Terms Of Energy Flux Research Articles

Linearised Fokker–Planck collision model for gyrokinetic simulations

Abstract We introduce a gyrokinetic, linearised Fokker–Planck collision model that satisfies conservation laws and is accurate at arbitrary collisionalities. The differential test-particle component of the operator is exact; the integral field-particle component is approximated using a spherical harmonic and a modified Laguerre polynomial expansion developed by Hirshman and Sigmar (1976 Phys. Fluids 19 1532). The numerical methods of the implementation in the δf-gyrokinetic code stella (Barnes et al 2019 J. Comput. Phys. 391 365–80) are discussed, and conservation properties of the operator are demonstrated. The collision model is then benchmarked against the collision model of the gyrokinetic solver GS2 in the limiting cases of a reduced test-particle collision operator and energy- and momentum-conserving operator. The accuracy of the full collision model is investigated by solving the parallel Spitzer-Härm problem for the transport coefficients. It is shown that retaining collisional energy flux and higher-order terms in the field-particle operator reduces errors in the transport coefficients from 10%–25% for a simple momentum- and energy-conserving model to under 1%.

Comparing local energy cascade rates in isotropic turbulence using structure-function and filtering formulations

Two common definitions of the spatially local rate of kinetic energy cascade at some scale $\ell$ in turbulent flows are (i) the cubic velocity difference term appearing in the ‘scale-integrated local Kolmogorov–Hill’ equation (structure-function approach), and (ii) the subfilter-scale energy flux term in the transport equation for subgrid-scale kinetic energy (filtering approach). We perform a comparative study of both quantities based on direct numerical simulation data of isotropic turbulence at Taylor-scale Reynolds number 1250. While in the past observations of negative subfilter-scale energy flux (backscatter) have led to debates regarding interpretation and relevance of such observations, we argue that the interpretation of the local structure-function-based cascade rate definition is unambiguous since it arises from a divergence term in scale space. Conditional averaging is used to explore the relationship between the local cascade rate and the local filtered viscous dissipation rate as well as filtered velocity gradient tensor properties such as its invariants. We find statistically robust evidence of inverse cascade when both the large-scale rotation rate is strong and the large-scale strain rate is weak. Even stronger net inverse cascading is observed in the ‘vortex compression’ $R>0$ , $Q>0$ quadrant, where $R$ and $Q$ are velocity gradient invariants. Qualitatively similar but quantitatively much weaker trends are observed for the conditionally averaged subfilter-scale energy flux. Flow visualizations show consistent trends, namely that spatially, the inverse cascade events appear to be located within large-scale vortices, specifically in subregions when $R$ is large.

Wigner Equations for Phonons Transport and Quantum Heat Flux

Starting from the quantum Liouville equation for the density operator and applying the Weyl quantization, Wigner equations for the acoustic, optical and Z phonons are deduced. The equations are valid for any solid, including 2D crystals like graphene. With the use of Moyal’s calculus and its properties, the pseudo-differential operators are expanded up to the second order in ħ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbar $$\\end{document}. An energy transport model is obtained by using the moment method with closure relations based on a quantum version of the Maximum Entropy Principle by employing a relaxation time approximation for the production terms of energy and energy flux. An explicit form of the thermal conductivity with quantum correction up to ħ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbar ^2$$\\end{document} order is obtained under a long-time scaling for the most relevant phonon branches.

Analysis of Combustion Noise Sources Using Doak's Momentum Potential Theory

Noise emissions of modern lean combustors are related to different sources. Direct combustion noise is generated by heat release fluctuations, while indirect noise sources include the acceleration of entropy and vorticity inhomogeneities through the nozzle-guide-vane or at the combustor exit. The latter noise source is characterized by the coupling of fluctuations convected in non-uniform mean flow, which can e.g. cause vortical or entropic fluctuations to be partly transferred into acoustics. Due to the complexity of the sources, a clear and quantitative separation of the different phenomena in terms of primitive variables presents a significant challenge. This study therefore proposes an alternative framework for the description of combustion noise based on Doak's Momentum Potential Theory (MPT). The MPT defines a Generalized Acoustic Field (GAF) and describes the sound production in terms of mean energy fluxes carried by the respective acoustic, thermal and turbulent fluctuating momentum components. To confirm the ability to identify the different combustion noise sources, the method was applied to Large-Eddy Simulation data of a non-reacting swirl-combustor simulator. Finally, the coherent character and spectral behavior of the GAF were investigated using a Spectral Proper Orthogonal Decomposition (SPOD) analysis and correlated to the source distributions.

