetic regions, such as the Pacific and Atlantic oceans. This study enhances reliability and feasibility of macroscale wave-period and wave-energy estimation and analyses, offering scientific support for wave energy development, wave climatology, and ocean engineering.

Spline-fitted measured spectrum as input for the evaluation of nonlinear energy transfer rate and its validation through accurate estimation of wave energy flux

Spline-fitted measured spectrum as input for the evaluation of nonlinear energy transfer rate and its validation through accurate estimation of wave energy flux

Generation and evaluation of energy and water fluxes from the HOLAPS framework: Comparison with satellite-based products during extreme hot weather

Improving our understanding of the energy and water exchanges between the land surface and the lower atmosphere (i.e. land–atmosphere interactions), and how climate change may affect them, is crucial to predict changes in temperature and precipitation extremes. Observations of energy and water fluxes at the land surface are typically retrieved from the eddy covariance method, which presents limitations related to spatial and temporal gaps, and the non-closure of the energy and water balances. Meanwhile, soil moisture (SM) products derived from satellite data have been widely used at regional and global scales, but they are limited to capture only surface soil water content and variations. The combination of remote sensing (RS) data and modelling frameworks is called to be the solution to improve the spatial coverage and vertical resolution of land–atmosphere interactions data, ensuring the energy and water balance closure. Here, we explore the combination of remote sensing and meteorological data with a physical-based modelling framework, the High resOlution Land Atmosphere Parameters from Space (HOLAPS). We used HOLAPS to produce hourly consistent estimates of energy and water fluxes over Europe at 5 km resolution. HOLAPS and other satellite-based evapotranspiration and sensible heat flux products from the literature are evaluated against the water balance method and eddy covariance measurements. HOLAPS SM estimates together with other RS-modelling products are also evaluated against ground-based measurements at the surface and in the root zone. The evaluation of HOLAPS ET estimates show similar performance to the other products with Kling–Gupta efficiency (KGE) ¿ -0.41 in comparison with eddy covariance measurements from FLUXNET in all seasons but in boreal winter. The simulation of H is more uncertain than for ET with KGE values ranging from -2.5 to 0.8 along the products and stations at monthly scales. HOLAPS reaches slightly better results than the rest of ET and H products at daily scales in summer (KGE ¿ 0.3 for ET and KGE ¿ 0.0 for H) and during hot conditions (KGE ¿ 0.2 for ET and KGE ¿-0.2 for H), while the state-of-the-art products show KGE ¿ 0.1 for ET and KGE ¿ -0.41 for H in summer and KGE ¿ -0.1 for ET and KGE ¿ -0.6 for H during hot conditions. All products evaluated here yield a reasonable performance (KGE ¿-0.41 at most sites) in simulating SM at the surface and in the root zone. Our results expose the need for further investigating and improving product performances during extreme conditions. The good performance of HOLAPS together with its inherent advantages (RS data driven, high temporal and spatial resolution, spatial and temporal continuity, soil moisture at different depths and long-term consistent evapotranspiration and sensible heat flux estimates) support its use for agricultural and forest management activities as well as to study land–atmosphere interactions based on Earth Observations.

Quantifying energy fluxes in Tarai region of India during post-monsoon season: Insights from METRIC model, ET station and remote sensing

Accurate evapotranspiration (ET) assessment is crucial for agricultural water management, encompassing crop water requirements, irrigation scheduling, water budgeting and drought monitoring. This study integrates remote sensing-based surface energy balance model with in-situ ET measurements to evaluate surface energy fluxes and ET in Pantnagar, Tarai region. The Mapping Evapotranspiration at high Resolution with Internalized Calibration (METRIC) model, using high-resolution remote sensing data, was validated against observations from an ET station equipped with large aperture scintillometer and micrometeorological tower, situated in sugarcane farm at Govind Ballabh Pant University of Agriculture & Technology (GBPUA&T), Pantnagar. On November 13, 2021, METRIC and Landsat-9 satellite data estimated an instantaneous ET of 7.39 mm day-1, closely aligned with the observed value of 6.72 mm day-1 recorded by the ET station. The findings confirm the METRIC model's high accuracy for spatial ET estimation and its associated micrometeorological variables. This study underscores the utility of the METRIC model, ET station and remote sensing in determining ET and energy flux which may be further utilised in the estimation of crop water requirement, energy fluxes and irrigation water management for sugarcane cultivation in the Tarai region.

