Direct Velocity Measurements Research Articles

Decay of bow thruster induced near-bed flow velocities at a vertical quay wall: A field measurement

During berthing operations of large vessels, the bow thruster jet deflecting on the quay wall and the bed can lead to high flow velocities near the bed. This may scour the bed when it is left unprotected, causing instability of the adjacent quay wall. Due to the complex flow field of the reflected jet, the decay in near-bed flow velocities perpendicular to the quay wall is unknown. This results in uncertainties in the design of bed protections, especially in the required width. In this research, the decay of the near-bed flow velocity perpendicular and parallel to the quay wall induced by a 4-channel bow thruster is studied. Field measurements have been conducted in the North Sea Port of Gent with one of the largest Dutch inland vessels. The near-bed flow velocities have been measured at multiple distances from the quay wall. For the flow velocity measurements four main parameters have been varied: the applied bow thruster power, quay wall clearance, number of thrusters, and the lateral distance between jet axis and measurement sensors. The highest flow velocities were measured near the quay wall, rapidly declining while moving away from the quay. Comparison of the measurement results to the Dutch and German guidelines generally leads to the conclusion that these guidelines are conservative. In addition, the dependency of the velocity on the total travelled distance by the jet as given in the Dutch method is not reflected in the measurement results. Furthermore, fundamentally different outcomes on the influence of the quay wall clearance on the near-bed flow velocity have been found. When the measured near-bed flow velocities are used as the sole input to calculate the required bed protection, significantly smaller rock sizes and asphalt mattress thickness would be necessary to withstand the hydraulic load of the jet in comparison to current guidelines. Further studies with different vessels and direct measurement of the efflux velocity of the thrusters are recommended.

Ex Ante Construction of Flow Pattern Maps for Pulsating Heat Pipes

A novel methodology is proposed for the development of empirical flow pattern maps for pulsating heat pipes (PHPs), which relies on the concept of virtual superficial velocity of the liquid and vapour phases. The virtual superficial velocity of each phase is defined using solely the design and operational parameters of the pulsating heat pipe, allowing the resulting flow pattern map to serve as a predictive instrument. This contrasts with existing flow pattern maps that necessitate direct measurements of temperatures and/or velocities within one or more channels of the pulsating heat pipe. Specifically, the virtual superficial velocities are derived from the relative significance of the driving forces and the resistances encountered by each phase during flow. The proposed methodology is validated using flow visualisation datasets obtained from two separate experimental campaigns conducted on flat-plate polypropylene pulsating heat pipe prototypes featuring transparent walls and meandering channels with three turns, five turns, seven turns, and eleven turns, respectively. The PHP prototypes were tested for gravity levels ranging between 0 g and 1 g and heat inputs ranging from 5 W to 35 W. The proposed approach enables the identification of empirical boundaries for flow pattern transitions as well as the establishment of an empirical criterion for start-up.

A pulsed power facility for studying the warm dense matter regime.

A pulsed power facility has been designed for studying the warm dense matter regime. It is based on the pulsed Joule heating technique, originally proposed by Korobenko and Rakhel [Int. J. Thermophy. 20, 1257 (1999)], where a 3.96µF capacitor bench is used for inducing a solid to plasma phase transition to metallic foils confined into a sapphire cell. The first experiments have been conducted on pure aluminum. Experimental data have been collected using electrical and optical diagnostics. Direct measurements of tension, current, pressure, and particle velocity allow us to evaluate the equation of state (EOS) and the DC conductivity of expanded aluminum. The results are compared to hydrodynamic simulations performed with various EOS models. As a result, collected data on aluminum highlight the relevance of our experimental procedure for improving EOS modeling in the warm dense matter regime.

