Motion State Research Articles

A multi-agent motion simulation method for emergency scenario deduction

Simulating crowd motion in emergency scenarios remains a challenge in computer graphics due to crowd heterogeneity and environmental complexity. However, existing crowd simulation methods homogenize the agent model and simplify target selection and motion navigation of emergency crowds. To address these problems, we propose a multi-agent motion simulation method for emergency scenario deduction. First, we propose a multi-agent model to simulate crowd heterogeneity. This model includes a personality-based heterogeneous agent model and an agent perception model that considers vision, hearing, and familiarity with the environment. Second, we propose a target selection strategy based on the motion patterns of actual pedestrians. This strategy employs mathematical models and our agent perception model to guide agents in selecting appropriate targets. Finally, we propose a global navigation algorithm that combines random sampling with heuristic search methods. Concurrently, we use our multi-agent model to adjust the agent’s local motion planning to deduce the motion states of emergency crowds naturally. Experimental results validate that our method can realistically and reasonably simulate crowd motion in emergency scenarios.

A preliminary study on the stability of bare footprint linear measurements in four motion states

In some crime scenes, there may be bare footprints. Analyzing and testing the linear measurements of bare footprints in crime scenes can play an important role in personal analysis and individual identification. However, the linear measurements of bare footprints may be influenced by different motion states, leading to changes in length and width or even significant deviations. Previous studies focused on the linear differences between static and dynamic footprints, and failed to take the speed factor into consideration. This paper studied the stability and change regularities of the linear measurements of bare footprints in four different motion states: standing, normal walking, fast walking and trotting. Dust footprints of the right feet were collected from 80 healthy young adults under these four motion states. Seven linear measurements were obtained for each footprint using the Reel method, totaling 2240 data sets. One-way repeated measures ANOVA was used to assess the measurement variations across the four states. The results showed that there were statistically significant variances in the length measurements (A1-A5) between the standing state and other motion states, whereas no statistically significant variances were observed between the three dynamic states. It was found that the mean values of the five length measurements (A1–A5) increased from static to dynamic state, and then gradually decreased slightly as the walking speed increased. Additionally, no significant differences were found in the two width measurements (MPJ Width and Calc Width) between the four motion states. As a preliminary study, this study can provide a reference for the analysis of bare footprints in different motion states extracted from crime scenes.

Detection-first tightly-coupled LiDAR-Visual-Inertial SLAM in dynamic environments

To address the challenges posed by the dynamic environment for Simultaneous Localization and Mapping (SLAM), a detection-first tightly-coupled LiDAR-Visual-Inertial SLAM incorporating lidar, camera, and inertial measurement unit (IMU) is proposed. Firstly, the point cloud clustering with semantic labels are obtained by fusing image and point cloud information. Then, a tracking algorithm is applied to obtain the information of the motion state of the targets. Afterwards, the tracked dynamic targets are utilized to eliminate extraneous feature points. Finally, a factor graph is used to jointly optimize the IMU pre-integration, and tightly couple the laser odometry and visual odometry within the system. To validate the performance of the proposed SLAM framework, both public datasets (KITTI and UrbanNav) and actual scene data are tested. The experimental results show that compared with LeGO-LOAM, LIO-SAM and LVI-SAM for public dataset, the root mean squared error (RMSE) of proposed algorithm is decreased by 44.56 % (4.47 m) and 4.15 % (4.62 m) in high dynamic scenes and normal scenes, respectively. Through actual scene data, the proposed algorithm mitigates the impact of dynamic objects on map building directly.

