Supersonic Wave Research Articles

Shear Wave Elastography in Evaluating the Efficacy of Liver Microwave Ablation: An Experimental Study

Background: The effect of microwave ablation on small hepatocellular carcinoma is not significantly different from that of surgical resection. Accurate assessment of the ablation effect is crucial for ensuring the safety and effectiveness of hyperthermia. Objectives: This study aimed to explore the feasibility and accuracy of supersonic shear wave elastography (SWE) in quantitatively evaluating the microwave ablation margin of the liver. Materials and Methods: Three surgeons were each randomly assigned 4 Wuzhishan miniature pigs (WZSPs) to perform 12 ablation procedures at an ablation power of 40 W. Based on the ablation time, the lesions were divided into 15, 30, and 60-second groups. Immediately after ablation, SWE and modulus measurements were performed 5 times for each ablation lesion. The SWE data were expressed as mean ± standard deviation. Within-group and between-group comparisons were made using repeated measures analysis of variance. Results: A total of 144 effective ablations and 131 effective pathological results were obtained. Within the same ablation time, the elastic modulus increased in the surrounding normal tissue, ablation margin, and ablation center regions in a stepwise manner (P < 0.01). However, in the ablation center region, the elastic modulus decreased in a stepwise manner with the shortening of ablation time [60 s (97.16 ± 14.58 kPa) > 30 s (77.84 ± 9.64 kPa) > 15 s (38.92 ± 3.12 kPa)], with statistically significant differences (F = 2,131.832, P < 0.01). The elastic modulus of the ablation margin region at different ablation times remained between 22.68 - 23.56 kPa. Conclusion: The elastic modulus range in the ablation margin region after microwave ablation is relatively fixed. Shear wave elastography aids in the quantitative evaluation of the ablation margin region of the liver and has high practical value in monitoring and evaluating ultrasound ablation.

Supersonic Waves Generated by the 18 November 2023 Starship Flight and Explosions: Unexpected Northward Propagation and a Man‐Made Non‐chemical Depletion

AbstractOn 18 November 2023, SpaceX launched the Starship, the tallest and the most powerful rocket ever built. The Super Heavy engine separated from the Starship spacecraft and exploded at 90 km of altitude, while the main core Starship continued to rise up to 149 km and exploded after ∼8 min of flight. In this work, we used data from ground‐based GNSS receivers and we analyzed total electron content (TEC) response to the Starship flight and the two explosions. For the first time, we observed large‐distance northward propagation of intensive 2,000 km V‐shaped ionospheric disturbances from the rocket trajectory. The observed perturbations, most likely, represent shock waves propagating with the cone angle of ∼14° on the North and ∼7° on the South against the flight track that corresponds to the Mach angle of the shock waves in the lower atmosphere. The Starship explosion also produced a non‐chemical depletion in the ionospheric TEC.

Characterization of similar Marshak waves observed at the LMJ

We detail results of two experiments performed at the Laser Mégajoule (LMJ) facility aimed at studying similar supersonic Marshak waves propagating in a low-density SiO2 aerogel enclosed in metallic tubes. Similar means here that these two experiments, driven by the same input radiation temperature history, use purposely very different tubes in terms of length (L = 1200 or 2000 μm), diameter (2R = 1000 or 2000 μm), nature of the wall (gold or copper), and aerogel densities (ρ = 30 or 20 mg/cm3), yet the transit time and the radiation temperature of the fronts at the tube exit are the same for both shots. Marshak waves are characterized at the exit using simultaneously for the first time to our knowledge, a one dimensional soft x-ray imager from which the radiation front transit time and curvature are measured and also a broadband x-ray spectrometer to infer its temperature history. These constraining results are then successfully compared to those from simple analytical models [Cohen et al., Phys. Rev. Res. 2, 023007 (2020) and Hurricane et al., Phys. Plasmas 13, 113303 (2006)] and from the three dimensional Lagrangian radiation-hydrodynamics code TROLL to get information on x-ray energy losses. Controlled compensation effects between the length, diameter, and nature of the tubes (governing these losses) are such that the radiation temperature drop along the tubes is eventually the same for these two similar shots.

Effect of Knee Angle, Contractile Activity, and Intensity of Force Production on Vastus Lateralis Stiffness: A Supersonic Shear Wave Elastography Pilot Study.

