Velocity Region Research Articles

Flow Visualization on Submerged Flow Conditions in Open Channel Weir Downstream

Submerged flow regimes are common phenomena observed in open channel flow, such as rivers and spillways, with or without weirs. These flow regimes involve a sudden rise in the liquid surface downstream when high-velocity liquid discharges into a region of lower velocity. The rapid deceleration of the flowing liquid results in an increase in height and a conversion of kinetic energy into potential energy, with some energy dissipated as turbulence and heat. In this study, flow visualization techniques were employed to investigate the two-dimensional hydrodynamic characteristics of submerged hydraulic jumps within the Froude number range of 1.0 to 5.4 over a fixed bed. The obtained results were compared with existing literature data, showing a good agreement. This research contributes to the understanding of submerged flow phenomena and provides valuable insights into the hydrodynamics of submerged hydraulic jumps.

The Effect of Spatial Velocity Gradients on Block-Matching Accuracy for Ultrasound Velocimetry

Block matching serves as the foundation for ultrasound velocimetry techniques such as blood speckle tracking and echo-particle image velocimetry. Any spatial velocity gradients (SVGs) inside a block-matching pair will result in tracking error, due to both the finite block size and the ultrasound point-spread-function. We assess, using an in silico sinusoidal flow phantom, the effect of SVG magnitude and beam-to-flow angle on block-matching bias and precision. Secondarily we assess the effect that SVGs have on velocimetry bias when using angled plane-wave compounding. The magnitude and angle of SVGs were varied by adjusting the wavelength and direction of a sinusoidal flow profile. Scatterers displaced by this flow profile were used for simulating ultrasound radio frequency data at discrete time points. After beamforming, the 2-D flow field was estimated using block matching. Two imaging sequences were tested, a single plane-wave and a three-angled plane-wave. Smaller sinusoidal flow wavelengths resulted in increased bias and reduced precision, revealing an inverse relationship between sinusoidal flow wavelength and tracking error, with median errors ranging from 69%-90% for the smallest flow wavelengths (highest SVGs) down to 3%-5% for the largest (lowest SVGs). The SVG angle was also important, in which lateral SVGs (with axially oriented flows) resulted in significant speckle decorrelation and high tracking errors in regions with high SVGs. Conversely, axial SVGs (laterally oriented flow) experienced higher bias in the peak velocity regions of the flow profile. Coherent compounding resulted in higher velocity errors than using a single transmission for lateral SVGs but not for axial SVGs. The highest SVGs that could be measured with ≤10% error was when the sinusoidal flow wavelength was less than 20 times the ultrasound pulse wavelength. The clinical significance is that the high SVGs present in high kinetic energy flows, such as severe carotid stenosis and aortic regurgitation, will limit the ability to accurately quantify the velocities in these flow structures.

Numerical simulation of virus-laden aerosol transmission in real human respiratory airways

In this study, the transport of virus-laden aerosols in real human airways is investigated through numerical simulations. Three different breathing modes (nasal, oral, and nasal–oral) are studied to analyze the behavior of the particle deposition in the respiratory airways of humans through realistic anatomical models. Increasing the flow rate typically leads to the augmentation of velocity profiles, turbulence, and pressure changes, specifically expanding the high velocity regions in the pharynx, larynx, and trachea. As a result, the deposition fractions of the total number of aerosols deposited in these regions increase, while a decrease in aerosol deposition is observed in the nasal and oral cavities. For the effects of increasing particle sizes, 2–10 μm particles exhibit a higher degree of clustering in the trachea for the nasal mode, in the larynx for the oral mode, and in the trachea for the nasal–oral mode, compared to the clustering of 1–10 μm particles. Considering the high deposition fraction in the upper airway regions, which are the primary factors contributing to the easy transmission of the virus through casual talking and coughing, the results demonstrate that the highest deposition fraction, exceeding 85%, is observed in the nasal mode with small aerosols ranging from 1 to 2 μm in diameter, and at the lowest flow rate of 15 LPM. In the lower airway regions, targeted drug delivery with the highest deposition fraction in the bronchial regions can be a solution for reducing respiratory diseases, such as asthma and chronic obstructive pulmonary disease, which are caused by inflammatory conditions in the bronchi.

