High-resolution Numerical Simulations Research Articles

Vertical Velocity Dynamics in the North Atlantic and Implications for AMOC

Abstract The Atlantic meridional overturning circulation (MOC) is traditionally monitored in terms of zonally-integrated transport either in depth space or density space. While this view has the advantage of simplicity, it obscures the rich and complex three-dimensional structure, so that the exact physics of the downwelling and upwelling branch remains poorly understood. The near-equivalence of the depth- and density-space MOC in the subtropics suggests that vertical and diapycnal volumes transports are intimately coupled, whereas the divergence of these two metrics at higher latitudes indicates that any such coupling is neither instantaneous nor local. Previous work has characterised the surface buoyancy forcing and mixing processes which drive diapycnal volume transport. Here, we develop a new analytical decomposition of vertical volume transport based on the vorticity budget. We show that most terms can be estimated from observations, and provide additional insights from a high-resolution numerical simulation of the North Atlantic. Our analysis highlights the roles (1) of relative vorticity advection for the sinking of overflow water at the northern subpolar North Atlantic boundaries and (2) the geostrophic β-effect for the sinking of dense waters in the inter-gyre region. These results provide insights into the coupling between density- and depth-space overturning circulations.

Relativistic head-on collisions of U(1) gauged Q -balls

We investigate the collision dynamics of U(1) gauged Q-balls by performing high-resolution numerical simulations in axisymmetry. Focusing on the case of relativistic head-on collisions, we consider the effects of the initial velocity, relative phase, relative charge, and electromagnetic coupling strength on the outcome of the collision. We find that the collision dynamics can depend strongly on these parameters; most notably, electromagnetic effects can significantly alter the outcome of the collision when the gauge coupling is large. When the gauge coupling is small, we find that the dynamics generally resemble those of ordinary (nongauged) Q-balls. Published by the American Physical Society 2024

TFUSFormer: Physics-Guided Super-Resolution Transformer for Simulation of Transcranial Focused Ultrasound Propagation in Brain Stimulation.

Transcranial focused ultrasound (tFUS) has emerged as a new mode of non-invasive brain stimulation (NIBS), with its exquisite spatial precision and capacity to reach the deep regions of the brain. The placement of the acoustic focus onto the desired part of the brain is critical for successful tFUS procedures; however, acoustic wave propagation is severely affected by the skull, distorting the focal location/shape and the pressure level. High-resolution (HR) numerical simulation allows for monitoring of acoustic pressure within the skull but with a considerable computational burden. To address this challenge, we employed a 4× super-resolution (SR) Swin Transformer method to improve the precision of estimating tFUS acoustic pressure field, targeting operator-defined brain areas. The training datasets were obtained through numerical simulations at both ultra-low (2.0 [Formula: see text]) and high (0.5 [Formula: see text]) resolutions, conducted on in vivo CT images of 12 human skulls. Our multivariable datasets, which incorporate physical properties of the acoustic pressure field, wave velocity, and skull CT images, were utilized to train three-dimensional SR models. We found that our method yielded 87.99 ± 4.28% accuracy in terms of focal volume conformity under foreseen skull data, and accuracy of 82.32 ± 5.83% for unforeseen skulls, respectively. Moreover, a significant improvement of 99.4% in computational efficiency compared to the traditional 0.5 [Formula: see text] HR numerical simulation was shown. The presented technique, when adopted in guiding the placement of the FUS transducer to engage specific brain targets, holds great potential in enhancing the safety and effectiveness of tFUS therapy.

