High Velocity Research Articles

Near-surface characterization using shear-wave resonances: A case study from offshore Svalbard, Norway

Shear-wave (S-wave) resonances are typically observed when the surficial marine sediments over a rock substrate have relatively low S-wave velocities. We observe these phenomena using ocean-bottom fiber-optic distributed acoustic sensing (DAS) in two subsea fiber-optic telecommunication cables in Svalbard, Norway. Strong seismic energy from sufficiently large earthquakes is required to trigger and enhance the multiple-order modes of S-wave resonances. Here, we use the interpreted S-wave resonance frequencies of the first two modes to determine the thickness and the S-wave velocity of the near-surface low-velocity layer (LVL) beneath the seafloor. In addition, we use existing active P-wave seismic reflection data to determine the LVL thickness and to help build a more accurate S-wave velocity model from the S-wave resonance frequencies. The estimated S-wave velocity varies laterally within the LVL formation. Here, we find that the sediments or deposits with high S-wave velocity presented in the estimated LVL model agree with the distribution of some glacigenic sediments and landforms deposited in the survey area. Therefore, S-wave resonances measured by ocean-bottom DAS can be used to characterize the corresponding near-surface LVLs.

Influence of external wind on fire characteristics and smoke dynamics in a stairwell adjacent to a room

A range of fire experiments were conducted to explore fire characteristics and smoke dynamics in a 1/6-scale stairwell adjacent to a room at different external wind velocities. The results indicated that the flame volume during the initial stage and the time taken for combustion to enter the steady stage both decrease with the increasing wind velocity. There are two opposite effects of the external wind on the fire combustion in a burning room adjacent to a stairwell. The inhibition effect plays an important role at lower wind velocities, leading to a decrease in the mass loss rate (MLR) of the pool fire. Conversely, the promotion effect dominates at higher wind velocities, resulting in an increase in the MLR. Stack effect and external wind demonstrate a synergistic relationship during experiments, and a correlation of the airflow velocity, wind velocity and heat release rate (HRR) is established. There are intersections in temperature curves at different wind velocities due to the smaller temperature decay rate in the stairwell and the lower smoke temperature near the pool fire at a higher velocity. Furthermore, a prediction model is also proposed for the smoke temperature distribution inside the stairwell, taking into account the wind velocity and HRR.

Thickener Behaviour in Rolling Elastohydrodynamic Lubrication Contacts

This paper focuses on the study of thickener behaviour in elastohydrodynamic contacts using fluorescence microscopy and optical interferometry. A standard Ball-on-disc configuration tribometer was used as well as a newly developed Ball-on-ring configuration tribometer mimicking the conditions in a 6314 deep groove ball bearing. Three types of custom-made greases were used with the same base oil and Coumarin 6 fluorescent dye on the thickener. These greases contained no additives and were of the lithium complex and alicyclic di-urea type. It was confirmed that the behaviour of the grease was directly influenced by both the structure and type of thickener, and the differences were successfully observed by fluorescence microscopy. The concentration of thickener was found to change due to the formation or breakdown of the deposited thickener layer on the track. At low speeds, the alicyclic di-urea forms a thickener layer on the track that is more pronounced than the lubricating film formed by the base oil alone. The thickener layer formation also occurs at higher speeds when fully flooded conditions are beneficial in building the layer. Experiments with a Ball-on-ring tribometer show that the natural replenishment of the real contact geometry is more effective than on a Ball-on-disc tribometer, but the formation of the thickener layer on the track is more limited than in a Ball-on-disc tribometer with artificial replenishment. At higher velocities, a smaller but stable layer is formed where the layer does not change much from a certain velocity.

Sound velocities in lunar mantle aggregates at simultaneous high pressures and temperatures: Implications for the presence of garnet in the deep lunar interior

