Directional Stability Research Articles

An innovative booster-assisted dynamically installed fish anchor and its installation characteristics considering the action of ocean currents

The fish anchor is an economically viable offshore foundation engineering technology that has been proposed in recent years. By fish anchor, we mean a fish-shaped dynamically installed anchor that can penetrate into the seabed through water by its own weight. However, the existing research studies seldom consider the hydrodynamic characteristics of its free fall installation, resulting in uncertainties regarding its underwater installation characteristics. Therefore, based on OpenFOAM, this study first investigated the directional stability of fish anchors during its underwater falling process through the static model analysis method and dynamic model analysis method. The findings indicated that the directional stability of fish anchors was insufficient, rendering them suitable only for release and installation at low heights (i.e., less than 4.2 times the anchor length) without marine environmental loads. Furthermore, the anchor inclination angle during installation is significant, thereby impacting its penetration depth and pull-out capacity in the seabed. To solve this problem, the concept of an innovative booster-assisted fish anchor is proposed, which can significantly enhance the directional stability of conventional fish anchors. Results show that the maximum installation height of the new booster-assisted fish anchor is increased by 2.4 times compared to the original design, thereby enhancing both the penetration speed and uplift capacity. Based on the findings, recommended installation and construction conditions are provided. Finally, a predictive formula for the installation height and verticality of the new booster-assisted fish anchor under current action is presented to offer guidance for engineering applications.

Hydrodynamic and bearing behaviors of two typical deepwater dynamically installed anchors: torpedo anchor and fish anchor

Dynamically installed anchors, such as torpedo and fish anchors, are innovative and cost-effective anchorage foundations. In this study, the advantages and disadvantages of these two types of dynamically installed anchors are discussed by comparing the hydrodynamic and bearing characteristics of torpedo and fish anchors commonly used in practical engineering. First, based on OpenFOAM, 3D numerical models were established to investigate the directional stability and simulate the underwater free-fall process of anchors using static and dynamic model analysis methods. Using the validated model, the hydrodynamic performances (i.e., inclination angle, installation offset distance, penetration velocity, and drag coefficient) of torpedo and fish anchors were explored and compared. Based on these findings, the installation height of each anchor was recommended. Finally, the bearing performances of the torpedo and fish anchors were investigated using ABAQUS, and the selection principles of these two types of dynamically installed anchors were presented based on their hydrodynamic and bearing behaviors.

Flow-induced vibration of two tandem square cylinders at low Reynolds number: transitions among vortex-induced vibration, biased oscillation and galloping

The flow-induced vibrations (FIVs) of two identical tandem square cylinders with mass ratio m* = 3.5 at Reynolds number Re = 150 are investigated through two-dimensional direct numerical simulation (DNS) and linear stability analysis over a parameter range of spacing ratio 1.5 ≤ L* ≤ 5 and reduced velocity 3 ≤ Ur ≤ 34. Three kinds of FIV responses, namely vortex-induced vibration (VIV), biased oscillation (BO) and galloping (GA), are identified. The FIVs are then further classified into the branches of initial VIV (IV), resonant VIV (RV and RV′), flutter-induced VIV (FV), desynchronized VIV (DV), VIV developing from GA (GV), transitional state between VIV and GA (TR), BO and GA based on the characteristics of the vibration responses. The transitions among different FIV branches are examined by combining the DNS with linear stability analysis, where the transition boundaries among the VIV, BO and GA branches over the concerned parameters are identified on the branch maps. The transition from IV to RV or RV′ is found to be related to the unstable wake mode, while the FV, transiting from RV or RV′, is induced by the unstable structural factor in the wake-structure mode. The structural instability is considered as the physical origin of GA, whereas the mode competition between unstable wake and structure leads to DV, GV and TR, and thus delays the appearance of GA. The transition from DV to BO with biased equilibrium position, accompanied by the even-order harmonic frequencies, is essentially induced by the symmetry breaking bifurcation.