SWIRL: The First Australian Operational Radar-Based 3D Wind Analysis System

Abstract In this paper, the first Australian operational radar-based three-dimensional (3D) wind analysis system named Synthetic Wind Information from Radar and Lidar (SWIRL) is described and evaluated. SWIRL employs a variational minimization formulation to combine results from four individual wind retrieval techniques of varied complexity to derive 3D winds in single-Doppler and multi-Doppler radar regions: a variational version of the traditional velocity azimuth display (VVAD) and double VAD (DVAD) techniques, a single-Doppler wind retrieval technique using optical flow horizontal wind proxies, and a multi-Doppler 3D wind retrieval technique. The SWIRL 3D wind components are evaluated against wind profiler observations and radar simulations using a very high-resolution (50 m) numerical simulation of a supercell thunderstorm. We find that SWIRL can retrieve very accurate horizontal winds, especially below 2-km height in the multi-Doppler regions, with mean absolute errors on wind speed and direction < 2 m s−1 and 10° on average and <2.5 m s−1 and 15°–20° 90% of the time. These errors do not increase noticeably with wind speed, highlighting the suitability of these retrieved winds to be used for damaging and destructive wind detection and nowcasting. The single-Doppler retrieval using optical flow is also found to provide reasonably accurate winds at these heights. The accurate retrieval of convective-scale updrafts and downdrafts, even using multi-Doppler information, is still a major challenge, with mean absolute errors of vertical velocity of about 50% on average. This can be attributed to the limitations of the current radar technology used operationally, imposing slow antenna speeds. Significance Statement Damaging and destructive winds have the potential to inflict significant damage to properties and assets and, tragically, result in loss of life. Efficient direction of emergency services to affected areas is essential for a prompt return to normal conditions. Wind farm operators require precise information on anticipated wind shifts to reduce the risk of energy grid failures. Strong winds also contribute to compound weather events, such as water ingress through hail-damaged roofs or structural damage to buildings caused by hailstones. The purpose of this work was to equip Australia with the first operational wind monitoring system, based on operational radar observations, to serve all these critical applications (and more).

A resolution-enhanced seventh-order weighted essentially non-oscillatory scheme based on non-polynomial reconstructions for solving hyperbolic conservation laws

In high-resolution numerical simulations of flows characterized by both multiscale turbulence and discontinuities, the conflict between spectral characteristics and stability becomes increasingly pronounced as the order of accuracy improves. To address this challenge, we proposed a novel seventh-order weighted essentially non-oscillatory scheme (WENO-K7). This scheme utilizes non-polynomial reconstructions by incorporating kriging interpolation and Gaussian exponential function. Then, a hyper-parameter associated with the Gaussian function is adaptively optimized to achieve higher convergence orders on sub-stencils, reducing numerical errors on global stencils. Additionally, a criterion based on monotone interpolations is devised to automatically identify problematic hyper-parameters, facilitating the transition from non-polynomial to polynomial reconstructions near discontinuities and preserving the essentially non-oscillatory property. Compared to the conventional seventh-order WENO-Z7 scheme, WENO-K7 scheme exhibits smaller computational error and reduced numerical dissipation in smooth regions while maintaining non-oscillatory and high-resolution capabilities around discontinuities. Results from various one- and two-dimensional benchmark cases demonstrate that the proposed WENO-K7 scheme outperforms the widely used WENO-Z7 scheme with only a 12% increase in computational cost. Moreover, the WENO-K7 scheme shares the same sub-stencils as the WENO-Z7 scheme, making it easily applicable to other variants of seventh-order WENO schemes and enhancing their spectral characteristics.

Resistively controlled primordial magnetic turbulence decay

Context. Magnetic fields generated in the early Universe undergo turbulent decay during the radiation-dominated era. The decay is governed by a decay exponent and a decay time. It has been argued that the latter is prolonged by magnetic reconnection, which depends on the microphysical resistivity and viscosity. Turbulence, on the other hand, is not usually expected to be sensitive to microphysical dissipation, which affects only very small scales. Aims. We want to test and quantify the reconnection hypothesis in decaying hydromagnetic turbulence. Methods. We performed high-resolution numerical simulations with zero net magnetic helicity using the PENCIL CODE with up to 20483 mesh points and relate the decay time to the Alfvén time for different resistivities and viscosities. Results. The decay time is found to be longer than the Alfvén time by a factor that increases with increasing Lundquist number to the 1/4 power. The decay exponent is as expected from the conservation of the Hosking integral, but a timescale dependence on resistivity is unusual for developed turbulence and not found for hydrodynamic turbulence. In two dimensions, the Lundquist number dependence is shown to be leveling off above values of ≈25 000, independently of the value of the viscosity. Conclusions. Our numerical results suggest that resistivity effects have been overestimated in earlier work. Instead of reconnection, it may be the magnetic helicity density in smaller patches that is responsible for the resistively slow decay. The leveling off at large Lundquist number cannot currently be confirmed in three dimensions.