Recent experimental and theoretical studies on lunar magma ocean crystallisation have suggested the presence of significant proportions of garnet in the deep lunar interior. While phase relation studies indicate a deep lunar mantle consisting of olivine, pyroxene, and garnet, the compatibility of such an assemblage with seismic models of the lunar interior is yet untested. In this study we report compressional and shear wave velocities in an iron-rich assemblage consisting of olivine, orthopyroxene, clinopyroxene, and garnet up to ∼8 GPa and 1300 K, by means of ultrasonic interferometry measurements combined with synchrotron techniques using the multi-anvil press apparatus. Sound velocity and density models of lunar mantle rocks along a selenotherm based on our experimental results find good agreement with the seismic and density profiles at lunar interior depths of 740–1260 km. Further models are constructed, allowing for the variation of chemical composition, phase proportion, and temperature; these suggest that a garnet-rich deep lunar mantle is compatible with present-day lower lunar mantle temperatures of between 1400–1800 K. Our results show that lunar mantle rocks with up to 33 wt.% garnet may provide an explanation for the observed high velocities of the lower lunar mantle. The presence of garnet in the lowermost part of the Moon's mantle has significant implications for the depth and temperature of the Moon's magma ocean as well as the composition, structure and internal dynamics of the solid Moon.

Achieving underwater stable drag reduction on superhydrophobic porous steel via active injection of small amounts of air

Over the years, numerous researchers have proposed air lubrication methods to reduce drag in underwater vehicles. This method is challenged by buoyancy and water flow, which facilitate air escape from solid surfaces, necessitating substantial air to achieve significant drag reduction. The adherence of hydrophobic interfaces to submerged air bubbles reduces air escape, stabilizing it on solid surfaces for effective drag reduction. However, high flow velocities or pressure conditions can destabilize the drag reduction effect by disrupting the air-water interface. To address this issue, the paper proposes a method that integrates superhydrophobic surfaces with active air injection. This approach involves preparing stable superhydrophobic surfaces by combining laser ablation, heat treatment, and spraying hydrophobic coatings on porous steel surfaces, and using active air injection to maintain the stability of the air layer. Flow field analysis revealed that active air injection into superhydrophobic porous steel sustains a stable air layer, even at high flow velocities, reaching a drag reduction exceeding 25%. Moreover, at high Reynolds numbers, high drag reduction can be achieved at significantly low flow rates compared to smooth surface. This approach shows promise for maintaining a stable air-water interface on superhydrophobic surfaces and sustaining drag reduction in engineering applications.

Research and application of Rayleigh wave imaging based on the Born–Jordan time‐frequency distribution

AbstractCurrently, the horizontal resolution of Rayleigh wave exploration is low. In this study, we propose the Born–Jordan time‐frequency distribution to analyse Rayleigh waves. The seismic signal was filtered with a wavelet transform for denoising, and the Rayleigh wave was separated in the time domain. Using the Born–Jordan time‐frequency distribution, the time waveform of each frequency comprising the Rayleigh wave from every seismic channel was obtained, and the time difference of the Rayleigh wave with the same frequency was calculated, based on which the dispersion curve between the two channels was obtained. Combined with the multichannel Rayleigh wave dispersion curve, phase velocity and frequency imaging under the seismic arrangement were obtained. Applying this method to detect abnormal geological bodies in engineering investigations showed that hard geologic bodies, such as comcrete rocks, have high velocity and frequency, whereas weak ones have low velocity and frequency. This strategy facilitated the detection of fractured zones, underground goafs and obstacles during pipe‐jacking construction near the surface.

The ventilatory effect of High Velocity Nasal Insufflation versus Non-invasive Positive Pressure Ventilation in the treatment of acute hypercapnic respiratory failure in patients with AECOPD.

The ventilatory effect of High Velocity Nasal Insufflation versus Non-invasive Positive Pressure Ventilation in the treatment of acute hypercapnic respiratory failure in patients with AECOPD.

Prediction of three-dimensional flow field inside realistic fibrous filter obtained from x-ray computed tomography images using deep convolutional neural networks

Deep-learning models garnered considerable attention in the field of fluid mechanics for physics discovery and approximation-model generation. This study aims to develop an approximation model to predict the flow field inside realistic fibrous filters based on an image-to-image approach to replace three-dimensional (3D) computational fluid dynamics (CFD) simulations, which are computationally expensive and difficult to apply to realistic fibrous filters. A data-driven framework is proposed using deep convolutional neural networks (CNNs) to provide a per-pixel prediction of the flow field. The model inputs are two-dimensional x-ray computed tomography images, whereas the outputs are the 3D distributions of the velocity vectors and pressure. High-resolution 3D CFD simulations are performed to create a database to train and test the CNN model. The model is applied to surgical and N95 face masks. The relative error of the CNN model over the test dataset is approximately 10% in regions with high velocity and pressure, and the model can provide a detailed high-resolution prediction of the flow field with a speedup of about three orders of magnitudes. A strict generalization test is conducted for completely unseen 3D segments with complex microstructures. The model generalizability still needs more improvements; however, the model can provide a low-resolution 3D flow field for those segments that can be used as the initial condition for CFD simulation to reduce the CFD computational time. This framework can be utilized for other types of filters and provides a basis for the design and optimization of fibrous filters.