Optimization of Vibrating Mesh Nebulizer Air Inlet Structure for Pulmonary Drug Delivery

The vibrating mesh nebulizer (VMN) has gained popularity for its compactness and noiselessness. This study investigates the impact of different air inlet structures on the deposition fraction (DF) of droplets generated by VMNs in an idealized mouth–throat (MT) airway model. Three homemade VMNs with semi-circular inlet, symmetrical four-inlet, and multiple-orifice inlet structures were evaluated through simulations and experiments. The changes in droplet DF of 0.9% w/v concentration of nebulized sodium chloride (NaCl) droplets as a function of inertial parameters were acquired under different inhalation flow conditions. Additionally, flow field distributions in models with different inlet structures were analyzed at a steady inspiratory flow rate of 15 L/min. The results indicate that optimizing the VMN’s air inlet structure significantly enhances droplet delivery efficiency. The multiple–orifice inlet structure outperformed the other designs, directing the airflow from the inlet position to the center of the mouthpiece and then into the oral cavity, achieving a DF of up to 20% at an inhalation flow rate of 15 L/min. The region of high airflow velocity between the mouthpiece and oral cavity proved to be a favorable VMN inlet optimization, reducing direct droplet–wall collisions and improving delivery efficiency. These findings offer insights for VMN design and optimization to enhance pulmonary drug delivery effectiveness and therapeutic outcomes.

Investigating 3-D Effects on Flashing Cryogenic Jets with Highly Resolved LES

For the development of upper stage rocket engines with laser ignition, the transition of oxidizer and fuel from the pure cryogenic liquid streams to an ignitable mixture needs to be better understood. Due to the near vacuum conditions that are present at high altitudes and in space, the injected fuel rapidly atomizes in a so-called flash boiling process. To investigate the behavior of flashing cryogenic jets under the relevant conditions, experiments of liquid nitrogen have been performed at the DLR Lampoldshausen. The experiments are accompanied by a series of computer simulations and here we use a highly resolved LES to identify 3D effects and to better interpret results from the experiments and existing 2D RANS. It is observed that the vapor generation inside the injector and the evolution of the spray in the combustion chamber differ significantly between the two simulation types due to missing 3D effects and the difference in resolution of turbulent structures. Still, the observed 3D spray dynamics suggest a suitable location for laser ignition that could be found in regions of relative low velocity and therefore expected low strain rates. Further, measured droplet velocities are compared to the velocities of notional Lagrangian particles with similar inertia as the measured droplets. Good agreement between experiments and simulations exists and strong correlation between droplet size and velocity can be demonstrated.

Magnetic resonance velocity imaging of turbulent gas flow in a packed bed of catalyst support pellets

Compressed sensing magnetic resonance methods have been used to image the time-averaged velocity and turbulent kinetic energy in 3D for turbulent gas flowing through a bed of porous, hollow cylindrical catalyst support pellets. Velocity and turbulent kinetic energy images were acquired at a spatial resolution of 0.70 mm (x) × 0.70 mm (y) × 1.0 mm (z) for particle Reynolds numbers, Rep, of 500, 2500 and 6500 in a bed with a tube-to-particle diameter ratio of 4.7. These data represent the first full-field measurements of turbulent gas flow in packed beds of non-spherical pellets. The resulting images reveal several interesting features of the hydrodynamics in this system. A large degree of flow heterogeneity is observed in the bed, with regions of high-speed fluid observed near the walls and in large voids, and regions of backflow observed in the wake of pellets, between pellets, and within the pellet holes. For increasing Rep, the normalized axial velocity at the wall is found to increase, and the normalized turbulent kinetic energy becomes more homogeneous throughout the bed. The correlation between the turbulent kinetic energy and time-averaged velocity shows that the highest turbulent kinetic energy occurs in regions of intermediate time-averaged velocity. Further, the turbulent kinetic energy profile at the pellet-scale is substantially different from the case of simple channel flow for Rep≥ 2500. Overall, these measurements clearly demonstrate the ability of magnetic resonance methods for acquiring full-field flow data in packed bed systems using commercially-relevant pellets and flow conditions.