Mediolateral Postural Sway Velocity as a Possible Indicator of Ground Reaction Force-Derived 180⁰ Turn Performance in Male Soccer Players: A Cross-Sectional Study

The main aim of the study was to investigate the relationship between ground reaction force (GRF) derived postural sway and 180° turn performance in soccer players on the axis of dominant and non-dominant legs. Twenty-seven male soccer players (mean age 22.45 ± 2.7 years) from the same league level agreed to participate in the study. The participants underwent GRF-derived postural sway and 180⁰ turn tests using a force plate in separate sessions, with at least 24-hour intervals between sessions. Postural sway was assessed in anteroposterior and mediolateral directions during a single-leg stance, while the 180° turn performance was evaluated through GRF-derived turn time and turn sway. The correlation, multiple regression, and group differences were computed to test study hypotheses. Positive correlations were observed between postural sway measures and 180⁰ turn time for dominant and non-dominant legs (r-range from 0.384 to 0.550). No measure of postural sway was significantly related to the 180⁰ turn sway (p> 0.05). Multiple stepwise regression analysis indicated that mediolateral sway velocity explained 30% and 17% of the variance of 180⁰ turn time for dominant and non-dominant legs, respectively. No statistical inter-limb differences were noted for 180⁰ turn and postural sway parameters. The results suggest that improving single-leg postural performance may enhance male soccer players' 180° turn performance. Therefore, unilateral stability in the mediolateral direction should be considered a potential indicator of change of direction-based performances.

Design and Fabrication of Tilting Trike

Safety is the most crucial factor for two-wheelers. The tilting mechanism boosts the maximum speed along bends. The adoption of tilting mechanisms in automobiles would reduce the number of skid-related incidents. It will improve the vehicle's dynamic and directional stability, road grip, and passenger comfort. The tilting trike has a system that comprises a parallelogram connection, allowing it to tilt like any other two-wheeler. The tadpole form of the trike gives more stability than the delta design. The tilting mechanism is operably attached to the vehicle's frame by a series of vertically aligned bearings that hold it in place. The system guarantees that the independent wheels remain properly aligned during all motions. Key Words: tadpole, trike, skidding, directional stability, parallelogram linkage

Cross-Education Effects of Hip Strengthening in Individuals with Chronic Ankle Instability

ABSTRACT Introduction/Purpose Chronic ankle instability (CAI) is associated with reduced balance, lumbopelvic stability, and hip strength. Accordingly, hip strengthening is an effective intervention for individuals with CAI. Cross-education through unilateral exercise is also beneficial to individuals with CAI, but cross-education effects of hip strengthening remain unknown. The purpose of this study was to determine cross-education effects of hip strengthening in individuals with CAI. Methods Thirty individuals with CAI were randomized into control (CON) and hip strengthening (HIP) groups. Baseline and postintervention tests of the uninvolved limb included lumbopelvic stability (unilateral hip bridge), handheld dynamometry (isometric hip extension, abduction, and external rotation strength), and balance (Star Excursion Balance Test (SEBT) in anterior, posterolateral (PL), and posteromedial directions). After baseline testing, HIP completed progressive hip strengthening of the involved limb three times per week for 8 wk, and CON did not. Repeated-measures analyses of variance assessed the effects of group and time on each outcome. Each group’s mean changes from baseline to postintervention were assessed via effect sizes. Statistical significance was set a priori at P < 0.05. Results Of the 30 participants enrolled, 10 did not complete the postintervention data collection. Multiple imputations estimated missing data, and an intention-to-treat analysis was conducted. There were no significant group-by-time interactions for hip strength, balance, or lumbopelvic stability. HIP exhibited moderate effect sizes for SEBT-PL and hip bridge. All other effect sizes were small or negligible. Conclusions We did not identify a clear cross-education effect following unilateral hip strengthening in a cohort with CAI. Examination of baseline to postintervention effect sizes indicate a potential trend toward improved balance and lumbopelvic stability of the HIP group.

Comparative analysis of postural stability and risk of falling and developing disability among overweight and obese women over 40 years

BackgroundIncreased body mass index (BMI) adversely affects the mechanics of the musculoskeletal system. It is known that obese people have poorer postural stability and mobility-related outcomes compared to normal weight people, but there is limited research comparing overweight and class 1 obese people, two consecutive and prevalent BMI categories. AimsTo compare postural stability, functional mobility, and risk of falling and developing disability between overweight and obese women, and to investigate the relationship of BMI and body weight with the outcomes. MethodsThirty women with class 1 obesity and 30 overweight women were included. Standing postural stability with eyes-open and eyes-closed and stability limits were assessed using the Prokin system. The Timed Up and Go Test (TUG) was used to assess functional mobility and risk of falling (≥11 s) and developing disability (≥9 s). ResultsThe average center of pressure displacements on the y-axis (COPY) obtained during quiet standing with both eyes-open and eyes-closed were higher in obese women than overweight women (p < 0.05) and the effect sizes were moderate for the results. The COPY values in the eyes-open and eyes-closed conditions were correlated with BMI (r = 0.295 and r = 0.285, p < 0.05). Furthermore, the COPX value in the eyes-open condition and the TUG score were correlated with body weight (r = 0.274 and r = 0.257, p < 0.05). ConclusionsObese women had poorer static standing stability in the anteroposterior direction than overweight women, while functional mobility and risk of falling and developing disability did not differ. Furthermore, BMI and body weight were related to poorer static standing stability.