A high-resolution numerical investigation of unsteady wake vortices for coaxial rotors in hover

High-resolution numerical simulations for wake vortical flows have long been a challenge in rotor aerodynamics. A novel spectrum-optimized sixth-order Weighted Essentially Non-Oscillatory (WENO) scheme is proposed to discretize inviscid fluxes on moving overset grids, and the Improved Delayed Detached Eddy Simulation (IDDES) is employed to resolve turbulent vortices. The integration of these methods facilitates a comprehensive numerical investigation into the unsteady vortical flows over coaxial rotors in hover. The results highlight the substantial improvement in numerical resolution, in terms of both spatial structure and temporal evolution of unsteady multiscale wake vortices. Coaxial rotors in hover manifest three primary scales of wake vortex structures: (A) the helical evolution of primary blade tip vortices and the periodic occurrence of strong Blade-Vortex-Interactions (BVI); (B) the continuous shedding of small-scale horseshoe-shaped vortices from the trailing edges of rotor blades, forming the vortex sheets; (C) the emergence of small-scale secondary vortex braids induced by interactions between rotor tip vortices and the vortex sheets. These vortex structures and their interactions cause high-frequency oscillations in rotor disk loads and induce unsteady perturbations in the local flow field. Interactions among these primary vortices, coupled with the generation of secondary vortices, result in the dissipation, distortion, and breakup of the rotor tip vortices, ultimately forming a vortex soup. Notably, a substantial quantity of seemingly weak small-scale secondary vortex braids significantly contribute to energy dissipation during the evolution of wake vortices for coaxial rotors in hover.

A Conceptual Model for the Development of Tornadoes in the Complex Orography of the Po Valley

Abstract The Po Valley in northern Italy is a hotspot for tornadoes in Europe in spite of being surrounded by two mountain ridges: the Alps in the north and the Apennines in the southwest. The research focuses on the case study of 19 September 2021, when seven tornadoes (four of them rated as F2) developed in the Po Valley in a few hours. The event was analyzed using observations and numerical simulations with the convection-permitting Modello Locale in Hybrid Coordinates (MOLOCH) model. Observations show that during the event in the Po Valley, there were two surface boundaries that created a triple point: an outflow boundary generated by convection triggered in the Alpine foothills and a dryline generated by downslope winds from the Apennines, while warm and moist air advected westward from the Adriatic Sea east (ahead) of the boundaries. Tornadoes developed about 20 km northeast of the triple point. Numerical simulations with 500-m grid spacing suggest that the development of supercells and drylines in the Po Valley was sensitive to the elevation of the Apennines. Simulated vertical profiles show that the best combination of instability and wind shear for the development of tornadoes was attained within a narrow area located ahead of the dryline. A conceptual model for the development of tornadoes in the Po Valley is proposed, and the differences between tornado environments over a flat terrain and over a region with complex terrain are discussed. Significance Statement The Po Valley is a highly populated area where some of the most violent tornadoes in Europe have developed. We investigated a tornado outbreak that occurred on 19 September 2021 in this region, in order to identify its main environmental characteristics. High-resolution numerical simulations revealed that values of instability and wind shear were compatible with the development of several tornadoes only in a narrow area close to the intersection of two surface boundaries (a triple point). Moreover, the atmospheric environment during the tornado outbreak was strongly influenced by the presence of mountain ridges surrounding the plain. We have summarized our results in a conceptual model that can potentially be used for forecasting applications.