Supersonic shear image (SSI) ultrasound elastography provides a quantitative assessment of tissue stiffness using the velocity of shear waves. SSI's great potential has allowed researchers in fields like biomechanics and muscle physiology to study the function of complex muscle groups in different conditions. The aim of this study is to use SSI to investigate changes in the stiffness of the vastus lateralis (VL) muscle as a consequence of passive elongation, isometric contraction, and repeated muscle activity. In a single session, 15 volunteers performed a series of isometric, concentric, and eccentric contractions. SSI images were collected from the VL to assess its stiffness before and after the contractions and at various knee angles. Two-way within-subjects ANOVA was used to test the effects of muscle contraction type and knee angle on VL stiffness. Linear regression analysis was employed to assess the relationship between muscle stiffness and the intensity of isometric contractions. After maximal contractions, VL stiffness increased by approximately 10% compared to baseline values, and following maximal isometric (p < 0.01) and eccentric contractions (p < 0.05). Yet, there was no change in VL shear modulus at the end of concentric contractions. The relaxed VL shear modulus increased with knee flexion both before and after the knee extensor contractions (p < 0.001). A linear relationship between the shear modulus and the degree of isometric contraction was observed, although with notable individual variation (R2 = 0.125). Maximal contractile activity produces modest increases in relaxed muscle stiffness. The SSI-measured shear modulus increases linearly with the degree of isometric contraction.

Design of a New Supersonic Shock Wave Generator and Application in Power Generation

Wind energy is a kind of renewable energy with great potential for development. This study mainly investigated the application of shock waves generated by high-pressure gases (wind energy) for generating energy. In this study, we designed a new supersonic shock wave generator that can be reused without disassembling and assembling bolts and developed a shock wave monitoring system. It could measure the velocity of the generated shock waves at about Mach 3–5, and the output pressure exceeded 900 kg/cm2 (more than 100 times the input pressure). Then, we developed a power generation system driven by supersonic shock waves based on the characteristics of the new shock wave generator, which could generate high-pressure and high-speed blast waves and could be reused. The shock wave generator can repeatedly generate high-pressure waves to drive the Tesla turbine and then rotate the magnetic energy generator for power generation. This paper used tank pressure, output pressure, gas flow, rotation speed, voltage, and current detected by the system to conduct power generation performance analysis. When the minimum rotation speed was set to 1500 rpm and three bulbs were turned on as loads, the system could generate an average voltage of 36.64 V and an average current of 211.01 mA as output (power about 7731.41 mW).

Acoustic resolvent analysis of turbulent jets

Abstract We perform a resolvent analysis of a compressible turbulent jet, where the optimisation domain of the response modes is located in the acoustic field, excluding the hydrodynamic region, in order to promote acoustically efficient modes. We examine the properties of the acoustic resolvent and assess its potential for jet-noise modelling, focusing on the subsonic regime. Resolvent forcing modes, consistent with previous studies, are found to contain supersonic waves associated with Mach wave radiation in the response modes. This differs from the standard resolvent in which hydrodynamic instabilities dominate. We compare resolvent modes with SPOD modes educed from LES data. Acoustic resolvent response modes generally have better alignment with acoustic SPOD modes than standard resolvent response modes. For the optimal mode, the angle of the acoustic beam is close to that found in SPOD modes for moderate frequencies. However, there is no significant separation between the singular values of the leading and sub-optimal modes. Some suboptimal modes are furthermore shown to contain irrelevant structure for jet noise. Thus, even though it contains essential acoustic features absent from the standard resolvent approach, the SVD of the acoustic resolvent alone is insufficient to educe a low-rank model for jet noise. But because it identifies the prevailing mechanisms of jet noise, it provides valuable guidelines in the search of a forcing model (Karban et al. in J Fluid Mech 965:18, 2023). Graphical abstract