4D printing bio-inspired chiral metamaterials for flexible sensors

Chiral metamaterials were a typical metamaterial configuration, which had broad application prospects in vibration isolation, energy absorption and other fields. Although 4D-printed chiral metamaterials have been investigated by introducing stimulus-responsive materials to achieve programmable properties of metamaterials, chiral metamaterials are mostly fabricated by single materials, which limits the adjustable domains of the mechanical properties and the design freedom of metamaterials. In this work, inspired by the configuration of collagen fibers of biological tissues, the bio-inspired chiral metamaterials with wave ligaments were developed. The bi-phase (TPE@PLA-SMP) composite chiral metamaterials were fabricated by combining active phase (shape memory polylactic acid, PLA-SMP) with passive phase (thermoplastic elastomer, TPE). The influences of geometric parameters, ligament gradient forms, and TPE distribution modes on the mechanical properties of the developed metamaterials were characterized. When the TPE was distributed at 0° and 45°, the deformation of the mechanical metamaterials occurred mainly in the TPE cells, resulting in the J-shaped displacement-force curve. The programmable and reconfigurable properties of the metamaterials (including configuration, and energy absorption performance) under thermal stimulation were demonstrated. The specific energy absorption (SEA) of the metamaterial 2θ = π/2 was realized to transform between 0.92 kJ/kg and 0.38 kJ/kg by shape memory programming. Flexible sensors based on TPE@PLA-SMP composite metamaterials were developed by filling CNC-CNT@PVA composite hydrogels (minimum resistivity 8.1 Ω m), which enabled stable output of electrical signals under repeated loads. A motion state monitor was developed and realized to monitor the wearer's movement such as running, demonstrating its potential application prospects in fields such as flexible electronics.

Direct Closed-Loop Control Structure for the Three-Axis Satcom-on-the-Move Antenna

The traditional Satcom-on-the-Move (SOTM) mechanical structure consists of a dual-axis configuration with an azimuth axis and a pitch axis. In this structure, when the pitch angle is 90 degrees, the rotation of the azimuth axis cannot change the antenna’s direction. To solve this issue, a three-axis SOTM mechanical structure has been developed. The traditional three-axis SOTM servo control system adopts a closed-loop control scheme. In this scheme, due to the difficulty in directly obtaining the antenna’s rotation angle, the angles of rotation for each axis are typically selected to represent the antenna’s rotation angle. The closed-loop feedback includes the angles and angular velocities of the axes, which cannot completely capture the antenna’s motion state, essentially constituting an indirect closed-loop control. Addressing the shortcomings of this indirect closed-loop control, this paper first establishes the kinematic relations between the axes of the three-axis SOTM antenna using the Denavit–Hartenberg (DH) method. Subsequently, the relationship between antenna pointing and the rotational states of the three axes was derived using the Jacobian operator. Building upon this foundation, a direct closed-loop control structure for a three-axis SOTM antenna was designed. To enable the control system to achieve rapid convergence with minimal overshoot, an Active Disturbance Rejection Control (ADRC) algorithm based on smooth continuous functions is introduced as the inner and outer loop controller algorithms within the direct closed-loop control structure. To address the nonlinearity in the design scheme, a piecewise linearization method is proposed to reduce the demands on the microprocessor’s performance and enhance the engineering feasibility of the solution. Finally, the effectiveness of the proposed approach is validated through experiments. The experimental results demonstrate that compared to traditional indirect closed-loop control methods, utilizing the direct closed-loop control method for the three-axis SOTM antenna presented in this paper can lead to higher precision in pointing the antenna towards satellites and enhance communication effectiveness.

Maneuvering extended target tracking method based on transformer network

This research introduces a new approach to address the challenges related to inaccuracies in shape estimation and motion state tracking during the tracking of maneuvering extended targets. The method combines a novel neural network model with a cubature Kalman filter. Initially, the target’s shape variation is represented using a second-order autoregressive model, and Bayesian filtering is employed for target contour estimation in static environments. Subsequently, the kinematic state tracking of maneuvering targets is enhanced by modifying a neural network model based on Transformer architecture. Through the effective integration of these techniques, precise tracking of maneuvering extended targets is achieved, facilitating accurate estimation of irregular contour information while tracking the targets’ motion state in real-time. The efficacy of the proposed approach is further confirmed through various simulation scenarios, underscoring its suitability for tracking maneuvering extended targets.