First detection of the [CII] 158 µm line in the intermediate-velocity cloud Draco

High-latitude intermediate-velocity clouds (IVCs) are part of the Milky Way’s H I halo and originate from either a galactic fountain process or extragalactic gas infall. They are partly molecular and can most of the time be identified in CO. Some of these regions also exhibit high-velocity cloud gas, which is mostly atomic, and gas at local velocities (LVCs), which is partly atomic and partly molecular. We conducted a study on the IVCs Draco and Spider, both were exposed to a very weak UV field, using the spectroscopic receiver upGREAT on the Stratospheric Observatory for Infrared Astronomy (SOFIA). The 158 µm fine-structure line of ionized carbon ([C II]) was observed, and the results are as follows: In Draco, the [C II] line was detected at intermediate velocities (but not at local or high velocities) in four out of five positions. No [C II] emission was found at any velocity in the two observed positions in Spider. To understand the excitation conditions of the gas in Draco, we analyzed complementary CO and H I data as well as dust column density and temperature maps from Herschel. The observed [C II] intensities suggest the presence of shocks in Draco that heat the gas and subsequently emit in the [C II] cooling line. These shocks are likely caused by the fast cloud’s motion toward the Galactic plane that is accompanied by collisions between H I clouds. The nondetection of [C II] in the Spider IVC and LVC as well as in other low-density clouds at local velocities that we present in this paper (Polaris and Musca) supports the idea that highly dynamic processes are necessary for [C II] excitation in UV-faint low-density regions.

Interstellar meteors from the tidal disruption of rocky planets on eccentric orbits around M dwarfs

Context. Low-mass stars appear to frequently host planetary systems. When these rocky planets develop high eccentricities as a result of secular torques or dynamical scatterings, they occasionally pass close to the host star. In these close passages, the planets can be tidally disrupted, and sheared into bound and unbound debris tails. To suffer such a disruption, the stellar density must be higher than the planetary density. Aims. This condition is met for the most common star and planet systems, M dwarf stars hosting rocky planets. We describe the dynamics of a tidal disruption, and estimate the typical velocities of unbound ejecta. Methods. We simulate the gas dynamics of a planetary tidal disruption, and show that disruptions preserve the layered structure of a rocky body, with the outermost layers flung into interstellar space with the highest velocities. Results. We compare these properties to those of the candidate interstellar meteoroid CNEOS-2014-01-08 (IM1). IM1's approximately 60 km s−1 excess speed relative to the local standard of rest is naturally reproduced by the unbound debris of the disruption of an Earth-like planet around an M dwarf star. We suggest that such an encounter might explain the interstellar kinematics of IM1, and its unusual composition, especially if it originated in the fastest-expelled crust of a differentiated rocky planet. Finally, we estimate that the disruption of ~10 M⊕ reservoirs of rocky planets per M dwarf are needed to reproduce the inferred rate of IM1-like objects.

Effect of binder phases on the microstructure and sliding wear properties of HVOF-sprayed WC-based coatings

This study aimed to evaluate the microstructure and wear properties of WC-10Co-4Cr, WC-12Co, and WC-17Co coatings on TC4 titanium alloy. The coatings were deposited using high velocity oxygen-fuel (HVOF) technique. To analyze the influence of binder phases, the coatings were thoroughly examined using scanning electron microscopy, X-ray diffractometer, microhardness tester, and friction and wear tester. The analysis of the results reveals that the primary phases in all three coatings consist mainly of WC, with smaller quantities of W2C and amorphous phases present. The WC-10Co-4Cr powder demonstrates a relatively even particle size distribution, high degree of sphericity, and rough porous surface, allowing for efficient heat absorption and uniform heat distribution, resulting in a dense coating. Notably, the WC-10Co-4Cr coating exhibits significantly smaller tungsten carbide grain size compared to the other coatings. Moreover, the microhardness of the WC-10Co-4Cr coating, measured at 1377.8 HV0.05, is significantly higher than that of the WC-12Co and WC-17Co coatings, which measured at 1258.8 HV0.05 and 1182.4 HV0.05, respectively. Additionally, the WC-10Co-4Cr coating demonstrates low friction coefficient and wear volume, indicating excellent wear resistance. Subsequently, a comprehensive analysis was conducted to determine the reasons for the relative enhancement in binder performance.