A Gaussian process approach for rapid evaluation of skin tension

Skin tension plays a pivotal role in clinical settings, it affects scarring, wound healing and skin necrosis. Despite its importance, there is no widely accepted method for assessing in vivo skin tension or its natural pre-stretch. This study aims to utilise modern machine learning (ML) methods to develop a model that uses non-invasive measurements of surface wave speed to predict clinically useful skin properties such as stress and natural pre-stretch. A large dataset consisting of simulated wave propagation experiments was created using a simplified two-dimensional finite element (FE) model. Using this dataset, a sensitivity analysis was performed, highlighting the effect of the material parameters and material model on the Rayleigh and supersonic shear wave speeds. Then, a Gaussian process regression model was trained to solve the ill-posed inverse problem of predicting stress and pre-stretch of skin using measurements of surface wave speed. This model had good predictive performance (R2 = 0.9570) and it was possible to interpolate simplified parametric equations to calculate the stress and pre-stretch. To demonstrate that wave speed measurements could be obtained cheaply and easily, a simple experiment was devised to obtain wave speed measurements from synthetic skin at different values of pre-stretch. These experimental wave speeds agree well with the FE simulations, and a model trained solely on the FE data provided accurate predictions of synthetic skin stiffness. Both the simulated and experimental results provide further evidence that elastic wave measurements coupled with ML models are a viable non-invasive method to determine in vivo skin tension. Statement of significanceTo prevent unfavourable patient outcomes from reconstructive surgery, it is necessary to determine relevant subject-specific skin properties. For example, during a skin graft, it is necessary to estimate the pre-stretch of the skin to account for shrinkage upon excision. Existing methods are invasive or rely on the experience of the clinician. Our work aims to present an innovative framework to non-invasively determine in vivo material properties using the speed of a surface wave travelling through the skin. Our findings have implications for the planning of surgical procedures and provides further motivation for the use of elastic wave measurements to determine in vivo material properties.

When discrete fronts and pulses form a single family: FPU chain with hardening-softening springs

We consider a version of the classical Hamiltonian FPU (Fermi–Pasta–Ulam) problem with nonlinear force-strain relation in which a hardening response is taken over by a softening regime above a critical strain value. We show that in addition to pulses (solitary waves) this discrete system also supports non-topological and dissipation-free fronts (kinks). Moreover, we demonstrate that these two types of supersonic traveling wave solutions belong to the same family. Within this family, solitary waves exist for continuous ranges of velocity that extend up to a limiting speed corresponding to kinks. As the kink velocity limit is approached from above or below, the solitary waves become progressively more broad and acquire the structure of a kink–antikink bundle. Direct numerical simulations and Floquet analysis of linear stability suggest that all of the obtained solutions are effectively stable. To motivate and support our study of the discrete problem we also analyze a quasicontinuum approximation with temporal dispersion. We show that this model captures the main effects observed in the discrete problem both qualitatively and quantitatively.

Evolution of Subsonic Shock Waves Associated with Reconnection Jets in Earth’s Magnetotail

Motivated by the signatures of nonlinear electrostatic waves observed by the Magnetospheric Multiscale spacecraft mission in reconnection jet regions of Earth's magnetotail, we have explored the dynamical features of ion-acoustic shock waves in the magnetotail. In this investigation, we have examined the dynamics and characteristics of ion-acoustic subsonic shock waves in non-Maxwellian space plasma comprising of two counterstreaming ion beams with suprathermal electrons, assumed to follow a kappa (κ) distribution. A reductive perturbation technique has been adopted to establish an evolution equation for small amplitude electrostatic shock structures. Importantly, subsonic waves only exist when the beam velocity exceeds a certain threshold, beyond which supersonic and subsonic waves may coexist. The combined effects of the beam velocity and the non-Maxwellian electron statistics have been analyzed to examine the characteristics of subsonic shock waves. Both symmetric and asymmetric (in relative beam density) models have been considered, leading to distinct possibilities in the evolution of subsonic shock waves. The findings of the investigation will help unfold the relatively unexplored dynamical characteristics of subsonic shock waves that may form and propagate in the magnetosphere.

A unified theory of the self-similar supersonic Marshak wave problem

We present a systematic study of the similarity solutions for the Marshak wave problem in the local thermodynamic equilibrium (LTE) diffusion approximation and in the supersonic regime. Self-similar solutions exist for a temporal power law surface temperature drive and a material model with power law temperature dependent opacity and energy density. The properties of the solutions in both linear and nonlinear conduction regimes are studied as a function of the temporal drive, opacity, and energy density exponents. We show that there exists a range of the temporal exponent for which the total energy in the system decreases, and the solution has a local maxima. For nonlinear conduction, we specify the conditions on the opacity and energy density exponents under which the heat front is linear or even flat and does possess its common sharp characteristic; this characteristic is independent of the drive exponent. We specify the values of the temporal exponents for which analytical solutions exist and employ the Hammer–Rosen perturbation theory to obtain highly accurate approximate solutions, which are parameterized using only two numerically fitted quantities. The solutions are used to construct a set of benchmarks for supersonic LTE radiative heat transfer, including some with unusual and interesting properties such as local maxima and non-sharp fronts. The solutions are compared in detail to implicit Monte Carlo and discrete-ordinate transport simulations as well gray diffusion simulations, showing a good agreement, which highlights their usefulness as a verification test problem for radiative transfer simulations.