Lab- and pilot- scale evaluation of bacterial inactivation and reactivation influenced by UV-LEDs arrangements in continuous flow water disinfection reactors

In the recent years, UV-LED has emerged as an alternative UV source due to its distinguish advantages. One of the primary benefits of UV-LEDs is their ability to facilitate fine-tuned regulation of UV radiation utilization in disinfection systems, which could increase the effective UV fluence in the reactor and thus improve the disinfection efficiency compared with conventional UV disinfection devices. This study evaluated the inactivation and reactivation performance of continuous flow UV-LED (265 nm) disinfection reactor with four different designs of UV-LEDs arrangement under both lab- and pilot- scale testing conditions. Lab-scale tests showed that UV-LEDs at the outlet position delivered a much higher E.coli disinfection efficiency compared with other three arrangements (UV-LEDs at inlet, center, and separated positions) under various of UV-LED outputs and flowrates. Mechanisms analysis indicated that the improved disinfection efficiency was because UV radiation was applied to the lower velocity region in the reactor, leading to a longer effective UV exposure time and thus a higher UV fluence generated. Sub-germicidal levels of UV irradiation prior to the high UV fluence region could also improve the overall disinfection efficiency for separated and outlet arrangement, with synergy values of 0.21 log (16.6 % of overall log reduction) and 0.53 log (21.4 % of overall log reduction) generated. The reactivation experiments showed that the inlet arrangement led to the highest photo repair rates. Dark repair was not affected by the different UV-LEDs arrangement due to the relatively slow dark repair rates. The key findings in the lab-scale tests were then validated in a small-scale (Total flowrate was 13.3 L/min) recirculatory aquaculture system (RAS) system for shrimp farming. The inactivation and reactivation results under pilot-scale tests were consistent with the lab-scale testing results, showing that UV-LEDs at outlet position provided an average total bacteria disinfection efficiency of 1.84 logs in an 8 week testing period, which was more than twice of that for the inlet position. After disinfection, samples from the outlet arrangement also exhibited at least 26.5 % less photoreactivation percentage compared with that when LEDs were at the inlet position. These findings proposed an optimal design of UV-LEDs arrangement for UV disinfection reactors and verified this design in pilot-scale testing condition. This information is important for future optimizations of UV LED disinfection system design.

Dynamics of polaron formation in 1D Bose gases in the strong-coupling regime

We discuss the dynamics of the formation of a Bose polaron when an impurity is injected into a weakly interacting one-dimensional Bose condensate. While for small impurity-boson couplings this process can be described within the Froehlich model as generation, emission and binding of Bogoliubov phonons, this is no longer adequate if the coupling becomes strong. To treat this regime we consider a mean-field approach beyond the Froehlich model which accounts for the backaction to the condensate, complemented with Truncated Wigner simulations to include quantum fluctuation. For the stationary polaron we find a periodic energy-momentum relation and non-monotonous relation between impurity velocity and polaron momentum including regions of negative impurity velocity. Studying the polaron formation after turning on the impurity-boson coupling quasi-adiabatically and in a sudden quench, we find a very rich scenario of dynamical regimes. Due to the build-up of an effective mass, the impurity is slowed down even if its initial velocity is below the Landau critical value. For larger initial velocities we find deceleration and even backscattering caused by emission of density waves or grey solitons and subsequent formation of stationary polaron states in different momentum sectors. In order to analyze the effect of quantum fluctuations we consider a trapped condensate to avoid 1D infrared divergencies. Using Truncated Wigner simulations in this case we show under what conditions the influence of quantum fluctuations is small.