High-resolution, non-hydrostatic simulation of internal tides and solitary waves in the southern East China Sea

The slope area northeast of Taiwan Island in the southern East China Sea (ECS) is well known as a hotspot for both internal tides and internal solitary waves (ISWs) despite uncertainties regarding their specific source and generation mechanism. This study investigates the generation and evolution processes of internal tides and ISWs northeast of Taiwan Island in the southern ECS, based on a super-high-resolution and non-hydrostatic numerical simulation. ISWs create a complex spatial pattern in both satellite images and our simulation, with wave propagation in multiple directions, including onshore and offshore. These ISWs, with the largest amplitudes reaching ∼50 m, are mainly generated by two mechanisms: local tide-topography interactions and disintegration of internal tides remotely generated over I-Lan Ridge. Locally generated ISWs propagate in various directions owing to the complex topography, whereas ISWs generated by the disintegration of remote internal tides are more consistent in their pathways. Strong barotropic to baroclinic energy conversions occur over both Mien-Hua Canyon and North Mien-Hua Canyon. For the baroclinic tidal energy fluxes, the advection flux is comparable to the pressure-work term in shallow water, while the pressure-work flux dominates in deep water. The nonlinear energy flux terms in shallow water are more important for the supertidal than the tidal signals. The semidiurnal energy flux features a clockwise pattern over the double-canyon region, indicating the formation of partial standing waves.

Comparison of the shape of focal spots in terms of intensity and energy flux for a high-aperture zone plate and a spiral zone plate

Using a finite-difference time-domain method, it has been shown that focal spots generated when tightly focusing a linearly polarized Gaussian beam by a Fresnel zone plate (FZP) and when focusing a Gaussian beam with an embedded optical vortex by a spiral zone plate (SZP) have different patterns of the intensity and energy flux. The most significant differences are observed when the value of the topological charge (TC) is equal to three. The energy flux has an annular distribution when the Gaussian beam is focused by the FZP, while the SZP produces a field whose patterns of intensity and energy flux have three local maxima. The number of local maxima corresponds to the order of the SZP. At a certain distance from the focus, the petal structure of the intensity (and energy flux) changes to a ring distribution.

Investigation of water substitution at RuII complexes by conceptual density function theory approach.

In this paper, we investigated water exchange reactions and substitution of aqua RuII complexes of general formula [Ru(terpy)(N^N)(H2 O)]2+ (where N^N=ethylenediamine (en), 1,2-(aminomethyl)pyridine (ampy) and 2,2'-bipyridine (bipy)) by ammonia and thioformaldehyde. These reactions were studied in detail by applying conceptual density functional theory. This approach enabled us to gain further insight into the underlying reaction mechanism at the microscopic level (involving only direct participants of the reaction, without the influence of the solvent) and to put the concept of reaction mechanism on a quantitative basis. The course of the chemical reaction along the reaction coordinate ξ, is rationalized in terms of reaction energy, force, dipole moment, and reaction electronic flux (REF). The results yield and characterize the significant influence of an intermolecular hydrogen bond formed between the entering and the spectator ligand to the overall energy barrier of the reactions.

Stormtime Energetics: Energy Transport Across the Magnetopause in a Global MHD Simulation