A reduced-order model for nonlinear radiative transfer problems based on moment equations and POD-Petrov-Galerkin projection of the normalized Boltzmann transport equation

A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor) equations for moments of the radiation intensity and (ii) the normalized Boltzmann transport equation (BTE). The multilevel system of moment equations is derived by projection of the BTE onto a sequence of subspaces which represent elements of the phase space of the problem. Exact closure for the moment equations is provided by the Eddington tensor. A Petrov-Galerkin (PG) projection of the normalized BTE is formulated using a proper orthogonal decomposition (POD) basis representing the normalized radiation intensity over the whole phase space and time. The Eddington tensor linearly depends on the solution of the normalized BTE. By linear superposition of the POD basis functions, a low-rank expansion of the Eddington tensor is constructed with coefficients defined by the PG projected normalized BTE. The material energy balance (MEB) equation is coupled with the effective gray low-order equations which exist on the same dimensional scale as the MEB equation. The resulting TRT ROM is structure and asymptotic preserving. A detailed analysis of the ROM is performed on the classical Fleck-Cummings (F-C) TRT multigroup test problem in 2D geometry. Numerical results are presented to demonstrate the ROM's effectiveness in the simulation of radiation wave phenomena. The ROM is shown to produce solutions with sufficiently high accuracy while using low-rank approximation of the normalized BTE solution. Essential physical characteristics of supersonic radiation wave are preserved in the ROM solutions.

Mechanism of periodic oscillation in low-Reynolds-number buffet around an airfoil at angle of attack 0

In this study, the low-frequency oscillations found in the compressible low-Reynolds-number regime, defined as low-Reynolds-number buffet, were investigated by numerical calculations and modal analysis. Dynamic mode decomposition (DMD) and compressive sensing methods were employed to extract periodic flow structures. Numerical simulation results showed low-Reynolds-number buffet and Kármán vortex shedding. Low- and high-frequency oscillations [St=O(0.01), O(1.0)] were extracted by DMD and named the buffet mode and vortex shedding mode, respectively. Low-Reynolds-number buffet does not necessarily exhibit supersonic regions or shock wave. Simulation results show that the thickness of the separated shear layer changes significantly under low-Reynolds-number buffet. The change in the thickness of the separated shear layer was confirmed by the buffet mode of DMD results. Two types of compression pressure waves, advecting upstream, were identified. DMD indicated that they resulted from vortex shedding. According to simulation and DMD results, the origin of the shock waves appears to be the condensation of compression pressure waves due to the vortex shedding mode and expansion in the supersonic region due to the buffet mode. The formation of the shock waves seems to be subordinated to the vortex shedding mode and the buffet mode. A feedback model for low-Reynolds-number buffet inherent in separated shear layers, which does not require supersonic regions or shock waves, was proposed. Supersonic regions highly condensed the compression pressure waves, inducing a larger separation region and amplifying the oscillation. The role of supersonic regions in determining oscillation amplitudes was evidenced, although supersonic regions are not essential to the mechanism of low-Reynolds-number buffet.

The Mechanism of Resonant Amplification of One-Dimensional Detonation Propagating in a Non-Uniform Mixture

The propagation of detonation waves (i.e., supersonic combustion waves) in non-uniform gaseous mixtures has become a matter of interest over the past several years due to the development of rotating detonation engines. It was shown in a number of recent theoretical studies of one-dimensional pulsating detonation that perturbation of the parameters in front of the detonation wave can lead to a resonant amplification of intrinsic pulsations for a certain range of perturbation wavelengths. This work is dedicated to the clarification of the mechanism of this effect. One-dimensional reactive Euler equations with single-step Arrhenius kinetics were solved. Detonation propagation in a gas with sine waves in density was simulated in a shock-attached frame of reference. We carried out a series of simulations, varying the wavelength of the disturbances. We obtained a non-linear dependence of the amplitude of these pulsations on the wavelength of disturbances with resonant amplification for a certain range of wavelengths. The gain in velocity was about 25% of the Chapman–Jouguet velocity of the stable detonation wave. The effect is explained using the characteristic analysis in the x-t diagram. For the resonant case, we correlated the pulsation period with the time it takes for the C+ and C− characteristics to travel through the effective reaction zone. A similar pulsation mechanism is realized when a detonation wave propagates in a homogeneous medium.