Experimental test, numerical analysis and thermal calculation modeling of hundreds kWth-class supercritical CO2 fossil-fired boiler system

Boiler is one of the important parts for supercritical CO2 (S–CO2) power system. Currently, most studies are based on theoretical calculations and lack experimental validation. Besides, low flue gas temperature and high wall temperature significantly enhance convection heat transfer (CHT), resulting in the failure possibility of existing thermal calculation models (neglect CHT). This study aims to construct a thermal calculation model suitable for S–CO2 boiler. Firstly, the hundreds kWth-class S–CO2 diesel/coal-fired boiler system was built, and steady-state experiments were carried out. Secondly, to further evaluate CHT, a numerical model was established, and the reliability of simulation was verified. The results indicate that the proportion of CHT can reach 44.52%. The entrainment effect caused by high-speed jet leads to a negative velocity region near the cooling wall. Furthermore, there are velocity disturbances of non-mainstream direction near the cooling wall. These two lead to great enhancement of CHT. According to the above analysis, a proposed thermal calculation model (DCTCM-1D) considering CHT and wall temperature was constructed. Compared to existing models, DCTCM-1D has the lowest error, with the root mean square error of flue gas temperature, heat load, wall temperature and S–CO2 temperature being 22.54 °C, 0.94 kW/m2, 6.40 °C and 2.29 °C.

The Application of OpenFOAM in Modelling Flow for Vegetated Channel

Vegetation plays an important role in the hydrodynamic behaviour of an open channel flow. This study attempted to investigate the flow characteristics of an emergent vegetated channel using Open-source Operations and Manipulation (OpenFOAM). InterFoam is an OpenFOAM solver used to model this simulation. It is one of the methods available to model free-flow surface flow. Results for flow velocity profile can be generated using ParaView software. This study used a constant inlet velocity of 0.0417 m/s. There are two sets of models including model L8 with a solid volume fraction (SVF) of 8% using 9 rigid dowels, and model 4S with SVF of 4% using 17 dowels within a 1.2 m2 study area. Dowels in L8 are arranged in linear formation compared to the 4S model in a staggered arrangement. The study found that in model 4S, the stem-scale vortices are developed individually after each dowel due to sparse staggered vegetation. Meanwhile, model 8L suggests oppositely the vortex is cramped from the closeness of the dowels. The shear layer is formed as the flow enters the vegetation patch at upstream and the instability causes the shear layer vortices between inside and outside the vegetation region. Both models agreed that as the flow moves downstream the vortices are greater and make the streamwise velocity region become slower. The vertical velocity profile acknowledges the shear layer patch-scale vortices have a greater influence on the flow of both models. The magnitude of turbulence intensity in lateral directions is bigger in model 4S than in model 8L. The influence of vortices shed by upstream cylinders has an increasing impact on the irregular shedding behaviour of downstream cylinders as plant density increases. In general, the TKE values of the Model 4S are higher than those of the Model 8L. Regardless of the solid volume percentage difference, the vegetation pattern between linear and staggered has an effect on the flow. Computational Fluid Dynamic (CFD) is indeed capable to solve complex hydrodynamic characteristics.

Effect of non-uniform incoming flow on the mixing enhancement in a scramjet cavity combustor

Mixing in the combustion chamber is influenced by the velocity distribution of the inlet airflow. Numerical simulations are carried out by using the 3D coupled implicit Reynolds-averaged Navier-Stokes (RANS) equations and the SST k-ω turbulence model. This article compares the flow field characteristics of non-uniform flows with uniform flows. The results show that the penetration depth increases by 22% in the case of a decreasing velocity distribution along the longitudinal direction compared to the increasing velocity condition. The difference in total pressure loss compared to uniform flow is greater than 4%. The mixing coefficient in the cavity is only 81% of uniform flow. The two-hole jet flow approach is able to rapidly reach 90%. The study shows that the non-uniform inlet has a considerable impact on fuel mixing. The high velocity region near the jet hole contributes to the mixing performance of the engine combustion chamber.