Extending our understanding on the retrievals of surface energy fluxes and surface soil moisture from the “triangle” technique

The present study demonstrates the capability of an inversion modelling scheme so-called the “triangle” to retrieve spatiotemporal estimates of surface energy fluxes and soil surface moisture (SSM) at high resolution using ASTER satellite imagery synergistically with SimSphere land biosphere model. In addition, as a further objective of this study is to examine the use of the technique for retrieving the Evaporative (EF) and the Non-Evaporative (NEF) Fractions as representations of the daytime average fluxes. The applicability of the investigated technique, is demonstrated for sixteen calendar days of year 2011 using in-situ data acquired from nine CarboEurope sites representing a variety of climatic, topographic and environmental conditions. Results indicated a close agreement between all the inverted parameters and the corresponding in-situ data. SSM predicted maps showed a small bias of 0.08 vol vol−1, a scatter of 0.18 vol vol−1 and a RMSD of 0.19 vol vol−1. The predicted LE fluxes showed a relatively low overall agreement (RMSD = 65.10 Wm-2), whereas for H flux reported RMSD was 85.02 Wm-2. The results also confirmed the ability of the investigated technique to provide meaningful estimates of the NEF and EF. All in all, the present study findings were at least comparable, or of higher accuracy, to those reported in other similar verification studies of the “triangle” using both high resolution (airborne) and low resolution (satellite) data. To our knowledge, this study represents the first comprehensive evaluation of the performance of this particular methodological implementation at a European setting combining the SimSphere SVAT model and ASTER EO datasets.

Development of a multidecadal land reanalysis over High Mountain Asia

Anthropogenic and climatic changes affect the water and energy cycles in High Mountain Asia (HMA), home to over two billion people and the largest reservoirs of freshwater outside the polar zone. Despite their significant importance for water management, consistent and reliable estimates of water storage and fluxes over the region are lacking because of the high uncertainties associated with the estimates of atmospheric conditions and human management. Here, we relied on multivariate data assimilation (MVDA) to provide estimates of energy and water storage and fluxes that reflect the processes occurring in the region such as greening and irrigation-driven groundwater depletion. We developed and employed an ensemble precipitation estimate by blending different precipitation products thereby reducing the uncertainties and inconsistencies associated with precipitation in HMA. Then, we assimilated five variables that capture the changes in hydrology in response to climate change and anthropogenic activities. Overall, our results have shown that MVDA has allowed a better representation of the land surface processes including greening and irrigation-driven groundwater depletion in HMA.

A First Exploration of the Ts/VI “Analytical Triangle” Technique with UAV Imagery for Deriving Key Surface Energy Balance Parameters at Very High Spatial Resolution

Knowledge on the spatiotemporal patterns of surface energy balance parameters is crucial for understanding climate system processes. To this end, the assimilation of Earth Observation data with land biosphere models has shown promising results, but they are still hampered by several limitations related to the spatiotemporal resolution of EO sensors and cloud contamination. With the recent developments on Unmanned Aerial Vehicles (UAVs), there is a great opportunity to overcome these challenges and gain knowledge of surface energy balance parameters at unprecedented resolutions. The present study examines, for the first time, the ability of an inversion-modeling scheme, the so-called “analytical triangle” method, to retrieve estimates of surface energy fluxes and soil surface moisture (SSM) at high spatial resolution using UAV data. A further aim of our study was to examine the representativeness of the SSM estimates for the SM measurements taken at different depths. The selected experimental site is an agricultural site of citrus trees located near the city of Palermo on 30 July 2019. The results of comparisons showed that the sensible and latent heat fluxes from UAV were consistent with those measured from the ground, with absolute differences in comparison to ground measurements being 5.00 Wm−2 for the latent heat (LE) flux and 65.02 Wm−2 for H flux, whereas for the daytime fluxes H/Rn and LE/Rn were 0.161 and 0.012, respectively. When comparing analytical triangle SSM estimates with SM measurements made at different depths, it was found that there was a gradual increase in underestimation with increasing measurement depth. All in all, this study’s results provide a credible demonstration of the significant potential of the technique investigated herein as a cost-effective and rapid solution for estimating key parameters characterizing land surface processes. As those parameters are required by a wide range of disciplines and applications, utilization of the investigated technique in research and practical applications is expected to be seen in the future.