Development and Validation of a Compressible Reacting Gas-Dynamic Flow Solver for Supersonic Combustion

An approach based on the OpenFOAM library has been developed to solve a high-speed, multicomponent mixture of a reacting, compressible flow. This work presents comprehensive validation of the newly developed solver, called compressibleCentralReactingFoam, with different supersonic flows, including shocks, expansion waves, and turbulence–combustion interaction. The comparisons of the simulation results with experimental and computational data confirm the fidelity of this solver for problems involving multicomponent high-speed reactive flows. The gas dynamics of turbulence–chemistry interaction are modeled using a partially stirred reactor formulation and provide promising results to better understand the complex physics involved in supersonic combustors. A time-scale analysis based on local Damköhler numbers reveals different regimes of turbulent combustion. In the core of the jet flow, the Damköhler number is relatively high, indicating that the reaction time scale is smaller than the turbulent mixing time scale. This means that the combustion is controlled by turbulent mixing. In the shear layer, where the heat release rate and the scalar dissipation rate have the highest value, the flame is stabilized due to finite rate chemistry with small Damköhler numbers and a limited fraction of fine structure. This solver allows three-dimensional gas dynamic simulation of high-speed multicomponent reactive flows relevant to practical combustion applications.

A deep learning super-resolution model for turbulent image upscaling and its application to shock wave–boundary layer interaction

Upscaling flow features from coarse-grained data is paramount for extensively utilizing computational physics methods across complex flow, acoustics, and aeroelastic environments where direct numerical simulations are computationally expensive. This study presents a deep learning flow image model for upscaling turbulent flow images from coarse-grained simulation data of supersonic shock wave–turbulent boundary layer interaction. It is shown for the first time that super-resolution can be achieved using only the coarsest-grained data as long as the deep learning training is performed using hundreds of fine-grained data. The unsteady pressure data are used in training due to their importance in aeroelasticity and acoustic fatigue occurring on aerospace structures. The effect on the number of images and their resolution features used in training, validation, and prediction is investigated regarding the model accuracy obtained. It is shown that the deep learning super-resolution model provides accurate spectra results, thus confirming the approach's effectiveness.

A computational investigation of shock wave train in diverse duct geometries using machine learning-adopted k-ω turbulence model

This research paper presents a thorough examination of shock wave train phenomena in various duct structures, utilizing a machine learning-optimized k-ω model. The focus of the study is to apply machine learning techniques to adapt the constant coefficients of the k-ω turbulence model, improving its accuracy and computational efficiency in capturing the dynamics of shock waves. An important aspect of this investigation is the impact of diverging sections within the duct, specifically how changes in the divergence angle, while maintaining a constant ratio of the exit area to the throat area, affect compressible flow parameters, shock wave positions, and other related characteristics of shock trains. The study systematically explores these effects and provides fresh insights into the behavior of shock wave trains under different divergence conditions. In a departure from the usual practices in supersonic research, this study compares the phenomena of shock wave trains in rectangular and circular duct geometries. The findings contribute valuable data and analyses to a field that has traditionally focused on rectangular configurations. The results indicate that the shape of the duct has a significant influence on the shock wave train, emphasizing the importance of considering geometric diversity in the study of supersonic flows and shock wave phenomena. This research sets the stage for further investigations into the interaction between duct geometry, shock wave propagation, and the dynamics of compressible flows.

Self-similar solutions for the non-equilibrium nonlinear supersonic Marshak wave problem

Similarity solutions to the nonlinear non-equilibrium Marshak wave problem with a time dependent radiation driving source are presented. The radiation transfer model used is the gray, non-equilibrium diffusion approximation in the supersonic regime. These solutions constitute an extension of existing non-equilibrium supersonic Marshak wave solutions, which are linear to the nonlinear regime that prevails in realistic high energy density systems. The generalized solutions assume a material model with power law temperature dependent opacities, a material energy density that is proportional to the radiation energy density, and a surface radiation temperature drive that obeys a temporal power law. The solutions are analyzed in detail, and it is shown that they take various qualitatively different forms according to the values of the opacity exponents. The solutions are used to construct a set of standardized benchmarks for supersonic non-equilibrium radiative heat transfer, which are nontrivial but straightforward to implement. These solutions are compared in detail to implicit Monte Carlo and discrete-ordinate transport simulations as well gray diffusion simulations, showing a good agreement, which demonstrates the usefulness of these solutions as a code verification test problem.