Update and extension of the mesoscale model for fast fluidization: Toward type C choking, high-density fast-bed, and flow-regime map

As a supplementary paper for “Mesoscale analysis on clusters in conjunction with fast fluidized bed modeling” published recently, this article aims to update and further extend the model toward type C choking, high-density fast-bed (HDFF), and flow-regime map. Starting from an argument on mesoscale shear-layer formation, a more mechanistic expression for the energy recovery coefficient of in-cloud circulation was derived; and the effective velocity factor for gas flow in the dilute phase was also modified, with which the type C choking for Geldart Group B particles was correctly predicted. Two different mechanisms for “type C choking”, actually the transition at the upper limit of solids flux for traditional fast fluidization in the low velocity region, were identified, i.e. Choking C(I), defined by Gsmax at dMs+/dβ=dMs−/dβ; and Choking C(O), characterized by the cluster diameter reaching Dcl=dp. A rough estimation method for Choking C(I) or C(O) was obtained, thereby. Following the general strategy of extrapolation from its onset, the detailed procedures for modeling of the incipient stage of HDFF, and the classical case, were derived and demonstrated, respectively. The method to predict the upper limit of Gs for HDFF was also obtained, making the flow regime map for fast fluidization fully complete. Simple two parameter criteria, i.e. uf−ut/Dt0.29 and Gs/ρsuf−ut, for sketchy scale-up of fast-beds with the same gas-particle properties were proposed. From those, acceptable flow regime maps for enlarged risers were successfully estimated. Finally, the transition from dilute-transport to fast-bed was revisited, and the reasons for reduction of the solids-wall friction factor, from its direct regression result to the value used in the model, were discussed along with further outlook.

Influence of vortical flow induced by a wall-mounted short cylinder with a streamlined front side on a horizontal air–solid two-phase flow

To induce large oscillations of air flow and suspend particles easily near the particle supply point in a low air velocity region of horizontal air-solid two-phase flow, a short cylinder model with a streamlined front side (refer to streamlined model) is proposed and is fixed on the bottom or top of the pipe in front of the particle feed. The streamlined front side of the model is designed to reduce the flow resistance, and the rectangular rear section of the model generates wake vortical flow so as to induce large airflow oscillation. The test tube consists of a horizontal pipe having an inner diameter of 80 mm and a length of 5 m. Spherical polyethylene particles with an average diameter of 2.3 mm and density of 978 kg/m3 were used as the test solid particles. Average air velocities and particle mass flow rates ranged from 9 to 16 m/s and 0.11 to 0.51 kg/s, respectively. Compared with the non-model air-solid two-phase flow, the streamlined model has reduced the pressure drop, critical and minimum conveying air velocities, power consumption, and additional pressure drop. This model achieved the highest reduction rate with a minimum air velocity of approximately 6% and an additional pressure loss of approximately 37.5%. According to particle image velocimetry measurement of air-solid two-phase flow, the time-averaged particle velocity and fluctuating particle velocity generated by the streamlined model are larger than those in the non-model flow, so even low air velocities can easily convey particles.

[formula omitted] wave teleseismic tomography of the subducted Chile rise

We investigate the crustal and upper mantle structure of the Aysén region of Chile from 44° to 49° S, a place where the diverging oceanic Nazca and Antarctic plates subduct beneath the South American continent. The Seismic Experiment in the Aysén Region of Chile (SEARCH) project operated a network of up to 60 land-based seismometers in this region between 2004 and 2006, centered over a 6 Myr old subducted spreading center. The data are used to examine the P wave velocity structure beneath the region using relative-arrival teleseismic travel time tomography, using 2534 P wave residuals from 173 teleseismic earthquakes. It is possible to image the velocity structure beneath the seismic network from ∼30 down to ∼300 km depth. The model can resolve structures at a spatial scale between ∼60 and ∼200 km and shows a large difference between the northern and southern parts of the region. To the north, a ∼100 km thick fast anomaly exists which dips away from the subduction trench; likely to be related to the subducting Nazca plate. Going to the south, as the age of this plate at the subduction trench decreases and arc volcanism shuts off, the fast anomaly migrates further from the trench, suggesting that the Nazca plate subducts at a reduced angle over a larger distance before the subduction angle steepens. The distinct sections of the fast anomaly suggest that slab tears exist across the fracture zones between subducted plate segments. Where the 6 Myr old subducted ridge segment is predicted to lie, there is a region of low velocity between ∼100 and ∼300 km depth, and no fast region associated with a subducting slab is present, indicating the presence of an asthenospheric window between the subducted Nazca and Antarctic plates.