Advancements in Key Parameters of Frequency-Modulated Continuous-Wave Light Detection and Ranging: A Research Review

As LiDAR technology progressively advances, the capability of radar in detecting targets has become increasingly vital across diverse domains, including industrial, military, and automotive sectors. Frequency-modulated continuous-wave (FMCW) LiDAR in particular has garnered substantial interest due to its efficient direct velocity measurement and excellent anti-interference characteristics. It is widely recognized for its significant potential within radar technology. This study begins by elucidating the operational mechanism of FMCW LiDAR and delves into its basic principles. It discuss, in depth, the influence of various parameters on FMCW LiDAR’s performance and reviews the latest progress in the field. This paper proposes that future studies should focus on the synergistic optimization of key parameters to promote the miniaturization, weight reduction, cost-effectiveness, and longevity of FMCW LiDAR systems. This approach aims at the comprehensive development of FMCW LiDAR, striving for significant improvements in system performance. By optimizing these key parameters, the goal is to promote FMCW LiDAR technology, ensuring more reliable and accurate applications in automated driving and environmental sensing.

Spatially-Resolved Freestream Velocity Measurements At The NASA Langley 31-Inch Mach 10 Air Tunnel Using FLEET

Freestream velocity measurements in the NASA Langley 31-inch Mach 10 wind tunnel are reported in this paper using Femtosecond Laser Electronic Excitation Tagging (FLEET). The freestream measurements acquired during the January 2023 test campaign were the first direct measurement of freestream velocity in this hypersonic wind tunnel facility. Spatial distributions of time-averaged and instantaneous velocity measurements were obtained at all three typical wind tunnel freestream unit Reynolds number conditions of Re∞ /L = 1800000 [1/m] , 3600000 [1/m], and 6400000 [1/m], though the current paper focuses on centerline measurements for the three Re∞ /L and spatial distributions for one Re∞ /L. Measured values for time-averaged velocity and mean of the instantaneous velocity at the wind tunnel centerline agree within 5 m/s or 0.4% of the calculated velocity from the facility data acquisition system. Measurements acquired at locations away from the wind tunnel centerline reveal the spatial extent of the core flow of the hypersonic facility.

Investigating Temporal Characteristics of Polarimetric and Electrical Signatures in Three Severe Storms: Insights from the VORTEX-Southeast Field Campaign

Abstract The dual-polarization radar characteristics of severe storms are commonly used as indicators to estimate the size and intensity of deep convective updrafts. In this study, we track rapid fluctuations in updraft intensity and size by objectively identifying polarimetric fingerprints such as ZDR and KDP columns, which serve as proxies for mixed-phase updraft strength. We quantify the volume of ZDR and KDP columns to evaluate their utility in diagnosing temporal variability in lightning flash characteristics. Specifically, we analyze three severe storms that developed in environments with low-to-moderate instability and strong 0–6-km wind shear in northern Alabama during the 2016–17 VORTEX-Southeast field campaign. In these three cases (a tornadic supercell embedded in stratiform precipitation, a nontornadic supercell, and a supercell embedded within a quasi-linear convective system), we find that the volume of the KDP columns exhibits a stronger correlation with the total flash rate. The higher covariability of the KDP column volume with the total flash rate suggests that the overall electrification and precipitation microphysics were dominated by cold cloud processes. The lower covariability with the ZDR column volume indicates the presence of nonsteady updrafts or a less prominent role of warm rain processes in graupel growth and subsequent electrification. Furthermore, we observe that the majority of cloud-to-ground (CG) lightning strikes a carried negative charge to the ground. In contrast to findings from a tornadic supercell over the Great Plains, lightning flash initiations in the Alabama storms primarily occurred outside the footprint of the ZDR and KDP column objects. Significance Statement This study quantifies the correlation between mixed-phase updraft intensity and total lightning flash rate in three severe storms in northern Alabama. In the absence of direct updraft velocity measurements, we use polarimetric signatures, such as ZDR and KDP columns, as proxies for updraft strength. Our analysis of polarimetric radar and lightning mapping array data reveals that the lightning flash rate is more highly correlated with the KDP column volume than with the ZDR column volume in all three storms examined. This contrasts with previous findings in storms over the central Great Plains, where the ZDR column volume showed higher covariability with flash rate. Interestingly, lightning initiation in the Alabama storms mainly occurred outside the ZDR and KDP column areas, contrary to previous findings.