Primena tehnika vizuelizacije strujanja za određivanje sile otpora projektila

The paper provides an overview of flow visualization methods. From the many ways of classifying flow visualization methods, the chosen method of classification is in accordance with the experimental procedure. Flow visualization methods that involve the addition of foreign material are the simplest, from the point of view of the required material and the experimental setup, in which one tracer and an adequate light source are most often applied, except for layers sensitive to pressure and shear stress. Their application is wide and most methods from this category can be modified very easily depending on the case. Visualization methods that involve addition of energy to the fluid flow use strong sources of electromagnetic radiation, most often lasers, to excite the molecules in the fluid stream, producing an adequate quantum-mechanical effect that enables visualization. Optical methods of flow visualization are based on changes in the refractive index of light caused by the presence of a fluid in motion in the test section, in addition, the principle of superposition of light waves is used in interferometry methods. Optical methods are mainly used in areas of supersonic flow and shock wave studies, but they are also present in exhaust gas propagation studies. As computational fluid dynamics is a separate subject, the physical laws on which CFD is based on are presented, as well as an example of flow visualization, which is an integral part of most calculations performed using this method. In addition to the classification and description of flow visualization methods, the paper provides an explanation of a approximate calculation procedure based on the use of one of the optical methods, Schlieren photography, in order to calculate the resistance force during supersonic projectile flow, as well as a comparison of results based on empirical data.

General concept for autoignitive reaction wave covering from subsonic to supersonic regimes

We consider a one-dimensional (1D) autoignitive reaction wave in a reactive flow system comprising unburned premixed gas entering from the inlet boundary and burned gas exiting from the outlet boundary. In such a 1D system at given initial temperature, it is generally accepted that steady-state solutions can only exist if the inlet velocity matches either the velocity of deflagration wave, as determined by the burning rate eigenvalue in the subsonic regime, or the velocity of detonation wave as dictated by the Chapman–Jouguet condition in the supersonic regime. Based on our recently published theory that ignition is equivalent to deflagration wave with unity Lewis number, we believe that it is possible to redefine deflagration wave from ignition. Thus, we have developed the general concept of “autoignitive reaction wave” and shown theoretically that there are two distinct regions that can maintain steady-state solutions in both the subsonic and supersonic regimes. Based on this theory, we selected inlet velocities that are predicted to yield either steady-state or flashback solutions and conducted numerical simulations. This novel approach revealed that steady-state solutions are possible not only at the velocity of the deflagration wave in the subsonic regime and the velocity of the detonation wave in the supersonic regime, but also across a broad range of inlet velocities. Furthermore, we identify a highly stable autoignitive reaction wave that emerges when the inlet velocity surpasses the velocity of detonation wave, devoid of the typical shock wave commonly seen in detonation waves. This “supersonic autoignitive reaction wave” lacks the instability-inducing detonation cell structure, suggesting the potential for the development of novel combustor concepts.

On the Existence of Subsonic Solitary Waves Associated with Reconnection Jets in Earth’s Magnetotail

The Magnetospheric Multiscale Spacecraft (MMS) has detected the signature of electrostatic solitary waves (ESWs) occurring in the reconnection jet site of the Earth’s magnetotail (Liu et al.). These observations have motivated us to explore the mechanism underlying the formation of fast- and slow-mode ion-acoustic solitary waves in the magnetotail region. To this end, we have formulated a three-component magnetized plasma model consisting of nonthermal electrons and two cold ion beams streaming parallel and antiparallel to the magnetic field, respectively. In this work, we have examined the existence conditions for ion-acoustic subsonic waves in a suprathermal space plasma comprising two counterstreaming (drifting) ion beams interacting with a suprathermal electron background. An exact (nonperturbative) nonlinear technique has been adopted to examine the role of the beam velocity and the spectral index on the evolution of subsonic waves. Linear analysis reveals that subsonic waves are unstable when the beam velocity is lower than a threshold value; hence in this regime, only conventional supersonic (fast) waves are formed. On the other hand, when the beam velocity exceeds the threshold, either supersonic or subsonic waves may exist. The combined impact of the beam velocity and electron superthermality on the characteristics of subsonic solitary waves has been analyzed. Our results are shown to be in good agreement with observations of slow ESWs by the MMS spacecraft. Our findings will help to unfold the so-far unexplored dynamical characteristics of subsonic waves that may occur in the reconnection site of Earth’s magnetotail.