The Effect of Fatigue on the Time to Stability in Head Movement in Soccer Players With a History of Anterior Cruciate Ligament Reconstruction

Background and Aims Delay in achieving stability is one of the factors that can cause injury and re-injury in athletes. Because many injuries occur during fatigue, the present study aimed to compare the effect of fatigue on the time to stability in the head movement of players who have undergone anterior cruciate ligament (ACL) reconstruction with healthy players. Methods The present study is quasi-experimental. Twenty-four professional soccer players participated in the study. Twelve healthy, active professional soccer players (control group) and 12 soccer players with reconstructed anterior cruciate ligament by hamstring graft (experimental group) participated in this study. Also, 6 to 24 months should have passed since their ligament reconstruction. After jumping and crossing an obstacle to a height of 7.5 cm, the participants performed the task of heading and landing on the force plate. These movements were repeated after the fatigue protocol. Information was collected by the force plate (Kistler Instruments Sweden). Multivariate analysis of variance at the significant level of P &lt;0.05 was used for comparison between groups. Results According to the findings, fatigue affected the time to stability in the internal-external direction (P &lt;0.05). However, no difference was observed between the two groups in the internal-external direction before fatigue. Also, no significant difference was observed between the two groups when achieving stability before and after fatigue in the anterior-posterior and vertical directions. Conclusion It seems that a plyometric fatigue training session cannot differentiate between healthy soccer players in the anterior-posterior and vertical directions from players who have undergone anterior cruciate ligament reconstruction. However, this difference was observed in the internal-external direction after fatigue.

Friend or foe? Reciprocal regulation between E3 ubiquitin ligases and deubiquitinases.

Protein ubiquitination is a post-translational modification that entails the covalent attachment of the small protein ubiquitin (Ub), which acts as a signal to direct protein stability, localization, or interactions. The Ub code is written by a family of enzymes called E3 Ub ligases (∼600 members in humans), which can catalyze the transfer of either a single ubiquitin or the formation of a diverse array of polyubiquitin chains. This code can be edited or erased by a different set of enzymes termed deubiquitinases (DUBs; ∼100 members in humans). While enzymes from these distinct families have seemingly opposing activities, certain E3-DUB pairings can also synergize to regulate vital cellular processes like gene expression, autophagy, innate immunity, and cell proliferation. In this review, we highlight recent studies describing Ub ligase-DUB interactions and focus on their relationships.

Solvent-Dependent Emissions Properties of a Model Aurone Enable Use in Biological Applications.

Fluorophores are powerful visualization tools and the development of novel small organic fluorophores are in great demand. Small organic fluorophores have been derived from the aurone skeleton, 2-benzylidenebenzofuran-3(2H)-one. In this study, we have utilized a model aurone derivative with a methoxy group at the 3' position and a hydroxyl group at the 4' position, termed vanillin aurone, to develop a foundational understanding of structural factors impacting aurone fluorescence properties. The fluorescent behaviors of the model aurone were characterized in solvent environments differing in relative polarity and dielectric constant. These data suggested that hydrogen bonding or electrostatic interactions between excited state aurone and solvent directly impact emissions properties such as peak emission wavelength, emission intensity, and Stokes shift. Time-dependent Density Functional Theory (TD-DFT) model calculations suggest that quenched aurone emissions observed in water are a consequence of stabilization of a twisted excited state conformation that disrupts conjugation. In contrast, the calculations indicate that low polarity solvents such as toluene or acetone stabilize a brightly fluorescent planar state. Based on this, additional experiments were performed to demonstrate use as a turn-on probe in an aqueous environment in response to conditions leading to planar excited state stabilization. Vanillin aurone was observed to bind to a model ATP binding protein, YME1L, leading to enhanced emissions intensities with a dissociation equilibrium constant equal to ~ 30 µM. Separately, the aurone was observed to be cell permeable with significant toxicity at doses exceeding 6.25 µM. Taken together, these results suggest that aurones may be broadly useful as turn-on probes in aqueous environments that promote either a change in relative solvent polarity or through direct stabilization of a planar excited state through macromolecular binding.