Backaction-evading receivers with magnetomechanical and electromechanical sensors

Today's mechanical sensors are capable of detecting extremely weak perturbations while operating near the standard quantum limit. However, further improvements can be made in both sensitivity and bandwidth when we reduce the noise originating from the process of measurement itself—the quantum-mechanical backaction of measurement—and go below this ‘standard’ limit, possibly approaching the Heisenberg limit. One of the ways to eliminate this noise is by measuring a quantum nondemolition variable such as the momentum in a free-particle system. Here, we propose and characterize theoretical models for direct velocity measurement that utilize traditional electric and magnetic transducer designs to generate a signal while enabling this backaction evasion. We consider the general readout of this signal via electric or magnetic field sensing by creating toy models analogous to the standard optomechanical position-sensing problem, thereby facilitating the assessment of measurement-added noise. Using simple models that characterize a wide range of transducers, we find that the choice of readout scheme—voltage or current—for each mechanical detector configuration implies access to either the position or velocity of the mechanical subsystem. This in turn suggests a path forward for key fundamental physics experiments such as the direct detection of dark matter particles. Published by the American Physical Society 2024

Sensitivity analysis of S waves and their velocity measurement in slow formations from monopole acoustic logging while drilling

Monopole acoustic logging while drilling (LWD) enables the direct measurement of S-wave velocity in slow formations, which has been corroborated by recent theoretical and experimental studies. However, this measurement is hampered by the weakness of the S-wave signal and the lack of techniques to amplify it. To address this challenge, we analytically compute the monopole LWD wavefields, considering centralized and off-center tools in various slow formations. Modeling analysis reveals that four parameters primarily influence the excitation of the formation S wave: the formation S-wave velocity, the source-to-receiver distance, the radial distance from the receiver to the wellbore, and the source frequency. S-wave signals can be enhanced by judiciously optimizing these parameters during tool design. Furthermore, our research suggests that the S-wave velocity can be accurately extracted through the slowness-time correlation method only when formation S-wave velocities are in a suitable range. This is because an overly high S-wave velocity causes shear arrivals to interfere with the inner Stoneley mode, whereas an ultraslow formation S-wave velocity results in S-wave signals too faint to detect. For the LWD model with an off-center tool, simulations demonstrate that tool eccentricity, especially large eccentricity, can amplify the S wave and improve its measurement accuracy, provided that waveforms received in the direction of tool movement are used. In a very slow formation, we successfully extract the S-wave velocity from synthetic full wave data at that azimuth under conditions of large eccentricity, a task not achievable with a centralized instrument.

Predicting capillary vessel network hemodynamics in silico by machine learning.

Blood velocity and red blood cell (RBC) distribution profiles in a capillary vessel cross-section in the microcirculation are generally complex and do not follow Poiseuille's parabolic or uniform pattern. Existing imaging techniques used to map large microvascular networks in vivo do not allow a direct measurement of full 3D velocity and RBC concentration profiles, although such information is needed for accurate evaluation of the physiological variables, such as the wall shear stress (WSS) and near-wall cell-free layer (CFL), that play critical roles in blood flow regulation, disease progression, angiogenesis, and hemostasis. Theoretical network flow models, often used for hemodynamic predictions in experimentally acquired images of the microvascular network, cannot provide the full 3D profiles either. In contrast, such information can be readily obtained from high-fidelity computational models that treat blood as a suspension of deformable RBCs. These models, however, are computationally expensive and not feasible for extension to the microvascular network at large spatial scales up to an organ level. To overcome such limitations, here we present machine learning (ML) models that bypass such expensive computations but provide highly accurate and full 3D profiles of the blood velocity, RBC concentration, WSS, and CFL in every vessel in the microvascular network. The ML models, which are based on artificial neural networks and convolution-based U-net models, predict hemodynamic quantities that compare very well against the true data but reduce the prediction time by several orders. This study therefore paves the way for ML to make detailed and accurate hemodynamic predictions in spatially large microvascular networks at an organ-scale.