Statistical investigation of decayless oscillations in small-scale coronal loops observed by Solar Orbiter/EUI

Decayless kink oscillations are omnipresent in the solar atmosphere, and they are a viable candidate for coronal heating. Although there have been extensive studies of decayless oscillations in coronal loops with lengths of a few hundred megameters, the properties of these oscillations in small-scale (∼10 mm) loops are yet to be explored. In this study, we present the properties of decayless oscillations in small loops embedded in the quiet corona and coronal holes. We use high-resolution observations from the Extreme Ultraviolet Imager on board Solar Orbiter with pixel scales of 210 km and a cadence of 5 s or better. We analysed 42 oscillations in coronal loops with loop lengths varying between 3 to 23 mm. The average displacement amplitude is found to be 134 km. The oscillations period has a range of 28 to 272 s, and the velocity amplitudes range from 2.1 to 16.4 km s−1. The variation in the loop length with the period does not indicate a significant correlation. The wave mode of these waves is uncertain, and standing waves are one possibility. Our results for the coronal seismology and energy flux estimates were obtained considering standing modes. The observed kink speeds are lower than those observed in active region coronal loops. We obtain an average magnetic field value of 2.1 G. We estimated the energy flux with a broad range of 0.6–313 W m−2. Moreover, we note that short-period decayless oscillations are not prevalent in the quiet Sun and coronal holes. Our study suggests that decayless oscillations in small-scale coronal loops are unlikely to provide enough energy to heat the quiet Sun and accelerate solar wind in coronal holes.

Can the Solar p-modes Contribute to the High-frequency Transverse Oscillations of Spicules?

Lateral motions of spicules serve as vital indicators of transverse waves in the solar atmosphere, and their study is crucial for understanding the wave-heating process of the corona. Recent observations have focused on high-frequency transverse waves (periods < 100 s), which have the potential to transport sufficient energy for coronal heating. These high-frequency spicule oscillations are distinct from granular motions, which have much longer timescales of 5–10 minutes. Instead, it is proposed that they are generated through the mode conversion from high-frequency longitudinal waves that arise from a shock-steepening process. Therefore, these oscillations may not solely be produced by the horizontal buffeting motions of granulation but also by the leakage of p-mode oscillations. To investigate the contribution of p-modes, our study employs a two-dimensional magneto-convection simulation spanning from the upper convection zone to the corona. During the course of the simulation, we introduce a p-mode-like driver at the bottom boundary. We reveal a notable increase in the mean velocity amplitude of the transverse oscillations in spicules, ranging from 10%–30%, and attribute this to the energy transfer from longitudinal to transverse waves. This effect results in an enhancement of the estimated energy flux by 30%–80%.

Estimating the magnitude and sensitivity of energy fluxes for stickleback hosts and Schistocephalus solidus parasites using the metabolic theory of ecology.

Parasites are ubiquitous, yet their effects on hosts are difficult to quantify and generalize across ecosystems. One promising metric of parasitic impact uses the metabolic theory of ecology (MTE) to calculate energy flux, an estimate of energy lost to parasites. We investigated the feasibility of using metabolic scaling rules to compare the energetic burden of parasitism among individuals. Specifically, we found substantial sensitivity of energy flux estimates to input parameters used in the MTE equation when using available data from a model host-parasite system (Gasterosteus aculeatus and Schistocephalus solidus). Using literature values, size data from parasitized wild fish, and a respirometry experiment, we estimate that a single S. solidus tapeworm may extract up to 32% of its stickleback host's baseline metabolic energy requirement, and that parasites in multiple infections may collectively extract up to 46%. The amount of energy siphoned from stickleback to tapeworms is large but did not instigate an increase in respiration rate in the current study. This emphasizes the importance of future work focusing on how parasites influence ecosystem energetics. The approach of using the MTE to calculate energy flux provides great promise as a quantitative foundation for such estimates and provides a more concrete metric of parasite impact on hosts than parasite abundance alone.