Parametric description of intermittent probability distribution functions in solar wind and magnetohydrodynamic turbulence

ABSTRACT In this work, we find empirical evidence that the scale-dependent statistical properties of solar wind and magnetohydrodynamic (MHD) turbulence can be described in terms of a family of parametric probability distribution functions (PDFs) known as Normal Inverse Gaussian (NIG). Understanding these PDFs is one of the most important goals in turbulence theory, as they are inherently connected to the intermittent properties of solar wind turbulence. We investigate the properties of PDFs of Elsasser increments based on a large statistical sample from solar wind observations and high-resolution numerical simulations of MHD turbulence. In order to measure the PDFs and their corresponding properties, three experiments are presented: fast and slow solar wind for experimental data and a simulation of reduced MHD (RMHD) turbulence. Conditional statistics on a 23-yr-long sample of WIND data near 1 au and high-resolution pseudo-spectral simulation of steadily driven RMHD turbulence on a $2048^3$ mesh are used to construct scale-dependent PDFs. The empirical PDFs are fitted to NIG distributions, which depend on four free parameters. Our analysis shows that NIG distributions accurately capture the evolution of the PDFs, with scale-dependent parameters, from large scales characterized by a Gaussian distribution, turning to exponential tails within the inertial range and stretched exponentials at dissipative scales. We also show that empirically-measured NIG parameters exhibit well-defined scaling properties that are similar across the three empirical data sets, which may be indicative of universal behaviour.

Numerical Simulations of Viscous Fingering in Fractured Porous Media

AbstractThe effect of heterogeneity induced by highly permeable fracture networks on viscous miscible fingering in porous media is examined using high-resolution numerical simulations. We consider the planar injection of a less viscous fluid into a two-dimensional fractured porous medium that is saturated with a more viscous fluid. This problem contains two sets of fundamentally different preferential flow regimes; the first is caused by the viscous fingering, and the second is due to the permeability contrasts between the fractures and the rock matrix. We study the transition from the regime where the flow is dominated by the viscous instabilities, to the regime where the heterogeneity induced by the fractures define the flow paths. Our findings reveal that even minor permeability differences between the rock matrix and fractures significantly influence the behavior of viscous fingering. The interplay between the viscosity contrast and permeability contrast leads to the preferential channeling of the less viscous fluid through the fractures. Consequently, this channeling process stabilizes the displacement front within the rock matrix, ultimately suppressing the occurrence of viscous fingering, particularly for higher permeability contrasts. We explore three fracture geometries: two structured and one random configuration and identify a complex interaction between these geometries and the development of unstable flow. While we find that the most important factor determining the effect of the fracture network is the ratio of fluid volume flowing through the fractures and the rock matrix, the exact point for the cross-over regime is dependent on the geometry of the fracture network.

Simulated WSR-88D Observations of the Streamwise Vorticity Current

The streamwise vorticity current (SVC) has been shown in recent research to have a role in the tornadogenesis process in some supercells. Although field experiments have succeeded in observing the feature using mobile radars, limited knowledge exists on how/if SVCs can be observed using operational radars. To explore this possibility, simple radar emulation software was used to create simulated Weather Surveillance Radar 1988 Doppler (WSR-88D) radar images of an SVC in a high-resolution numerical simulation of a supercell thunderstorm. This proof-of-concept approach shows that SVCs likely can be observed in an operational setting under idealized circumstances. Two analysis times from the simulation are used to compare the signatures of both a weak and a strong SVC. This study suggests that results are highly contingent on radar viewing angle, and quality observations of the SVC may only be possible when a storm is within 45 km of the radar site. In Plan Position Indicator (PPI) scans, SVCs are found to be associated with inflow winds that penetrate more rearward with height downstream of the mesocyclone. Range Height Indicator (RHI) reconstructions show a reflectivity billow that resembles a density current head containing a Kelvin-Helmholtz (KH) billow, as well as a radial velocity couplet co-located with the SVC. A vertical shear product is introduced to visualize low-level vertical wind shear in the vicinity of the SVC to facilitate identification of the feature without interrogation of multiple elevation angles of radial velocity data.