PROJECT-J: JWST Observations of HH46 IRS and Its Outflow. Overview and First Results

We present the first results of the JWST program PROJECT-J (PROtostellar JEts Cradle Tested with JWST), designed to study the Class I source HH46 IRS and its outflow through NIRSpec and MIRI spectroscopy (1.66–28 μm). The data provide line images (∼6.″6 in length with NIRSpec, and up to ∼20″ with MIRI) revealing unprecedented details within the jet, the molecular outflow, and the cavity. We detect, for the first time, the redshifted jet within ∼90 au from the source. Dozens of shock-excited forbidden lines are observed, including highly ionized species such as [Ne iii] 15.5 μm, suggesting that the gas is excited by high velocity (>80 km s−1) shocks in a relatively high-density medium. Images of H2 lines at different excitations outline a complex molecular flow, where a bright cavity, molecular shells, and a jet-driven bow shock interact with and are shaped by the ambient conditions. Additional NIRCam 2 μm images resolve the HH46 IRS ∼110 au binary system and suggest that the large asymmetries observed between the jet and the H2 wide-angle emission could be due to two separate outflows being driven by the two sources. The spectra of the unresolved binary show deep ice bands and plenty of gaseous lines in absorption, likely originating in a cold envelope or disk. In conclusion, JWST has unraveled for the first time the origin of the HH46 IRS complex outflow demonstrating its capability to investigate embedded regions around young stars, which remain elusive even at near-IR wavelengths.

Vertical Distribution of Rip Currents Generated by Intersecting Waves in a Sandbar–Groin Systems

To analyze the impacts of groins, sandbars, and channels on the three-dimensional features of rip currents, we conducted experimental investigations on the vertical distribution of rip currents under intersecting waves along barred beaches with channels. This study employed ADV flow velocity measurements at two distinct locations: within channel and on a sandbar. The results indicate that in nodal sections within channel and on a sandbar, the rip head region manifests surface flow characteristics, characterized by high velocities near water surface. In a rip neck location, the vertical distribution of rip currents on a sandbar exhibits greater variability, whereas within channel, the distribution is more homogeneous. The vertical distribution of rip currents in nodal sections within channel aligns with the logarithmic distribution law. The vertical distributions of the alongshore velocity of rip currents display a consistent pattern of higher at the top and lower at the bottom. However, this pattern varies slightly depending on the wave period. The presence of groins influences the fluctuation characteristics of the alongshore velocity of rip currents by regulating the nearshore circulation system. This results in the alongshore velocity of rip currents in channel pointing towards the groin. In contrast, the alongshore velocity of rip currents on sandbar, situated farther away from groin, exerts a weaker effect on the alongshore velocity of a rip current.

Influence of Substitutions and Roles on Kinematic Variables in Professional Soccer Players.

In soccer, roles, and substitutions could make unclear how different physical capacities decrease over time and impact performance. This investigation aimed to analyze kinematic parameters and their changes over game time and provide information to effectively prescribe training programs. Data from four professional teams were analyzed, and all the teams competed in the Premier Division championship. Average metabolic power and high-intensity activities associated with critical moments in the match were considered in the comparisons. The video analysis system STATS SportVU collected the data during official matches. Players were assigned to a specific group according to their time played, categorized as follows: 0-15', 15-30', 30-45', 45-60', 60-75', 75-90', and > 90 min. Different roles, including forwards and wingers (FW), midfielders (MF), center-backs (CB), and side-backs (SB) were also considered. Significant differences (p<0.05) were found in different roles and within roles at different times played. The results highlighted how MF performance decreased over time, whereas CB was unaffected by time. SB spent more time at very high velocity than other roles, independently from the time played. These findings provide valuable information about the physical demands of official soccer games and could be used to review training prescriptions.