Coupling between the solar wind and magnetosphere can be expressed in terms of energy transfer through the separating boundary known as the magnetopause. Geospace simulation is performed using the Space Weather Modeling Framework (SWMF) of a multi-ICME impact event on February 18–20, 2014 in order to study the energy transfer through the magnetopause during storm conditions. The magnetopause boundary is identified using a modified plasma β and fully closed field line criteria to a downstream distance of −20Re. Observations from Geotail, Themis, and Cluster are used as well as the Shue 1998 model to verify the simulation field data results and magnetopause boundary location. Once the boundary is identified, energy transfer is calculated in terms of total energy flux K, Poynting flux S, and hydrodynamic flux H. Surface motion effects are considered and the regional distribution of energy transfer on the magnetopause surface is explored in terms of dayside X>0, flank X<0, and tail cross section X=Xmin regions. It is found that total integrated energy flux over the boundary is nearly balanced between injection and escape, and flank contributions dominate the Poynting flux injection. Poynting flux dominates net energy input, while hydrodynamic flux dominates energy output. Surface fluctuations contribute significantly to net energy transfer and comparison with the Shue model reveals varying levels of cylindrical asymmetry in the magnetopause flank throughout the event. Finally existing energy coupling proxies such as the Akasofu ϵ parameter and Newell coupling function are compared with the energy transfer results.

A minimal subwavelength focal spot for the energy flux

It is shown theoretically and numerically that circularly and linearly polarized incident beams produce at the tight focus identical circularly symmetric distributions of an on-axis energy flux. It is also shown that the on-axis energy fluxes from radially and azimuthally polarized optical vortices with unit topological charge are equal to each other. An optical vortex with azimuthal polarization is found to generate the minimum focal spot measured for the intensity (all other parameters being equal). Slightly larger (by a fraction of a percent) is the spot size calculated for the energy flux for the circularly and linearly polarized light. The spot size in terms of intensity is of importance in light-matter interaction, whereas the spot size in terms of energy flux affects the resolution in optical microscopy.

Splash detachment of sand particles under varying contact stress field of wind‐driven raindrop impact

AbstractThe effects of wind‐driven rain (WDR) on sand detachment were studied under various raindrop obliquities. Results suggested a significant reduction in compressive stress on sand surfaces for a two‐dimensional experimental set‐up in a wind tunnel. During experiments, sand particles in splash cups were exposed to both wind‐free rain (WFR) and WDR driven by horizontal winds of 6.4, 8.9 and 12.8 m s−1and rainfall intensities of 50, 60, 75 and 90‐mm h−1to assess the sand detachment rate (D, in g m−2 s−1). The effects of sand moisture state (dry and wet) on the detachment of different‐sized particles (0.20–0.50 and 0.50–2.00 mm, respectively) were also tested. Factorial analysis of variance showed that shear and compressive stress components evaluated by horizontal and vertical kinetic energy flux terms (KExand KEy, respectively, in J m−2 s−1) along with their vector sum (KEr, in J m−2 s−1) explained the variation inD. Neither sand size nor sand moisture was statistically significant alone although binary interactions of KEr, KExand KEywith the sand size and three‐way interaction of KEx, sand size and moisture were statistically significant. These results can be explained by size‐dependent variation in sand compressibility and surface friction related to the total stress field developed by a given partition of shear and compressive stresses of wind‐driven oblique raindrops (KEx/KEy). Further analysis of the variation of the unit sand detachment rate (Du = D/KEr = g J−1) with rain inclination (α, in degrees) better revealed the effect of WDR obliquity onDuthat further changed with sand size class and moisture state. Finally, the difference in the resulting stress field differentiable by the oblique raindrop trajectories of the experiment over sand surface significantly affected the non‐cohesive particle detachment rates, to some extent interacted with size‐dependent compressibility and interface shear strength of sand grains.

Understanding the summertime warming in canyon and non-canyon surfaces

Urban landscapes, made of unique buildings, pavements, and vegetation, create complex influences on the atmosphere. These influences induce increased nighttime warming and daytime cooling, especially in arid regions. This study compared three types of surfaces, including rooftop, turfgrass, and canyons, in terms of surface temperature and surface energy fluxes. A 68 sq.km parcel in Phoenix, AZ was considered for comparison. The study found that the canyons' land surface temperatures (LST) were 5 °C lower than the rooftop surfaces. The turfgrass surfaces were 4 °C cooler than the canyon surfaces. Moreover, north and south (N-S) oriented canyons were 2 °C cooler than east and west (E-W) oriented canyons. No significant changes were observed in net radiation for rooftop, turfgrass, or canyon surfaces. However, conductive fluxes, warranting nighttime warming, showed higher absorption of 45 W/m2 on the rooftop surfaces, than in the canyons. The turfgrass showed nighttime cooling, as the heat absorption was 210 W/m2 lower than the rooftop surfaces and 165 W/m2 lower than the canyons. Additionally, a 50 W/m2 difference of heat absorption was observed between N-S oriented canyons and E-W oriented canyons. The study concludes that canyons are major causes of daytime cooling and nighttime warming.