The centroid speed as a characteristic of the group speed of solar coronal fast magnetoacoustic wave trains

ABSTRACT The highly filamented nature of the coronal plasma significantly influences dynamic processes in the corona such as magnetohydrodynamic waves and oscillations. Fast magnetoacoustic waves, guided by coronal plasma non-uniformities, exhibit strong geometric dispersion, forming quasi-periodic fast-propagating (QFP) wave trains. QFP wave trains are observed in extreme-ultraviolet imaging data and indirectly in microwaves and low-frequency radio, aiding in understanding the magnetic connectivity, energy, and mass transport in the corona. However, measuring the field-aligned group speed of QFP wave trains, as a key parameter for seismological analysis, is challenging due to strong dispersion and associated rapid evolution of the wave train envelope. We demonstrate that the group speed of QFP wave trains formed in plane low-β coronal plasma non-uniformities can be assessed through the propagation of the wave train’s effective centre of mass, referred to as the wave train’s centroid speed. This centroid speed, as a potential observable, is shown empirically to correspond to the group speed of the most energetic Fourier harmonic in the wave train. The centroid speed is found to be almost insensitive to the waveguide density contrast with the ambient corona, and to vary with the steepness of the transverse density profile. The discrepancy between the centroid speed as the group speed measure and the phase speed at the corresponding wavelength is shown to reach 70 per cent, which is crucial for the energy flux estimation and interpretation of observations.

Available energy of trapped electrons in Miller tokamak equilibria

Available energy (Æ), which quantifies the maximum amount of thermal energy that may be liberated and converted into instabilities and turbulence, has shown to be a useful metric for predicting saturated energy fluxes in trapped-electron-mode-driven turbulence. Here, we calculate and investigate the Æ in the analytical tokamak equilibria introduced by Milleret al.(Phys. Plasmas, vol. 5, issue, 4, 1998, pp. 973–978). The Æ of trapped electrons reproduces various trends also observed in experiments; negative shear, increasing Shafranov shift, vertical elongation and negative triangularity can all be stabilising, as indicated by a reduction in Æ, although it is strongly dependent on the chosen equilibrium. Comparing Æ with saturated energy flux estimates from the TGLF (trapped gyro-Landau fluid) model, we find fairly good correspondence, showcasing that Æ can be useful to predict trends. We go on to investigate Æ and find that negative triangularity is especially beneficial in vertically elongated configurations with positive shear or low gradients. Furthermore, we extract a gradient-threshold-like quantity from Æ and find that it behaves similarly to gyrokinetic gradient thresholds: it tends to increase linearly with magnetic shear, and negative triangularity leads to an especially high threshold. We next optimise the device geometry for minimal Æ and find that the optimum is strongly dependent on equilibrium parameters, for example, magnetic shear or pressure gradient. Investigating the competing effects of increasing the density gradient, the pressure gradient, and decreasing the shear, we find regimes that have steep gradients yet low Æ, and that such a regime is inaccessible in negative-triangularity tokamaks.

Eddy covariance fluxes over managed ecosystems extrapolated to field scales at fine spatial resolutions

To enable an evidence-based management of ecosystems to adapt to the climate crisis, we require fine spatiotemporal resolution estimates of carbon, water, and energy fluxes at the field scale. To overcome the limitations resulting from the coarse spatial resolution of existing flux products, e.g. 500 m (Running et al., 2015), and the challenges in matching eddy covariance (EC) footprints with land use field scales, we for the first time investigate the influence of satellite resolution on flux estimation, which is to support the fine-scale extrapolation of EC fluxes from the tower footprint to the field scale. We validate the extrapolation at 206 FLUXNET2015 tower sites to pave the way for estimating field-scale fluxes extrapolated from three towers in a managed European grazing pasture on a fine-scale, 30 m spatial resolution. The findings suggest that (a) tower-level flux estimates from 30 m satellites were in agreement with fluxes estimated from moderate-resolution satellites, which are extensively employed in literature (R2 difference ≪ 0.1); (b) flux estimates were in reasonable agreement with EC measurements (R2: 0.7 and annual bias < 2 Mg ha−1 yr−1 for carbon fluxes); (c) Sentinel-2 was advantageous in capturing land-use variability over other satellites in European pastures; (d) the machine-learning extrapolation algorithm was resistant to livestock grazing.

Plasma–liquid interactions: an experiment and simulation study on plasma dynamic behaviors near the gas–liquid interfacial layer

Plasma–liquid interaction processes are essential to various plasma applications such as sewage disposal, biomedicine, and synthesis of nanomaterials. However, the near gas–liquid interfacial behavior of plasma property remains inadequately understood, hindering the controllability of the application process. This study combines experimental diagnostics and simulations to investigate the production and transport of plasma-generated reactive species near (∼35 μm) the gas–liquid interfacial layer. The experimental results are used to benchmark densities obtained from a zero-dimensional plasma chemical kinetics simulation, which reveals the time evolutions of plasma-generated active species. A large number of neutral particles (like OH, H2O2) and water cluster ions (like H9O4 +) were produced as a result of the evaporation effect of the cathode solution surface. The estimation of energy flux from the gaseous plasma to liquid surface showed that the hydration process of positive ions plays the key role in the resulted water evaporation at the gas–liquid interfacial layer.