Modelling the Flow Conditions and Primary Atomization of an Air-Core-Liquid-Ring (ACLR) Atomizer Using a Coupled Eulerian–Lagrangian Approach

AbstractThe Air-Core-Liquid-Ring atomizer is a pioneering internal-mixing pneumatic atomization technique designed for energy-efficient spray drying of highly viscous liquid feeds with substantial solid contents. However, it can suffer internal flow instabilities, which may lead to spray droplets with a wide variation in diameter. Experimental investigation of how flow conditions mechanistically determine the resulting droplet sizes is hindered by high velocities near the nozzle outlet. Therefore, this study addressed the issue by implementing a numerical model, employing a coupled Eulerian-Lagrangian approach with adaptive mesh refinement, to simulate the breakup of the liquid into ligaments and droplets. Additionally, Large Eddy Simulation was incorporated to replicate turbulent flow conditions observed in experiments. The numerical model demonstrated significant improvement in predicting liquid film thickness, compared to previous work. Additionally, the simulated droplet size distributions mirrored experimental trends, shifting to smaller sizes as pressure increased. Unfortunately, while reduced, there is a persistent underestimation of the lamella thickness and the droplet sizes at 0.2 MPa. In spite of this, the fact that the error propagates between the two phenomena underscores the effective coupling between Eulerian and Lagrangian approaches.

A possible relation between global CO excitation and massive molecular outflows in local ULIRGs

Local ultra-luminous infrared galaxies (ULIRGs) have been observed to host ubiquitous molecular outflows, including the most massive and powerful ever detected. These sources have also exceptionally excited global, galaxy-integrated CO ladders. A connection between outflows and molecular gas excitation has however never been established, since previous multi-J CO surveys were limited in spectral resolution and sensitivity and so they could only probe the global molecular gas conditions. In this work, we address this question using new, ground-based, sensitive heterodyne spectroscopy of multiple CO rotational lines (up to CO(7−6)) in a sample of 17 local ULIRGs. We used the Atacama Pathfinder Experiment (APEX) telescope to survey the CO(Jup ≥ 4) lines at a high signal-to-noise ratio, and complemented these data with CO(Jup ≤ 3) APEX and Atacama Large Millimeter Array (ALMA and ACA) observations presented in Montoya Arroyave et al. (2023, A&amp;A, 673, A13). We detected a total of 74 (out of 75) CO lines, with up to six transitions per source. The resulting CO spectral line energy distributions (SLEDs) show a wide range in gas excitation, in agreement with previous studies on ULIRGs. Some CO SLEDs peak at Jup ∼ 3, 4, which we classify as “lower excitation”, while others plateau or keep increasing up to the highest-J CO transition probed, and we classify these as “higher excitation”. Our analysis includes for completeness the results of CO SLED fits performed with a single large velocity gradient component, but our main focus is the investigation of possible links between global CO excitation and the presence of broad and/or high-velocity CO spectral components that can contain outflowing gas. We discovered an increasing trend of line width as a function of Jup of the CO transition, which is significant at the 4σ level and appears to be driven by the eight sources that we classified as higher excitation. We further analyzed such higher-excitation ULIRGs, by performing a decomposition of their CO spectral profiles into multiple components, and we derived CO ladders that are clearly more excited for the spectral components characterized by higher velocities and/or velocity dispersion. Because these sources are known to host widespread molecular outflows, we favor an interpretation whereby the highly excited CO-emitting gas in ULIRGs resides in galactic-scale massive molecular outflows whose emission fills a large fraction of the beam of our APEX high-J CO observations. On the other hand, our results challenge alternative scenarios for which the high CO excitation in ULIRGs can be explained by classical component of the interstellar medium, such as photon- or X-ray dominated regions around the nuclear sources.

Do galaxy mergers prefer under-dense environments?