Comprehensive linear and nonlinear analysis of the effects of spinning on dynamic balancing ability in Hungarian folk dancers

PurposeIn the case of Hungarian folk dancers, it is crucial to maintain correct posture and promptly respond to imbalances. However, traditional dances often lack specific training to develop these skills.MethodsIn this present study, twelve dancers (8 male, 4 female, age: 21.7 ± 3.6 years) and ten non-dancers subjects forming a control group (6 male, 4 female, age: 21.6 ± 2.87 years) participated. During the measurements a 60-second long bipedal balancing test on the balance board was completed two times, and a spinning intervention was inserted in between the two sessions. The balance capabilities of the two groups were assessed through the characterization of motion on an unstable board, and the analysis of subject’s center of mass and head movements.ResultsDancers applied a more sophisticated and resource-intensive strategy to address the balancing task, yielding a better balancing performance in terms of balance board parameters. By preferring a solid stability in the medio-lateral direction, a greater fluctuation in the anterior-posterior direction can be observed (e.g., significantly lower SampEn values). The overall more successful performance is further evidenced by within-subject comparison since significant differences were observed mostly within the control group. Based on the results, the advanced balancing ability of the folk dancer group is more likely to be acquired through years of experience.ConclusionThe results indicate that additional specialized training could further enhance this ability, encouraging the reliance on poorly memorized corrective movements and reducing the risk of injury.

Transition to fully developed turbulence in liquid-metal convection facilitated by spatial confinement

Using thermal convection in liquid metal, we show that strong spatial confinement not only delays the onset Rayleigh number $Ra_c$ of Rayleigh–Bénard instability but also postpones the various flow-state transitions. The $Ra_c$ and the transition to fully developed turbulence Rayleigh number $Ra_f$ depend on the aspect ratio $\varGamma$ with $Ra_c\sim \varGamma ^{-4.05}$ and $Ra_f\sim \varGamma ^{-3.01}$ , implying that the stabilization effects caused by the strong spatial confinement are weaker on the transition to fully developed turbulence when compared with that on the onset. When the flow state is characterized by the supercritical Rayleigh number $Ra/Ra_{c}$ ( $Ra$ is the Rayleigh number), our study shows that the transition to fully developed turbulence in strongly confined geometries is advanced. For example, while the flow becomes fully developed turbulence at $Ra\approx 200Ra_c$ in a $\varGamma =1$ cell, the same transition in a $\varGamma =1/20$ cell only requires $Ra\approx 3Ra_c$ . Direct numerical simulation and linear stability analysis show that in the strongly confined regime, multiple vertically stacked roll structures appear just above the onset of convection. With an increase of the driving strength, the flow switches between different-roll states stochastically, resulting in no well-defined large-scale coherent flow. Owing to this new mechanism that only exists in systems with $\varGamma &lt;1$ , the flow becomes turbulent in a much earlier stage. These findings shed new light on how turbulence is generated in strongly confined geometries.

Enhance the Performance of Directional Feature-based Palmprint Recognition by Directional Response Stability Measurement

Enhance the Performance of Directional Feature-based Palmprint Recognition by Directional Response Stability Measurement

The margin of stability is affected differently when walking under quasi-random treadmill perturbations with or without full visual support.