Merger-driven multiscale ICM density perturbations: testing cosmological simulations and constraining plasma physics

ABSTRACT The hot intracluster medium (ICM) provides a unique laboratory to test multiscale physics in numerical simulations and probe plasma physics. Utilizing archival Chandra observations, we measure density fluctuations in the ICM in a sample of 80 nearby (z ≲ 1) galaxy clusters and infer scale-dependent velocities within regions affected by mergers (r < R2500c), excluding cool-cores. Systematic uncertainties (e.g. substructures, cluster asymmetries) are carefully explored to ensure robust measurements within the bulk ICM. We find typical velocities ∼220 (300) km s−1 in relaxed (unrelaxed) clusters, which translate to non-thermal pressure fractions ∼4 (8) per cent, and clumping factors ∼1.03 (1.06). We show that density fluctuation amplitudes could distinguish relaxed from unrelaxed clusters in these regions. Comparison with density fluctuations in cosmological simulations shows good agreement in merging clusters. Simulations underpredict the amplitude of fluctuations in relaxed clusters on length scales <0.75 R2500c, suggesting these systems are most sensitive to ‘missing’ physics in the simulations. In clusters hosting radio haloes, we examine correlations between gas velocities, turbulent dissipation rate, and radio emission strength/efficiency to test turbulent re-acceleration of cosmic ray electrons. We measure a weak correlation, driven by a few outlier clusters, in contrast to some previous studies. Finally, we present upper limits on effective viscosity in the bulk ICM of 16 clusters, showing it is systematically suppressed by at least a factor of 8, and the suppression is a general property of the ICM. Confirmation of our results with direct velocity measurements will be possible soon with XRISM.

Real-time Experimental Demonstrations of a Photonic Lantern Wave-front Sensor

The direct imaging of an Earth-like exoplanet will require sub-nanometric wave-front control across large light-collecting apertures to reject host starlight and detect the faint planetary signal. Current adaptive optics systems, which use wave-front sensors that reimage the telescope pupil, face two challenges that prevent this level of control: non-common-path aberrations, caused by differences between the sensing and science arms of the instrument; and petaling modes: discontinuous phase aberrations caused by pupil fragmentation, especially relevant for the upcoming 30 m class telescopes. Such aberrations drastically impact the capabilities of high-contrast instruments. To address these issues, we can add a second-stage wave-front sensor to the science focal plane. One promising architecture uses the photonic lantern (PL): a waveguide that efficiently couples aberrated light into single-mode fibers (SMFs). In turn, SMF-confined light can be stably injected into high-resolution spectrographs, enabling direct exoplanet characterization and precision radial velocity measurements; simultaneously, the PL can be used for focal-plane wave-front sensing. We present a real-time experimental demonstration of the PL wave-front sensor on the Subaru/SCExAO testbed. Our system is stable out to around ±400 nm of low-order Zernike wave-front error and can correct petaling modes. When injecting ∼30 nm rms of low-order time-varying error, we achieve ∼10× rejection at 1 s timescales; further refinements to the control law and lantern fabrication process should make sub-nanometric wave-front control possible. In the future, novel sensors like the PL wave-front sensor may prove to be critical in resolving the wave-front control challenges posed by exoplanet direct imaging.