High-resolution observations and numerical simulations provide insight into solar atmospheric heating

High-resolution observations and numerical simulations provide insight into solar atmospheric heating

On the Sensitivity of Large-Eddy Simulations of the Atmospheric Boundary Layer Coupled with Realistic Large-Scale Dynamics

Abstract We present a new ensemble of 36 numerical experiments aimed at comprehensively gauging the sensitivity of nested large-eddy simulations (LES) driven by large-scale dynamics. Specifically, we explore 36 multiscale configurations of the Weather Research and Forecasting (WRF) Model to simulate the boundary layer flow over the complex topography at the Perdigão field site, with five nested domains discretized at horizontal resolutions ranging from 11.25 km to 30 m. Each ensemble member has a unique combination of the following input factors: (i) large-scale initial and boundary conditions, (ii) subgrid turbulence modeling in the gray zone of turbulence, (iii) subgrid-scale (SGS) models in LES, and (iv) topography and land-cover datasets. We probe their relative importance for LES calculations of velocity, temperature, and moisture fields. Variance decomposition analysis unravels large sensitivities to topography and land-use datasets and very weak sensitivity to the LES SGS model. Discrepancies within ensemble members can be as large as 2.5 m s−1 for the time-averaged near-surface wind speed on the ridge and as large as 10 m s−1 without time averaging. At specific time points, a large fraction of this sensitivity can be explained by the different turbulence models in the gray zone domains. We implement a horizontal momentum and moisture budget routine in WRF to further elucidate the mechanisms behind the observed sensitivity, paving the way for an increased understanding of the tangible effects of the gray zone of turbulence problem. Significance Statement Several science and engineering applications, including wind turbine siting and operations, weather prediction, and downscaling of climate projections, call for high-resolution numerical simulations of the lowest part of the atmosphere. Recent studies have highlighted that such high-resolution simulations, coupled with large-scale models, are challenging and require several important assumptions. With a new set of numerical experiments, we evaluate and compare the significance of different assumptions and outstanding challenges in multiscale modeling (i.e., coupling large-scale models and high-resolution atmospheric simulations). The ultimate goal of this analysis is to put each individual assumption into the wider perspective of a realistic problem and quantify its relative importance compared to other important modeling choices.

A Numerical Study of Clear-Air Turbulence over North China on 6 June 2017

On 6 June 2017, four severe clear-air turbulence (CAT) events were observed over northern China within 3 h. These events mainly occurred at altitudes between 8.1 and 9.5 km. The characteristics and possible mechanisms of the CAT events in the different regions are investigated here using the weather research and forecasting (WRF) model. The simulated wind and temperature fields in a 27 km coarse domain were found to be in good agreement with those of the ERA5 (European Centre for Medium-Range Weather Forecasts Reanalysis v5) and the observed soundings of operational radiosondes over northern China. In terms of synoptic features, the region where the turbulence occurred is characterized by a southwest–northeast upper-level jet stream. The upper-level jet stream observed at an altitude of 10.4 km consistently moved eastwards, with a maximum wind speed of 61.7 m/s. Simultaneously, the upper-level front–jet system on the cyclonic shear side of the upper-level jet stream also exhibited an eastward motion. The developed upper-level front–jet system induced significant vertical wind shear (VWS) and tropopause folding in the vicinity of these CAT events. Despite the high stability resulting from tropopause folding, the presence of strong VWS (1.90 × 10−2 s−1–2.55 × 10−2 s−1) led to a low Richardson number (Ri) (0.24–0.88) and caused Kelvin–Helmholtz instability (KHI), which ultimately induced CAT. Although a standard numerical weather forecast resolution of tens of kilometers is adequate to capture turbulence for most CAT events, it is still necessary to use high-resolution numerical simulations (such as 3 km) to calculate more accurate CAT indices (such as Ri) for CAT prediction in some specific cases.