Sensory-motor perturbations have been widely used to assess astronauts' balance in standing during pre-/post- spaceflight. However, balance control during walking, where most falls occur, was less studied in these astronauts. A study found that applying either visual or platform oscillations reduced the margin of stability (MOS) in the anterior-posterior direction (MOSap) but increased MOS in the medial-lateral direction (MOSml) as a tradeoff. This tradeoff induced an asymmetric gait. This study extended the current knowledge to investigate overall stability under unpredictable environments. This study aimed to determine (1) whether quasi-random treadmill perturbations with or without full vision support would result in a significant reduction in MOSap but an increase in MOSml and (2) regardless of whether vision support was provided, quasi-random treadmill perturbations might result in asymmetric gait patterns. Twenty healthy young adults participated in this study. Three experimental conditions were semi-randomly assigned to these participants as follows: (1) the control condition (Norm), walking normally with their preferred walking speed on the treadmill; (2) the treadmill perturbations with full vision condition (Slip), walking on the quasi-random varying-treadmill-belt-speeds with full vision support; and (3) the treadmill perturbations without full vision condition (Slip_VisionBlocked, blackout vision through customized vision-blocked goggles), walking on the quasi-random varying-treadmill-belt-speeds without full vision support. The dependent variables were MOSap, MOSml, and respective symmetric indices. A one-way repeated ANOVA measure or Friedman Test was applied to investigate the differences among the conditions mentioned above. There was an increase in MOSap in Slip (p=0.001) but a decrease in MOSap in Slip_VisionBlocked (p=0.001) compared to Norm condition. The MOSml was significantly greater in both Slip and Slip_VisionBlocked conditions compared to the Norm condition (p=0.011; p<0.001). An analysis of Wilcoxon signed-rank tests revealed that the symmetric index of MOSml in Slip_VisionBlocked (p=0.002) was greater than in the Norm condition. The novelty of this study was to investigate the effect of vision on the overall stability of walking under quasi-random treadmill perturbations. The results revealed that overall stability and symmetry were controlled differently with/without full visual support. In light of these findings, it is imperative to take visual support into consideration while developing a sensory-motor training protocol. Asymmetric gait also required extra attention while walking on the quasi-random treadmill perturbations without full vision support to maintain overall stability.

Observer‐based adaptive controller for a class of fractional‐order uncertain systems subject to unknown input and output quantizers and input nonlinearities

This work addresses design of an adaptive controller for nonlinear fractional‐order (FO) systems in the strict‐feedback form. The system is subject to unknown dynamics, unavailable state variables, quantized input and output, and input nonlinearity. The fuzzy logic system (FLS) is used to estimate the unknown dynamics, and instead of updating all the regressor weights, only the maximum of their norms is updated, which significantly reduces the computational load. Limitations imposed by data transmission bandwidth have been addressed by incorporating sector‐bounded quantizers, which include both logarithmic and hysteresis quantizers at the system input and output, and their errors have been considered in the controller design. It is assumed that system states are not measured. To estimate the system states, a linear observer has been used. Because of output quantization, the continuous output signal is not available, and therefore the observer has been designed based on the quantized output signal. In addition, the constraints of input nonlinearities, including symmetric and asymmetric saturation, backlash, hysteresis, and dead‐zone, have been considered in the controller design. Input nonlinearity and input quantization have been investigated simultaneously, which makes the analysis more challenging. Moreover, it is assumed that the type of input nonlinearity and its characteristics are not known, which makes the controller design more difficult. These problems have been resolved by using two novel adaptive laws. The adaptive backstepping method and the direct Lyapunov stability analysis have been used to construct the controller, and a nonlinear modified FO filter is used to avoid the explosion of complexity occurring in the traditional backstepping technique. Stability of the closed loop system has been established, and it has been shown that the tracking and state estimation errors converge to a small neighborhood of the origin. Finally, the proposed controller performance has been demonstrated via three simulation examples.

Effect of Silicon Oil with Nano Particles in Direct Absorption of Solar Thermal Collectors

We discussed about various aspects of solar energy, including its growth due to technological advancements and government support. It explores the utilization of solar energy in different climatic conditions, techno-economic analyses for hydrogen production, and solar-assisted biomass conversion. The section on Solar Thermal Collectors highlights different collector types, their efficiencies, and environmental impacts. The Nano Platelets section delves into the use of graphene nanoplatelets in direct absorption solar collectors, their structure, stability, and potential applications. Additionally, the paragraph touches on the application of graphene in coatings, cement-based composites, and nanocomposites, showcasing their impact on thermal and electromagnetic properties. The discussion extends to silicon oil-based materials, detailing their use in engine bearing alloys, transformer insulation, and environmental considerations. The findings emphasize the multifunctional benefits of graphene and nanocomposites in enhancing various properties, making them promising for future energy solutions. Keywords: Solar Energy, Solar Thermal Collectors, Thermal Nano Platelets, Silicon Oils.