Expansion and ongoing cosmic ray acceleration in HESS J1731−347

Diffusive shock acceleration in supernova remnants (SNRs) is considered one of the prime mechanisms of galactic cosmic ray (GCR) acceleration. It is still unclear, however, whether SNRs can contribute to the GCR spectrum up to the “knee” (1 PeV) band as acceleration to such energies requires an efficient magnetic field amplification process around the shocks. The presence of such a process is challenging to test observationally. Here, we report on the detection of fast variability in the X-ray synchrotron emission from the forward shock in the SNR HESS J1731−347, which implies the presence of a strong (∼0.2 mG) field exceeding background values, and thus of effective field amplification. We also report a direct measurement of the high forward shock expansion velocity of 4000–5500 km s−1, confirming that the SNR is expanding in a tenuous wind bubble blown by the SNR progenitor, is significantly younger (2.4–9 kyr) than previously assumed by some authors, and only recently started interacting with the dense material outside of the bubble. We finally conclude that there is strong evidence for ongoing hadronic GCR acceleration in this SNR.

Dynamic Structure of Eddies of the Brazil‐Malvinas Confluence Zone Revealed by Direct Measurements and Satellite Altimetry

AbstractThe goal of this work is to study the dynamical structure of eddies of the Brazil‐Malvinas Confluence zone (BMC eddies) using direct velocity measurements carried out by Shipborne Acoustic Doppler Current Profiler during five oceanographic cruises performed in 2016–2022. In total, in situ data of 13 BMC eddies, including nine anticyclones and four cyclones are available. These data show that the orbital velocity in such eddies can reach 189 cm/s and their vertical structure is highly barotropic. In several eddies, the velocities exceeding 100 cm/s are observed down to a depth of 560 m and at a depth of 800 m they are still higher than 80 cm/s. The spatial structure of velocity and horizontal shear in the eddies is strongly asymmetric, with higher velocities in the southern part near the intense thermohaline BMC front. Altimetry data show qualitative agreement with in situ data, but underestimate the horizontal velocity shear and the maximum velocities at the periphery of the BMC eddies. We also use satellite altimetry and Argo float measurements to study these eddies, and estimate their impact on the thermohaline structure. The analysis shows that the eddies with orbital velocities exceeding 100 cm/s cause intense temperature and salinity anomalies reaching 7–9°C and 1 psu in anticyclones and −4°C and 0.8 psu in cyclones at 100–300 m depth.

Inferring damage state and evolution with increasing stress using direct and coda wave velocity measurements in faulted and intact granite samples

SUMMARY A better understanding of damage accumulation before dynamic failure events in geological material is essential to improve seismic hazard assessment. Previous research has demonstrated the sensitivity of seismic velocities to variations in crack geometry, with established evidence indicating that initial crack closure induces rapid changes in velocity. Our study extends these findings by investigating velocity changes by applying coda wave interferometry (CWI). We use an array of 16 piezoceramic transducers to send and record ultrasonic pulses and to determine changes in seismic velocity on intact and faulted Westerly granite samples. Velocity changes are determined from CWI and direct phase arrivals. This study consists of three sets of experiments designed to characterize variations in seismic velocity under various initial and boundary conditions. The first set of experiments tracks velocity changes during hydrostatic compression from 2 and 191 MPa in intact Westerly granite samples. The second set of experiments focuses on saw-cut samples with different roughness and examines the effects of confining pressure increase from 2 to 120 MPa. The dynamic formation of a fracture and the preceding damage accumulation is the focus of the third type of experiment, during which we fractured an initially intact rock sample by increasing the differential stress up to 780 MPa while keeping the sample confined at 75 MPa. The tests show that: (i) The velocity change for rough saw cut samples suggests that the changes in bulk material properties have a more pronounced influence than fault surface apertures or roughness. (ii) Seismic velocities demonstrate higher sensitivity to damage accumulation under increasing differential stress than macroscopic measurements. Axial stress measured by an external load cell deviates from linearity around two-third through the experiment at a stress level of 290 MPa higher than during the initial drop in seismic velocities. (iii) Direct waves exhibit strong anisotropy with increasing differential stress and accumulating damage before rock fracture. Coda waves, on the other hand, effectively average over elastic wave propagation for both fast and slow directions, and the resulting velocity estimates show little evidence for anisotropy. The results demonstrate the sensitivity of seismic velocity to damage evolution at various boundary conditions and progressive microcrack generation with long lead times before dynamic fracture.