Influence of submergence ratio on flow and drag forces generated by a long rectangular array of rigid cylinders at the sidewall of an open channel

This paper discusses how the submergence ratio, defined as the ratio between the flow depth, D, and the height, h, of the solid rigid cylinders forming the array affects flow and turbulence structure inside and around a rectangular array of cylinders placed adjacent to one of the channel sidewalls. As the array becomes submerged, a vertical shear layer develops in between the top face of the array and the free surface, which strongly increases flow three-dimensionality and modifies how the momentum exchange between the array and the surrounding open water regions occurs with respect to the case of an emerged array where only a horizontal shear layer forms as part of the incoming flow approaching the array is deflected laterally. Eddy-resolving simulations are conducted for several values of the solid volume fraction, ϕ, and of the submergence ratio, 1.0 ≤ D/h ≤ 4.0. Similar to the limiting case of an emerged array (D/h = 1.0), the width- and depth-averaged streamwise velocity inside the array reaches a constant value after an initial adjustment region in the submerged-array cases. For D/h ≥ 1.33, the mean normal velocities through the top and side faces of the array do not become equal to zero downstream of the initial adjustment region. The flow inside the array reaches an equilibrium regime where the local flux of fluid leaving the array through its side face is balanced by the local flux of fluid entering the array through its top face. This regime is observed until close to the end of the array. For D/h ≥ 2.0, the horizontal shear layer vortices do not generate successive regions of high and low streamwise velocity and bed friction velocity inside the array, as is observed in the emerged cases. With respect to the emerged case, the size of the shear layer vortices and the shear layer width increase for low submergence ratios before decreasing rapidly for D/h ≥ 1.33. Significant three-dimensional effects are present inside the array and the horizontal shear layer for cases with both emerged and submerged arrays. In the ϕ = 0.08 cases, strong upwelling and downwelling motions are observed inside the array for D/h ≥ 1.33, while the circulation of the streamwise-oriented cell of secondary flow forming close to the lateral face of the array peaks when the submergence ratio is close to 1.33. For constant ϕ, the total streamwise drag force normalized with the height and width of the array increases with increasing submergence ratio. As the array submergence increases, the cylinders near the front of the array contribute less to the total force acting on the cylinders forming the array. For constant D/h, the total streamwise drag force acting on the array increases with ϕ for the submerged and emerged cases.

Quantifying How Turbulence Enhances Boundary Layer Skin Friction and Surface Heat Transfer

Transitional and turbulent boundary layer (BL) flows possess dramatically larger wall-shear stresses and surface heat fluxes than their laminar counterparts. Locally, this can be explained by appealing to the presence of spatiotemporally coherent velocity and temperature regions that enhance the momentum and thermal transport across the BL. However, these coherent structures are seldom present alone, but usually influenced by other physical phenomena, such as the streamwise growth of BLs or freestream pressure gradients. A moment of enthalpy integral equation is introduced to quantify how turbulence and other flow phenomena enhance surface heat flux. Results from a direct numerical simulation of a transitional and turbulent BL are used to demonstrate the proposed analysis method and to form a quantitative assessment of the BL physics. The integral analysis demonstrated in this paper for canonical turbulent flows provides an interpretable analysis tool for unlocking key BL physics, including future extensions to compressible BLs, freestream pressure gradients, and the evaluation of flow control schemes.

Improving RGB-D SLAM accuracy in dynamic environments based on semantic and geometric constraints

Most current visual SLAM systems rely on static environment assumptions. However, in dynamic environments, the presence of dynamic objects can severely impair the performance of visual SLAM systems. To address this issue, we propose an algorithm that combines semantic segmentation and geometric constraints to eliminate the impact of dynamic objects on visual SLAM trajectory accuracy in dynamic indoor environments. First, a missed detection compensation algorithm based on the constant velocity model and region growing algorithm is proposed, which improves the accuracy of semantic or instance segmentation network and realizes accurate segmentation of dynamic objects at the semantic level in the new thread. Second, for the dynamic objects that cannot be recognized by the semantic segmentation network, a geometric constraint model based on the position correlation between feature points is presented to further eliminate the dynamic feature points that do not meet the motion consistency. Thereafter, the proposed method is integrated into the front-end of the ORB-SLAM2 system and evaluated using the RGB-D dataset. Experimental results demonstrate that the proposed method can improve the absolute trajectory accuracy of the ORB-SLAM2 system by an average of 96.90% in high dynamic scenes.