Legacy Effects Following Fire on Surface Energy, Water and Carbon Fluxes in Mature Amazonian Forests

AbstractThe ongoing deforestation process in Amazonia has led to intensified forest fires in the region, particularly in Brazil, after more than a decade of effective forest conservation policy. This study aims to investigate the recovery of two mature sub‐montane ombrophile Amazonian forests affected by fire in terms of energy, water and carbon fluxes utilizing remote sensing (MODIS) and climate reanalysis data (GLDAS). These two forest plots, mainly composed of Manilkara spp. (Maçaranduba), Protium spp. (Breu) (∼30 m), Bertholletia excelsa (Castanheira) and Dinizia excelsa Ducke (Angelim‐Pedra) (∼50 m), occupy areas of 100.5 and 122.1 km2 and were subject to fire on the same day, on September 12, 2010. The fire significantly increased land surface temperature (0.8°C) and air temperature (1.2°C) in the forests over a 3 years interval. However, the forests showed an ability to recover their original states in terms of coupling between the carbon and water cycles comparing the 3‐year periods before and after the fires. Results from a wavelet analysis showed an intensification in annual and seasonal fluctuations, and in some cases (e.g., daily net radiation and evapotrasnspiration) sub‐annual fluctuation. We interpreted these changes to be consistent with overall intensification of the coupling of energy balance components and drivers imposed by climate and solar cycle seasonality, as well as faster time scale changes, consistent with a shift toward greater forest openness and consequent reduction in the interception of incoming solar radiation by the canopy.

Improving the representation of cropland sites in the Community Land Model (CLM) version 5.0

Abstract. The incorporation of a comprehensive crop module in land surface models offers the possibility to study the effect of agricultural land use and land management changes on the terrestrial water, energy, and biogeochemical cycles. It may help to improve the simulation of biogeophysical and biogeochemical processes on regional and global scales in the framework of climate and land use change. In this study, the performance of the crop module of the Community Land Model version 5 (CLM5) was evaluated at point scale with site-specific field data focusing on the simulation of seasonal and inter-annual variations in crop growth, planting and harvesting cycles, and crop yields, as well as water, energy, and carbon fluxes. In order to better represent agricultural sites, the model was modified by (1) implementing the winter wheat subroutines following Lu et al. (2017) in CLM5; (2) implementing plant-specific parameters for sugar beet, potatoes, and winter wheat, thereby adding the two crop functional types (CFTs) for sugar beet and potatoes to the list of actively managed crops in CLM5; and (3) introducing a cover-cropping subroutine that allows multiple crop types on the same column within 1 year. The latter modification allows the simulation of cropping during winter months before usual cash crop planting begins in spring, which is an agricultural management technique with a long history that is regaining popularity as it reduces erosion and improves soil health and carbon storage and is commonly used in the regions evaluated in this study. We compared simulation results with field data and found that both the new crop-specific parameterization and the winter wheat subroutines led to a significant simulation improvement in terms of energy fluxes (root-mean-square error, RMSE, reduction for latent and sensible heat by up to 57 % and 59 %, respectively), leaf area index (LAI), net ecosystem exchange, and crop yield (up to 87 % improvement in winter wheat yield prediction) compared with default model results. The cover-cropping subroutine yielded a substantial improvement in representation of field conditions after harvest of the main cash crop (winter season) in terms of LAI magnitudes, seasonal cycle of LAI, and latent heat flux (reduction of wintertime RMSE for latent heat flux by 42 %). Our modifications significantly improved model simulations and should therefore be applied in future studies with CLM5 to improve regional yield predictions and to better understand large-scale impacts of agricultural management on carbon, water, and energy fluxes.