Trade Off between Hydrodynamic and Thermodynamic Forces at the Liquid-Liquid Interface.

Viscous fingering (VF) instability has been investigated in the case of a partially miscible binary system by nonlinear numerical simulations. Partially miscible fluid systems offer the possibility of phase separation coupled with VF instability. The thermodynamics of such systems are governed by the Margules parameter (interaction parameter) as well as the fluid concentrations. Kinetics of the decomposition is also influenced by dynamical parameters such as the viscosity of the fluid, which incidentally also affects the hydrodynamic forces. Here, we explore the effects of concentration and Margules parameter in order to ascertain the trade-offs incurred between hydrodynamic and thermodynamic effects at the interface as well as the thermodynamics of the bulk. Based on the Gibb's free energy versus concentration curve, we select concentrations (i) outside spinodal and binodal regions, (ii) within binodal but outside the spinodal, and (iii) within the spinodal curve. We solve the modified Cahn-Hilliard-Hele-Shaw equation employing the COMSOL Multiphysics software. Applying high-resolution numerical simulations, we show a strong dependence of the thermodynamic forces on the concentration of the mixtures. Rapid phase separation and hence a faster rate of droplet formation have been found when the concentration lies inside the spinodal region. Further, we have investigated the correlation between the fractal dimension and dynamics of the system. The spatiotemporal studies presented in this work clearly illustrate the competition between hydrodynamic and thermodynamic forces and provide insights on the kinetics of decomposition and growth of interfacial instabilities.

Amplification of Supersonic Microjets by Resonant Inertial Cavitation-Bubble Pair.

We reveal for the first time by experiments that within a narrow parameter regime, two cavitation bubbles with identical energy generated in antiphase develop a supersonic jet. High-resolution numerical simulation shows a mechanism for jet amplification based on toroidal shock wave and bubble necking interaction. The microjet reaches velocities in excess of 1000 m s^{-1}. We demonstrate that potential flow theory established for Worthington jets accurately predicts the evolution of the bubble gas-liquid interfaces unifying compressible and incompressible jet amplification.

Effects of Orography on the High-Temperature Event on 22 June 2023 in North China

An extreme high-temperature event occurred in North China on 22 June 2023, with the maximum temperature reaching 41.8 °C. The high-temperature centers preferentially occurred at the foothills of the Taihang and Yanshan Mountains, indicating an important role of the underlying orography. In the present work, we study the orographic effects of this extreme high-temperature event according to high-resolution numerical simulations using the Weather Research and Forecasting model. The results show that the presence of the mountains in North China contributed notably to the high-temperature event, which can enhance the 2 m air temperature by up to 3 °C. In the daytime, the enhancement of temperature is primarily due to the diabatic heating of sensible heat flux at the terrain surface caused by solar shortwave radiation, whereas the well-known foehn effect has little contribution. Indeed, the dynamically forced downslope flow of foehn is totally suppressed by the upslope flow of the thermally driven mountain-plain circulation. In the nighttime, the sensible heat flux at the terrain surface changes to weakly negative, given the cooling of land surface longwave radiation. As a result, the enhancement of near-surface temperature at the terrain foothill is dominated by the adiabatic warming of downslope flow. Yet, the near-surface temperature far away from the mountain is enhanced by the subsidence warming of a synoptic anomalous anti-cyclone, which is induced by the diabatic heating over the mountains in the daytime. These findings help improve the understanding of the thermal and dynamical effects of orography on the occurrence of high-temperature events.

DESIGN OF THE POSITION OF THE BLOCKING MATERIAL IN THE WATERFLOODED HIGH-PERMEABLE INTERLAYER OF OIL RESERVOIR FOR FIVE-SPOT FLOODING SCHEME

The comparative analysis of the effectiveness of various arrangements of blocking material in a thin, high-permeable water-cut layer of an oil reservoir is presented in order to reduce unproductive injection and in- crease oil recovery. Efficiency calculation was performed using high-resolution numerical simulation in the vertical section of the typical stream tube for a five-spot waterflooding scheme. Three types of location of isolation intervals are considered for two representative ratios of the viscosity of the water and oil phases.