Multimodal soft sensor integrated with hydrogel-optoelectronic for wrist motion monitoring

Developing a multimodal flexible sensor capable of incorporating multiple sensing mechanisms in a restricted space remains difficult. In this study, we propose a unique multimodal soft sensor that utilizes a rectangular transparent conductive hydrogel as both strain resistance and optoelectronic propagation channel to achieve the integration of both resistive and optoelectronic sensing mechanisms in a single geometrical unit, which further enables the detection of multiple mechanical deformation modes. This sensor exhibits excellent sensitivity (1.92 for stretching, 4.43 rad−1 for width-bending, 1.78 rad−1 for height-bending), a large measurement range (0-90° for bidirectional bending, 0–100 % for stretching), and high stability (drift 3.0 % for stretching, 2.9 % for width-bending, 1.9 % for height-bending). And a Bidirectional Long Short-Term Memory Network (BiLSTM) is created to address the strong coupling issue in multimodal sensing, to achieve decoupling of different deformation signals, and to further realize accurate monitoring of complex wrist motion states.

An enhanced mathematical model for evaluating grid-to-rod fretting wear under complex boundary

Grid-to-rod fretting wear is a significant cause of fuel failure in pressurized water reactors and poses a challenge in fuel performance evaluation. As burnup increases, neutron irradiation can lead to complex changes in the grid-to-rod system, affecting its dynamic behavior. This paper presents an enhanced mathematical model that can simulate the coupled axial-lateral motion and complex boundary conditions, including relaxation support, friction, and gap constraint. Through multiple parametric studies, the model has revealed valuable results. Notably, grid relaxation of 10%–30% significantly impacts wear. Multiple critical excitation frequencies can cause drastic changes in vibration and wear. The increase in holding force due to rod swelling and the early opening of the gap due to creep down require careful attention. Moreover, the effect of axial force on changes in natural frequency and increased wear should be considered.

Analysis of temperature characteristics of high‐speed train wheelset system under complex operating conditions

AbstractWith the rapid advancements in high‐speed train technology, the importance of ensuring the safety of train operations has become paramount. Bearings, being a critical component of train bogies, have garnered significant attention for their role in maintaining safety standards. Monitoring the temperature of bearings to evaluate their motion state is a common practice in high‐speed trains, emphasizing the need for further research into temperature fluctuations. In this study, a dynamic model is developed for the bearing rotor system of high‐speed trains. By considering the contact points between raceways and rolling elements, the power loss in the bearing is obtained and a transient temperature‐field model of the system is established. The relationship between node temperature and factors such as ambient temperature, train running speed, and load is illustrated, with a detailed presentation of the influence of bearing fault type and size on node temperature. The analysis results reveal that the node temperature increases with higher values corresponding to those quantifiable factors and is most affected by rolling element fault. Additionally, it is observed that the temperature rises rapidly in the initial stage and gradually flattens out over time. The comparative analysis of temperature under different fault conditions shows that the node temperature is most affected by the rolling element fault. Experiments and actual line temperature data are used to verify the validity of the model. The comparison results show that the simulation aligns well with experimental and line data. The transient temperature‐field model of the bearing rotor system in high‐speed trains can effectively simulate and predict the temperature change process of each node of the system. The simulation results hold certain theoretical guiding significance for further research and practical applications in ensuring train operation safety.

Data driven digital twin system for the cross-domain vehicle

The Cross-Domain Vehicle (CDV) is a sophisticated marine equipment capable of performing tasks across different domains. This paper aims to develop a data-driven digital twin system for the CDV to achieve precise motion control and data monitoring during its operation. Leveraging the kinematic physical characteristics of the CDV, the digital twin system constructs a virtual counterpart of the vehicle, establishing a mapping relationship between the physical and virtual entities. The use of a Long Short-Term Memory (LSTM) network model is proposed for forecasting the motion state of the CDV within the digital twin framework, supporting the vehicle's autonomous motion decision-making process. Additionally, an innovative model predictive control strategy is employed to achieve surface speed tracking control for the CDV, leveraging predictive data within the digital twin system. Utilizing the digital twin system to optimize control parameters, better underwater depth control effects can be achieved for the CDV. Finally, through the system implementation and experiment verification, the effectiveness of the digital twin system is successfully demonstrated, providing reliable results for both surface speed tracking control and underwater depth control.