HST-1 as a window into the energetics of the jet spine of M 87

We present a new interpretation of the optical knot, HST-1, in the jet of M 87. High-sensitivity 22 GHz Very Large Array images have located HST-1 to within 6 mas of the jet axis immediately upstream. Based on 1.7 GHz Very Long Baseline Array images of a bright flare in 2005, we see that preponderance of emission in the early stages originates from an elongated region that is tilted 12.5° from the jet axis. The superluminal motion, shape, location, and the large jet-aligned optical/UV polarization suggest an identification with the putative relativistic spine of the jet. As such, energy flux estimates for HST-1, ∼870 mas from the nucleus, published in 2006, indicate that the central engine injected, Qspine ≈ 2.5 × 1041 ergs s−1, into the base of the spine about 200 yr earlier. Furthermore, previous studies have revealed a tubular protonic jet on sub-mas scales that envelopes a low luminosity core, presumably the faint spine base. It was estimated that the central engine injected, Qtubular jet ≈ 6.1 × 1041 ergs s−1, about 1.5 yr earlier. If one component of the jet is inherently more powerful, a firm constraint on total jet power in the recent past would then exist. If the emitted jet is inherently dominated by the spine (tubular jet), then the total bilaterally symmetric jet power emitted from the central engine was &lt; 4Qspine ≈ 1.0 × 1042 ergs s−1 (&lt; 4Qtubular jet ≈ 2.4 × 1042 ergs s−1) ∼200 (∼1.5) yr earlier. Assuming a nearly constant central engine injected jet power for ∼200 yr indicates a total jet power of ≲2 × 1042 ergs s−1 in epochs of modern observation or ≲3.5% jet production efficiency for an accretion rate of 0.001 M⊙ yr−1. Seemingly, the focus of Event Horizon Telescope Collaboration (EHTC) numerical models should be biased toward jet powers of ≲2 × 1042 ergs s−1, as opposed to larger estimates from ejections many centuries or millennia earlier.

Surface Energy Dynamics and Canopy Structural Properties in Intact and Disturbed Forests in the Southern Amazon

AbstractThe Brazilian Amazon has been a focus of land development with large swaths of forests converted to agriculture. Forest degradation by selective logging and fires has accompanied the agricultural frontier and has resulted in significant impacts on Amazonian ecosystems. Changes in forest structure resulting from forest disturbances have large impacts on the surface energy balance, including on land surface temperature (LST) and evapotranspiration (ET). This study's objective is to assess the effects of forest disturbances on water fluxes and forest structure in a transitional forest site in the Southern Amazon. We used ET and LST products from MODIS and Landsat 8 and GEDI‐derived forest structure data to address our research questions. We found that disturbances induced seasonal water stress, more pronounced in croplands/pastures than in forests (differences up to 20% in the dry season), and more pronounced in second‐growth and recently burned areas than in logged and intact forests (differences up to 12% in the dry season). Moreover, ET and LST were negatively related, with more consistent relationships across disturbance classes in the dry season (R2: 0.41–0.87) than in the wet season (R2: 0.18–0.49). Forest and cropland or pasture classes showed contrasting relationships in the dry season. Finally, we found that forest structure exhibited stronger relationships with ET and LST in the most disturbed forests (R2: 0.01–0.43) than in the least disturbed forests (R2 &lt; 0.05). Our findings help to elucidate degraded forests functioning under a changing climate and to improve estimates of water and energy fluxes in Amazonian degraded forests.

Estimates of energy fluxes associated with sprites in the mesosphere

We present calibrated estimates of photon flux, lightning peak Poynting flux and Joule heating associated with the brightest region of sprites observed in the mesosphere over South Africa. The sprites' photon fluxes were estimated using 28 sprites events (observed during the 2019 sprites campaign) calibrated by stars in the sprite's image background. The lightning driven background electric field associated with the brightest region of sprites were found to vary from 0.1 to 6.7 Ek (local air breakdown field). The lightning return stroke at lower frequencies (4 Hz - 2 kHz) has more influence in carrot sprites than in column sprites formation processes. The lightning peak Poynting flux and Joule heating were estimated from calibrated electromagnetic field measurements made in parallel with eight sprites events (observed during the 2020 sprites campaign). The photon flux, peak Poynting flux, and peak Joule heating associated with the brightest region of sprites were found to be 1.1 × 10−7 W/m2, 12.7 W/m2, and 4.7 × 10−3 W/m2 on average, respectively. The altitude/distance-normalised lightning peak Poynting flux decreases with increasing atmospheric altitude. The photon flux from column sprites decreased with increased altitude of the brightest region. Column sprites have a shorter time delay (<30 ms) from their parent lightning strokes than carrot sprites (up to 145 ms).