Context. Galaxy mergers play a crucial role in galaxy evolution. However, the correlation between mergers and the local environment of galaxies is not fully understood. Aims. We aim to address the question of whether galaxy mergers prefer denser or less dense environments by quantifying the spatial clustering of mergers and non-mergers. We use two different indicators to classify mergers and non-mergers – classification based on a deep learning technique (f) and non-parametric measures of galaxy morphology, Gini-M20 (g). Methods. We used a set of galaxy samples in the redshift range 0.1 &lt; z &lt; 0.15 from the Galaxy and Mass Assembly (GAMA) survey with a stellar mass cut of log(M⋆/M⊙) &gt; 9.5. We measured and compared the two-point correlation function (2pCF) of the mergers and non-mergers classified using the two merger indicators f and g. We measured the marked correlation function (MCF), in which the galaxies were weighted by f to probe the environmental dependence of galaxy mergers. Results. We do not observe a statistically significant difference between the clustering strengths of mergers and non-mergers obtained using 2pCF. However, using the MCF measurements with f as a mark, we observe an anti-correlation between the likelihood of a galaxy being a merger and its environment. Our results emphasise the advantage of MCF over 2pCF in probing the environmental correlations. Conclusions. Based on the MCF measurements, we conclude that the galaxy mergers prefer to occur in the under-dense environments on scales &gt; 50 h−1 kpc of the large-scale structure (LSS). We attribute this observation to the high relative velocities of galaxies in the densest environments that prevent them from merging.

Inertial mixing of acoustically levitated droplets for time‐lapse protein crystallography

AbstractVarying the chemical consistency of acoustically levitated droplets opens up an in situ study of chemical and biochemical reactions in small volumes. However, the optimization of the mixing time and the minimization of the positional instability induced by solution dispensing are necessary for practical applications such as the study of the transient state of macromolecules crystallography during the ligand binding processes. For this purpose, we study the inertial mixing in a configuration compatible with the room‐temperature crystallography using the acoustic levitation diffractometer, therein solution drops ejected at high velocity collide and coalesce with droplets dispensed on acoustically levitated and rotating polymer thin‐film sample holders. With the proposed method, we are able to achieve the mixing time of ∼0.1 s for sub‐micro and a few microliter droplets. The observed short mixing time is ascribed to the rapid penetration of the solution into the droplets and confirmed by a computational fluid dynamic simulation. The demonstrated accelerated solution mixing is tested in a pilot time‐lapse protein crystallography experiment using the acoustic levitation diffractometer. The results indicate the detection of transient ligand binding state within 2 s after the solution dispensing, suggesting the feasibility of the proposed method for studying slow biochemical processes.

Exploring the Regimes of Particle Behavior upon Impact via the Discrete Element Method.

Discrete element method simulations are conducted to probe the various regimes of post-impact behavior of particles with solid surfaces. The impacting particles are described as spherical agglomerates consisting of smaller constituent (or primary) particles held together via surface adhesion. Under the influence of a wide range of impact velocities and particle surface energies, five distinct behavioral regimes-rebounding, vibration, fragmentation, pancaking, and shattering-are identified, and force transmission patterns are linked to post-impact behavior. In the rebounding regime, the coefficient of restitution decreases linearly as impact velocity increases and the particle agglomerate experiences compaction. In the fragmentation regime, rebound velocity generally decreases with increasing fragment size. The rebound velocity of fragments decreases with time except for the smallest fragments, which can increase in velocity due to collisions with other fragments of high velocity. Particle breakage in the pancaking regime does not follow common mechanistic models of breakage.

Investigation of equivalent spherical bubble diameter at high inlet velocity pool scrubbing conditions

This study investigates Equivalent Spherical Diameter (ESD) estimation at high inlet velocity pool scrubbing conditions using the Interfacial Area Transport Equation (IATE) diameter model including bubble-induced turbulence and interphase modeling. The compatibility of area-averaged Sauter Mean Diameter (SMD), area-averaged Local Equivalent Diameter (LED) and void-weighted area-averaged LED approaches to estimate the ESD are explored and the proposed model is validated against available experimental data. The study reveals that the prevalent constant ESD assumption in pool scrubbing codes is not universal by showcasing a decreasing trend along the column due to intensive bubble breakup. The area-averaged LED approach fails to capture this trend, while the area-averaged SMD and void-weighted area-averaged LED approaches provide accurate estimations aligned with experimental data. Turbulence parameters, interfacial forces, and diameter modeling are identified as crucial for accurate predictions of flow and geometrical variables by setting up the OpenFOAM framework. A sensitivity analysis indicates that the inlet velocity has an acceptable effect on the ESD along the column. The ESD increases near the exit and decreases in the swarm region by increasing the inlet velocities. Turbulent intensity reduces ESD across all column sections while changes in aspect ratio minimally impact ESD. The study shows promise in developing correlations that take into account the spatial variation of ESD in pool scrubbing conditions.