Unveiling the contourite depositional system in the Vema Fracture Zone (Central Atlantic)

A combination of a high sediment input and intense bottom currents often leads to the formation of contourites (sediments deposited or significantly reworked by bottom currents). Both of these components are present in the Vema Fracture Zone valley which is the most important passageway for the distribution of the Antarctic Bottom Water from the West to the North-East of the Atlantic. However, no contourite drifts, moats or contourite channels have been found in this region in more than half a century of research. The prevailing sedimentation paradigm postulates that turbidity currents have predominantly governed sedimentation in this region during the Pleistocene. This work describes the first example of contourite depositional system identified in the Vema Fracture Zone. The discovery was made through detailed high-resolution sub-bottom profiling, as well as numerical modeling and direct measurements of bottom current velocities. Such systems are exceptionally uncommon in fracture zones. This study highlights the importance of further research of contourites along the Vema Fracture Zone based on modern concepts of contourite and mixed depositional systems. The work also emphasizes the need to reevaluate the impact of bottom currents on sedimentation in this region, and particularly in the narrow segments of the fracture zone valley.

Measuring the hot ICM velocity structure function using XMM–Newton observations

ABSTRACT It has been shown that the gas velocities within the intracluster medium (ICM) can be measured by applying the novel XMM–Newton EPIC-pn energy scale calibration, which uses instrumental Cu Kα as reference for the line emission. Using this technique, we have measured the velocity distribution of the ICM for clusters involving AGN feedback and sloshing of the plasma within the gravitational well (Virgo and Centaurus) and a relaxed one (Ophiuchus). We present a detailed study of the kinematics of the hot ICM for these systems. First, we compute the velocity probability distribution functions (PDFs) from the velocity maps. We find that for all sources, the PDF follows a normal distribution, with a hint of a multimodal distribution in the case of Ophiuchus. Then, we compute the velocity structure function (VSF) for all sources in order to study the variation with scale as well as the nature of turbulence in the ICM. We measure a turbulence driving scale of ∼10–20 kpc for the Virgo cluster, while the Ophiuchus cluster VSF reflects the absence of strong interaction between the ICM and a powerful Active Galactic Nucleus (AGN) at such spatial scales. For the former, we compute a dissipation time larger than the jet activity cycle, thus indicating that a more efficient heating process than turbulence is required to reach equilibrium. This is the first time that the VSF of the hot ICM has been computed using direct velocity measurements from X-ray astronomical observations.

Strong effect of liquid Fe–S on elastic wave velocity of olivine aggregate: Implication for the low velocity anomaly at the base of the lunar mantle

The origin of the seismic low velocity zone (LVZ) observed at the base of the lunar mantle is important for understanding the nature of the lunar mantle. Liquid Fe–S is considered as a possible candidate of the cause of the LVZ. However, effect of liquid Fe–S on elastic wave velocity of mantle rock has been considered to be minor, according to theoretical estimation based on the high dihedral angle of liquid Fe–S in olivine aggregate observed in previous microstructural analysis of polished sample cross sections. Here we carry out direct measurements of elastic wave velocities of liquid Fe–S-bearing olivine aggregate and report strong reduction of the elastic wave velocities in the presence of liquid Fe–S. The effects of liquid Fe–S in olivine aggregates are much more pronounced than the theoretical estimation. Three-dimensional X-ray microtomography analysis reveals that the geometry of liquid Fe–S strongly depends on the size, with larger liquid Fe–S blobs having low aspect ratios, which may predominantly affect elastic wave velocity. Since smaller spherical Fe–S blobs are much more abundant than the larger elongated blobs, conventional dihedral angle analyses based on scanning electron microscope images tend to statistically over-sample smaller blobs and under-sample larger blobs. Our results suggest that the LVZ at the base of the lunar mantle can be explained by the presence of 4.3–5.0 vol.% liquid Fe–S. The LVZ may be a hidden reservoir of highly siderophile elements (HSEs), which may explain the low abundance of HSEs in the lunar mantle compared to the Earth.