Numerical simulation of droplet dispersion within meso-porous membranes

Analysis of membrane processes in fluid processing, and their main influencing operating conditions are relevant in a variety of industrial applications. Increasing regulatory scrutiny and environmental considerations are forcing industries across all sectors, from food and pharma to oil and gas, to further understand and optimise the handling and formulation of liquid systems for efficient process design. In a generic setup for emulsification and liquid formulation the flow and dispersion behaviour of a liquid oil droplet on its way through a porous water filled membrane is analysed. A set of high-resolution numerical simulations of a single oil droplet dispersed in water through a porous membrane structure with varying contact angles is performed. In this work cluster analysis of volume-of-fluid simulation results to obtain statistical droplet size distributions is conducted and further analysed to highlight the effect of the contact angle as well as pressure drop on the dynamics of the system. It is observed that based on the membrane surface activity the droplet behaviour changes from filtration with coalescence when the membrane is lipophilic to emulsification with droplet break-up when the membrane is lipophobic. Furthermore, the pressure drop is identified as a key factor for the dynamics of the droplet process and the frame in which it occurs. These results highlight that the membrane wettability is a determining factor for the emulsification or filtration effectiveness of a membrane for various applications.

Stellar feedback in the star formation–gas density relation: Comparison between simulations and observations

Context. The impact of stellar feedback on the Kennicutt–Schmidt (KS) law, which relates the star formation rate (SFR) to the surface gas density, is a topic of ongoing debate. The interpretation of high-resolution observations of individual clouds is challenging due to the various processes at play simultaneously and inherent biases. Therefore, a numerical investigation is necessary to understand the role of stellar feedback and identify observable signatures. Aims. In this study we investigate the impact of stellar feedback on the KS law, aiming to identify distinct signatures that can be observed and analysed. By employing magnetohydrodynamic simulations of an isolated cloud, we specifically isolate the effects of high-mass star radiation feedback and protostellar jets. High-resolution numerical simulations are a valuable tool for isolating the impact of stellar feedback on the star formation process, while also allowing us to assess how observational biases may affect the derived relation. Methods. We used high-resolution (<0.01 pc) magnetohydrodynamic numerical simulations of a 104 M⊙ cloud and followed its evolution under different feedback prescriptions. The set of simulations contained four types of feedback: one with only protostellar jets, one with ionising radiation from massive stars (>8 M⊙), one with the combination of the two, and one without any stellar feedback. In order to compare these simulations with the existing observational results, we analysed their evolution by adopting the same techniques applied in the observational studies. Then, we simulated how the same analyses would change if the data were affected by typical observational biases: counting young stellar objects (YSO) to estimate the SFR, the limited resolution for the column density maps, and a sensitivity threshold for detecting faint embedded YSOs. Results. Our analysis reveals that the presence of stellar feedback strongly influences the shape of the KS relation and the star formation efficiency per free-fall time (ϵff). The impact of feedback on the relation is primarily governed by its influence on the cloud’s structure. Additionally, the evolution of ϵff throughout the star formation event suggests that variations in this quantity can mask the impact of feedback in observational studies that do not account for the evolutionary stage of the clouds. Although the ϵff measured in our clouds is higher than what is usually observed in real clouds, upon applying prescriptions to mimic observational biases we recover a good agreement with the expected values. From that, we can infer that observations tend to underestimate the total SFR. Moreover, this likely indicates that the physics included in our simulations is sufficient to reproduce the basic mechanisms that contribute to setting ϵff. Conclusions. We demonstrate the interest of employing numerical simulations to address the impact of early feedback on star formation laws and to correctly interpret observational data. This study will be extended to other types of molecular clouds and ionising stars, sampling different feedback strengths, to fully characterise the impact of H II regions on star formation.