Damping of Inertial Motions through the Radiation of Near-Inertial Waves in a Dipole Vortex in the Iceland Basin

Abstract Along with boundary layer turbulence, downward radiation of near-inertial waves (NIWs) damps inertial oscillations (IOs) in the surface ocean; however, the latter can also energize abyssal mixing. Here we present observations made from a dipole vortex in the Iceland Basin where, after the period of direct wind forcing, IOs lost over half their kinetic energy (KE) in two inertial periods to radiation of NIWs with minimal turbulent dissipation of KE. The dipole’s vorticity gradient led to a rapid reduction in the NIW’s lateral wavelength via ζ refraction that was accompanied by isopycnal undulations below the surface mixed layer. Pressure anomalies associated with the undulations were correlated with the NIW’s velocity yielding an energy flux of 310 mW m−2 pointed antiparallel to the vorticity gradient and a downward flux of 1 mW m−2 capable of driving the observed drop in KE. The minimal role of turbulence in the energetics after the IOs had been generated by the winds was confirmed using a large-eddy simulation driven by the observed winds. Significance Statement We report direct observational estimates of the vector wave energy flux of a near-inertial wave. The energy flux points from high to low vorticity in the horizontal, consistent with the theory of ζ refraction. The downward energy flux dominates the observed damping of inertial motions over turbulent dissipation and mixing.

Estimating the energy flux of transverse waves associated with Kelvin-Helmholtz instability in solar coronal loops

Context. The energy flux of kink waves in coronal loops has been estimated in previous studies. Recent numerical simulations have revealed that kink oscillations can induce a Kelvin-Helmholtz Instability (KHI) in magnetic flux tubes. This non-linear process breaks the assumptions that have typically been included in previous eigenmode analyses. Therefore, the current analytical expressions of energy flux need to be re-examined. Aims. In the present work, we aim to compare our numerical energy flux with previous analytical formulae and establish modifications to the estimation of the energy flux of kink waves in coronal loops. Methods. Working within the framework of ideal magnetohydrodynamics (MHD), we conducted three-dimensional (3D) simulations of kink oscillations in coronal cylinders. Forward models were also employed to translate our numerical results into observables using the FoMo code. Results. We find that the previous estimation of the energy flux of kink waves is reasonable up to the point before the KHI is fully developed. However, as small vortices develop, the energy flux derived from the analytical formula becomes smaller than the total Poynting flux calculated from our numerical results. Furthermore, when degrading the original numerical resolution to match a realistic instrumental resolution, for instance, the Extreme Ultraviolet Imager (EUI) on board the Solar Orbiter (SO), the energy flux becomes much smaller than the numerical value. Conclusions. The energy flux calculated from the analytical formula should be modified by multiplying it by a factor of about 2. When it comes to the energy flux estimation based on SO/EUI observations, this factor should be between about 3 and 4.

Generation of nonlinear internal waves on the northern continental shelf south of Hainan Island

Nonlinear internal waves (NLIWs) are prevalent on the northern continental shelf south of Hainan Island in the South China Sea. However, our understanding of these NLIWs is still in a preliminary state. In the study, we take a step toward fully elucidating the generation and propagation process of the NLIWs on the northern continental shelf south of Hainan Island through a synergistic analysis of satellite observations, in situ measurements, and numerical simulations. Both mooring and satellite observations suggest that the Xisha Islands remotely generate the NLIWs on the northern continental shelf south of Hainan Island; moreover, more than one source exists in the Xisha Islands. Based on the realistic topography, stratification, and tidal forcing, two-dimensional numerical simulations using the MITgcm reveal that the NLIWs observed on the continental shelf can be generated from the Xisha Islands through the internal tidal beam regime. Furthermore, the internal tide energy flux estimation shows that the locally generated internal tides that arise from the continental shelf break mostly carry their energy toward the deep water and have little effect on the generation of NLIWs on the shelf.