The evolution of fast turbulent deflagrations to detonations

We use advanced experimental techniques to explore turbulence-induced deflagration-to-detonation transition (tDDT) in hydrogen–air mixtures. We analyze the full sequence of turbulent flame evolution from fast deflagration-to-detonation using simultaneous direct measurements of pressure, turbulence, and flame, shock, and flow velocities. We show that fast turbulent flames that accelerate and develop shocks are characterized by turbulent flame speeds that exceed the Chapman–Jouguet deflagration speed in agreement with the tDDT theory and direct numerical simulation (DNS) results. Velocity and pressure evolutions are provided to detail the governing mechanisms that drive turbulent flame acceleration. Turbulent flame speeds and fluctuations are examined to reveal flow field characteristics of the tDDT process. This work contributes to the understanding of fundamental mechanisms responsible for spontaneous initiation of detonations by fast turbulent flames.

Finite velocity of ECG signal propagation: preliminary theory, results of a pilot experiment and consequences for medical diagnosis

A satisfactory model of the biopotentials propagating through the human body is essential for medical diagnostics, particularly for cardiovascular diseases. In our study, we develop the theory, that the propagation of biopotential of cardiac origin (ECG signal) may be treated as the propagation of low-frequency endogenous electromagnetic wave through the human body. We show that within this approach, the velocity of the ECG signal can be theoretically estimated, like for any other wave and physical medium, from the refraction index of the tissue in an appropriate frequency range. We confirm the theoretical predictions by the comparison with a direct measurement of the ECG signal propagation velocity and obtain mean velocity as low as v=1500 m/s. The results shed new light on our understanding of biopotential propagation through living tissue. This propagation depends on the frequency band of the signal and the transmittance of the tissue. This finding may improve the interpretation of the electric measurements, such as ECG and EEG when the frequency dependence of conductance and the phase shift introduced by the tissue is considered. We have shown, that the ECG propagation modifies the amplitude and phase of signal to a considerable extent. It may also improve the convergence of inverse problem in electrocardiographic imaging.

Indirect measurements of gas velocities in galaxy clusters: effects of ellipticity and cluster dynamic state

ABSTRACT While awaiting direct velocity measurements of gas motions in the hot intracluster medium, we rely on indirect probes, including gas perturbations in galaxy clusters. Using a sample of ∼80 clusters in different dynamic states from Omega500 cosmological simulations, we examine scaling relations between the fluctuation amplitudes of gas density, δρ/ρ, pressure, δP/P, X-ray surface brightness, Sunyaev–Zel’dovich (SZ) y-parameter, and the characteristic Mach number of gas motions, M1d. In relaxed clusters, accounting for halo ellipticities reduces δρ/ρ or δP/P by a factor of up to 2 within r500c. We confirm a strong linear correlation between δρ/ρ (or δP/P) and M1d in relaxed clusters, with the proportionality coefficient η ≈ 1. For unrelaxed clusters, the correlation is less strong and has a larger η ≈ 1.3 ± 0.5 (1.5 ± 0.5) for δρ/ρ (δP/P). Examination of the M1d − δρ/ρ relation shows that it is almost linear for relaxed clusters, while for the unrelaxed ones, it is closer to $\delta \rho /\rho \propto M_{\rm 1d}^2$. In agreement with previous studies, we observe a strong correlation of M1d with radius. Correcting for these correlations leaves a residual scatter in M1d of ∼4(7) per cent for relaxed (perturbed) clusters. Hydrostatic mass bias correlates with M1d as strongly as with δρ/ρ in relaxed clusters. The residual scatters after correcting for derived trends is ∼6−7 per cent. These predictions can be verified with existing X-ray and SZ observations of galaxy clusters combined with forthcoming velocity measurements with X-ray microcalorimeters.