Research on the Structure Optimization Design of Automobile Intake Pipe

As the front end of the intake system, the intake dirty pipe is responsible for delivering sufficient and stable air to the air filter. Therefore, in order to meet the requirements of low intake resistance, it is necessary to correspondingly improve the flow resistance performance of the intake dirty pipe. In this study, the main research object was the intake pipe in the intake system of gasoline engine vehicles, and the internal gas flow field was simulated and analyzed. The results show that there are clear discrete velocity regions at the inlet and elbow, which affect the uniformity of the overall fluid flow and cause a certain pressure loss. After structural optimization, the total pressure difference at the inlet and outlet of the pipeline was reduced by 22.67% compared to the original model, and the total pressure loss was significantly reduced. A simplified model was used to make samples of the intake dirty pipes before and after performance improvement, and flow resistance tests were conducted respectively. The difference between test data and simulation data is within a reasonable range, and the simulation results are relatively reliable.

Properties of singular points in a special case of orthorhombic media

The position of singular lines for orthorhombic (ORT) media with fixed diagonal elements of the elasticity matrix cij, i=1…6 is studied under the condition that c11, c22, c33>c66>c44>c55. In this case, the off-diagonal coefficients of the elasticity matrix c12, c13, c23 are chosen so that some of the values of d12=c12+c66, d13=c13+c55, d23=c23+c44 are zero. For orthorhombic medium, where the only one of d12, d13, d23 is zero, contains only singular points in the planes of symmetry. If two or all three dij are zero, then the ORT medium contains singular lines and discrete singular points. We call such media pathological. A degenerate ORT medium with positive d12, d13, d23 has at most two singular lines, which are the intersection of a quadratic cone with a sphere. The pathological media may have up to 6 singular lines on the surface of the slowness. Singular lines for pathological media are described by more complex equations than conventional degenerate ORT models. The article proposes to using squares x, y, z of the components of the slowness vector in the equations. In a new coordinate system, equations defining singular lines for pathological media become linear or quadratic. Intersecting with the plane x+y+z =1, they define the straight lines, ellipses, or hyperbolas. If non-zero values d12, d13, d23 increase, the singular lines pass through four fixed points on the plane x+y+z =1, which makes it possible to describe the evolution of their change. Conditions are derived under which the singular curves of pathological ORT models are limiting the singular curves for degenerate ORT models with positive values of d12, d13, d23. Formulas are derived for transforming surfaces of slowness and singular lines of pathological media into the region of group velocities. The results are demonstrated with examples of pathological models obtained from the standard model of the ORT medium by changing the elasticity coefficients c12, c13, c23 so that some of the values d12, d13, d23 are zero

Tidal Response of Seismic Wave Velocity at Shallow Crust in Japan

AbstractMicrocracks in geomaterials cause variations in the elastic moduli under applied strain, thereby creating seismic wave velocity variations. These are crucial for understanding the dynamic processes of the crust, such as fault‐zone damage, healing, and volcanic activities. Solid earth tides have been used to detect seismic velocity changes responding to crustal‐scale deformations. However, no prior research has explored the characteristics of the seismic velocity variations caused by large‐scale tidal deformation. To systematically evaluate the tidal response to velocity variations, we developed a new method that utilized the flexibility of a state‐space model. The tidal response was derived from hourly stacked noise autocorrelations using a seismic interferometry method throughout Japan. In particular, large tide‐induced seismic velocity changes were observed in the low S‐wave velocity region of the shallow crust. Overall, the tidal responses of velocity variations can provide new insights into the response mechanisms of the shallow crust to applied strain.