Experimental study on the course stability of a towed barge model

The course instability problem of towed objects is discussed in the paper. It is noted that many non-selfpropelled vessels do not have directional stability, as a result of which they make oscillatory movements relative to the course of the towing ship. Increased yaw rate leads to a decrease in towing speed, an increase in loads on the elements of the towing device and a significant increase in the width of the running lane. These factors can lead to an emergency and significantly complicate the towing process, especially on inland waterways. Two main ways to increase directional stability are considered. These are towing “on V-line”, that is a system in which the towing rope is divided into two parts and attached to two points of the towed barge, located symmetrically relative to the centerline, and the installation of skegs in the stern. To determine the effect of these methods, tests of a model of the mixed riversea navigation oil barge 2731 are carried out in calm deep water conditions in the experimental tank of the Admiral Makarov State University of Maritime and Inland Shipping. The root end of the towing rope is attached to the pylon of the towing tank trolley and, thus, the reverse influence of the barge on the characteristics of the tug movement is not taken into account. Sixteen options are considered. The half-width of the running lane is taken as a criterion for the stability of barge movement. As follows from the test results, with increasing towing speed and towing rope length, the width of the running lane increases slightly. The installation of end washers on the skegs has no effect on the stability of the barge. To reduce the width of the running lane occupied by the barge, it is recommended to use towing “on the V-line” and use skegs with fixed flaps.

Automotive wheel torque control systems

The approaches of foreign specialists to improving electronic control systems for the dynamic state of vehicles (traction, directional stability, rollover resistance) to improve their safe operation are analyzed. The three main components of the Active Transmission Torque Management (ADTM) system are considered: the center clutch, the electronic limited slip differential (ELSD), and the torque vectoring system. The possibilities and limitations of using active torque control systems to ensure vehicle safety are shown. Keywords: electronic control, vehicle dynamics, wheel torque, torque vectoring, active safety. alexey.scherbin@nami.ru

The influence of jump-landing direction on dynamic postural stability following anterior cruciate ligament reconstruction

BackgroundTraditional testing prior to return to sport following anterior cruciate ligament reconstruction typically involves jump-landing tasks in the forward direction. As injury is most likely the result of multiplanar neuromuscular control deficits, assessment of dynamic postural stability using landing tasks that require multiplanar stabilization may be more appropriate. The purpose of this study was to examine how dynamic postural stability is affected when performing jump-landing tasks in three different directions. MethodsFifteen athletes [11 females (18.0 ± 3.0 years) and 4 males (18.5 ± 3.1 years)] following anterior cruciate ligament reconstruction performed a series of single-limb jump-landing tasks in 3 directions. Individual directional stability indices and a composite dynamic postural stability index were calculated using ground reaction force data and were compared using separate one-way repeated measures ANOVAs. FindingsAll directional stability indices demonstrated a significant main effect for jump-landing direction (medial-lateral P < 0.001, η2p = 0.95; anterior-posterior P < 0.001, η2p = 0.97; vertical P = 0.021, η2p = 0.24). The diagonal jump-landing direction produced increased medial-lateral stability and vertical stability scores, while the forward and diagonal jump-landing directions produced increased anterior-posterior stability scores. There was no significant effect for the composite dynamic stability index score. InterpretationJump-landing direction affects dynamic postural stability in all 3 planes of movement in athletes following anterior cruciate ligament reconstruction. Results indicate the potential need to incorporate multiple jump-landing directions to better assess dynamic postural stability prior to return to sport.

Stability Analysis for High-Speed Boundary-Layer Flow with Cavities

This study uses direct numerical simulation and stability analysis methods to investigate the impact of wall cavity defects on the instability of boundary layers at Ma=5.92 and Ma=1.38. For flow at Ma=5.92, synchronization points with equal phase velocities in both fast and slow modes play a crucial role in controlling disturbance wave growth. When the inlet disturbance wave frequency (ω=0.98) approaches the synchronization point frequency, the impact of cavity size on the growth of the disturbance wave can be divided into three regions in the (L/δ99, D/δ99) plane, namely, region A, region B, and region C. Region A refers to small cavities with L/δ99<2, which have the weakest suppression effect. Region B includes large cavities with L/δ99>2 and D/δ99<1.5 and exhibits the best suppression effect. Finally, region C covers cavities with L/δ99>3 and D/δ99>1.5 and shows a non-monotonic control effect on the growth of disturbance wave as the cavity depth varies. For flow at Ma=1.38, cavities of different sizes always enhance the growth of disturbance waves. The widest and shallowest cavities (L/δ99>5, D/δ99<2) exhibit the most significant enhancement.