Calculating the temperature of strongly radiative shocks

A new method of calculating the temperature of strongly radiative shocks (Mihalas number of order unity or lower) is proposed. By including ionization, radiative energy, and radiative flux terms in the Rankine–Hugoniot jump conditions across the shock front, a new, self-consistent method of calculating the temperature of radiative shocks is developed. The method is compared to those used to calculate temperature in previous studies using similar methods, including those which partially included radiative and/or ionization effects. The method is also compared to experimental data, taken from the literature, as well as the SESAME equation of state tables and radiative hydrodynamics simulations. The results show the importance of including all radiative terms for the case of strongly radiative shocks. This result has important implications for the design and interpretation of future laboratory experiments where even faster radiative shocks may be generated. Previously unseen phenomena could be accessible when the radiative energy plays a significant role in the system.

Validation of Spring Wheat Responses to Elevated CO2, Irrigation, and Nitrogen Fertilization in the Community Land Model 4.5

AbstractThe Community Land Model (CLM) started to incorporate crop growth models since version 4.0 in 2012. Since then, the crop model in CLM has been evolved remarkably, but some of the key crop growth responses to environmental conditions (such as the elevated CO2) have not been well validated. Here, we set up single point simulations with CLM (version 4.5) and validated spring wheat growth response against the Maricopa spring wheat Free Air CO2 Enrichment (FACE) experiment that consisted of multiyear paired treatments to understand the growth response to elevated CO2, irrigation, nitrogen fertilization, and their interactions. Overall, CLM showed too positive growth response to elevated CO2 but insufficient growth response to irrigation. The overestimated growth response to elevated CO2 may be due to ignoring factors (e.g., leaf traits) that will limit crop growth under elevated CO2. The insufficient response to irrigation is due to CLM simulating lower latent heat flux during April and May, which resulted in higher soil moisture. In response to nitrogen fertilization, CLM underestimated leaf area index increase but overestimated grain yield increase. In terms of energy fluxes, CLM showed decreased latent heat flux in response to elevated CO2 but increased latent heat flux in response to nitrogen fertilization, but the response magnitude was much smaller than the observations. Based on these validations, we summarized further model developments for CLM to better simulate crop growth process.

What is extinction? Operational definition of the extinguished power for plane waves and collimated beams

We discuss an operational scheme for measuring the power extinguished by a single particle in terms of physical energy fluxes. Illumination by an infinite plane wave and a collimated Gaussian beam is considered. For the case of a collimated beam, consideration of extinguished power presents an apparent paradox, which is resolved in this paper. It is then shown that the extinguished power is measurable as a flow of energy for a narrow, collimated incident beam and a small scatterer. In this case, the extinguished power is simply removed from the transmitted beam. If we relax the above assumptions, definition of the extinguished power in terms of measurable energy fluxes is still possible but becomes more nuanced.

Vertex Approximate Gradient discretization preserving positivity for two-phase Darcy flows in heterogeneous porous media

In this article, a new nodal discretization is proposed for two-phase Darcy flows in heterogeneous porous media. The scheme combines the Vertex Approximate Gradient (VAG) scheme for the approximation of the gradient fluxes with an Hybrid Upwind (HU) approximation of the mobility terms in the saturation equation. The discretization in space incorporates naturally nodal interface degrees of freedom (d.o.f.) allowing to capture the transmission conditions at the interface between different rock types for general capillary pressure curves. It is shown to guarantee the physical bounds for the saturation unknowns as well as a nonnegative lower bound on the capillary energy flux term. Numerical experiments on several test cases exhibit that the scheme is more robust compared with previous approaches allowing the simulation of 3D large Discrete Fracture Matrix (DFM) models.

Impact of land surface physics in WRF on the simulation of sea breeze circulation over southeast coast of India

In this work, the impact of land surface physics in simulating the sea and land breeze circulation along the south east coast of India near Kalpakkam is studied using the Weather Research and Forecasting (WRF) model for emergency response application. Simulations were conducted with three different land surface models (LSMs)—5-Layer soil thermal diffusion scheme (5-Layer), Noah land surface model (Noah) and Noah Multi-Physics land surface model (Noah-MP) for different days in summer and southwest monsoon. Observations from meteorological towers, automated weather stations, sonic anemometers and GPS Radiosonde profiles were used for comparison. Results indicate that the Noah-MP followed by Noah schemes produce more realistic simulations of the sea breeze circulation in terms of intensity, onset time, duration, horizontal and vertical extents in most of the studied cases compared to the 5-Layer scheme. Results indicate that the 5-Layer model grossly overestimated air temperature, heat flux and boundary layer height relative to Noah and Noah-MP schemes. The Noah-MP scheme better represented the land-surface feedback in terms of soil temperature, skin temperature and surface energy fluxes leading to more realistic simulations of sea breeze and boundary layer characteristics.

Benthic-pelagic coupling in lake energetic food webs

Understanding how energy and matter flow among habitats is a central issue in ecology. In lake ecosystems, benthic-pelagic coupling (B-P coupling) was mainly studied based on the diets of top consumers at a population level or through food chains. However, how B-P coupling operates at the ecosystem level is largely unknown.In the present study, we revealed B-P coupling within an energetic food web framework, combining stable isotope analyses and mass balanced model. We constructed the energetic food webs of two large shallow lakes of different trophic status based on field survey data. We also defined benthic and pelagic components based on the proportion of consumer energy uptake from phytoplankton (benthic: <50%; pelagic:>50%; benthivore: <20%; planktivore:>80%; coupler: 20–80%) and quantified the energy flux through B-P coupling in the two lake food webs.The total consumption was estimated to be 699 t/km2/y in Lake Erhai (mesoeutrophic lake) and 2094 t/km2/y in Lake Dianchi (hypereutrophic lake), and the B-P coupling energy was 405 t/km2/y and 213 t/km2/y, respectively. In these lakes, B-P coupling occurred on multiple trophic levels; lower trophic level consumers contributed the largest proportion (90% and 98%), while top consumers were of limited importance; most coupling links were weak, and energy exchange was highly asymmetric with the total amount of energy exported from benthic part to pelagic part being over 4 folds of the counter flux.The quantity and pattern of B-P coupling vary between the mesoeutrophic and hypereutrophic lakes. In terms of energy flux per unit area, the total system throughput in the mesoeutrophic lake (Lake Erhai) was 3.73 times of that in the hypereutrophic lake (Lake Dianchi), while the proportion of coupling energy was much lower in the former (19%) than the latter (31%). A greater energy flux through pelagic-to-benthic pathways was found in the hypereutrophic lake, and most of the coupling energy was contributed by consumers at higher trophic levels. Besides, the coupling strength was stronger in the hypereutrophic than the mesoeutrophic lake.We showed for the first time how B-P coupling operates in lake energetic food webs. Our results provided new insights into understanding the energy flux through B-P coupling of lake ecosystems, and how such coupling could be changed by environmental disturbances. We also provided a new approach to reveal habitat coupling within an energetic food web framework.

Role of Asian summer monsoon subsystems in the inter-hemispheric progression of deglaciation

The responses of Asian monsoon subsystems to both hemispheric climate forcing and external orbital forcing are currently issues of vigorous debate. The Indian summer monsoon is the dominant monsoon subsystem in terms of energy flux, constituting one of Earth’s most dynamic expressions of ocean–atmosphere interactions. Yet, the Indian summer monsoon is grossly under-represented in Asian monsoon palaeoclimate records. Here, we present high-resolution records of Indian summer monsoon-induced rainfall and fluvial runoff recovered in a sediment core from the Bay of Bengal across Termination II, 139–127 thousand years ago, including coupled measurements of the oxygen isotopic composition and Mg/Ca, Mn/Ca, Nd/Ca and U/Ca ratios in surface-ocean-dwelling foraminifera. Our data reveal a millennial-scale transient strengthening of the Asian monsoon that punctuates Termination II associated with an oscillation of the bipolar seesaw. The progression of deglacial warming across Termination II emerges first in the Southern Hemisphere, then the tropics in tandem with Indian summer monsoon strengthening, and finally the Northern Hemisphere. We therefore suggest that the Indian summer monsoon was a conduit for conveying Southern Hemisphere latent heat northwards, thereby promoting subsequent Northern Hemisphere deglaciation. During deglacial warming at Termination II, about 130,000 years ago, the Indian summer monsoon helped convey heat northwards as deglaciation progressed from the Southern to the Northern Hemisphere, according to sediment records from the Bay of Bengal.