A four unknown non-polynomial theory for the free vibration of angle-ply plates

This research evaluates a non-polynomial type plate theory with four unknowns for the frequency analysis of angle-ply laminated plates. By incorporating exponential functions in terms thickness coordinates, this theory does not need correction factor in order to account for shear deformation effects. A significant advancement of this theory is its ability to satisfy zero shear conditions at the top and bottom surfaces of the plate, streamlining the analysis with only four-unknown variables compared to the five required by traditional first-order plate theory. Equations of motion and boundary conditions are derived using Hamilton’s principle. Utilizing Navier’s approach, the study focuses on the free vibration analysis of laminated plates with simple end conditions. Several numerical examples of angle-ply laminated plates are solved in this paper to verify the accuracy of the proposed theory. The natural frequencies predicted by the proposed theory are rigorously compared against those derived from other established theories and exact solutions to validate the proposed theory. This comparative analysis reveals that the natural frequencies calculated from the developed theory are in remarkable agreement with those obtained from the exact elasticity approach. This research contributes to the field vibration analysis of plates by offering a more efficient and accurate method for estimating the frequencies of angle-ply laminated plates.

Multiscale interaction underlying 2022 concurrent extreme precipitation in Pakistan and heatwave in Yangtze River Valley

Unprecedentedly extreme precipitation occurred in Pakistan (PAK), and mega heat waves persisted along the Yangtze River Valley (YRV) from July to August 2022. Using the advanced multiscale window transform-based canonical transfer attribution framework, we quantitatively delineated intra-scale and inter-scale interactions leading to record-breaking spatially concurrent extremes in 2022 and comprehensively revealed differences in dynamic processes affecting extreme events in July and August. The basic flow scale window lost the available potential energy (APE), and through APE canonical transfers to the intraseasonal-scale and synoptic-scale windows, the inter-scale dynamic processes and barotropic instability of the basic flow scale preserved the concurrent extreme in July. In August, the eruptive synoptic-scale kinetic energy convergence provided dynamic conditions for the sinking motion of the YRV and its advection to PAK from the Indian Ocean. Consequently, the interaction between high- and low-frequency processes drove atmospheric circulation in summer, but the high-frequency process in August played a vital role in extreme events. Additionally, the heat source in the tropical western-central Pacific is considered one of the key drivers for localized repetitive bursts of energy. This study emphasizes both the interactions between multiple scales of atmospheric dynamics and reveals the driving mechanisms behind the impacts of warming on extreme events, linking the external forcing issue with the free problem of atmospheric internal instability.

A multi-scale attributes fusion model for travel mode identification using GPS trajectories

ABSTRACT Travel mode recognition is a key issue in urban planning and transportation research. While traditional travel surveys use manual data collection and have limited coverage, poor timeliness, and insufficient sample capacity, recent advancements in Global Positioning System (GPS) technology allow large-scale data collection and offer novel opportunities to enhance travel mode recognition. However, existing studies often neglect regular differences and changes in motion states across different travel modes and fail to fully integrate multi-scale spatio-temporal features, which limits the accurate classification of travel modes. To fill this gap, this study proposes a multi-scale spatio-temporal attribute fusion (MSAF) model for precise travel mode identification using solely GPS trajectories without altering their sampling rate. The MSAF model segments GPS trajectories into various temporal and spatial scales, extracting local motion states and spatial features at multiple scales. The spatio-temporal feature extraction module is constructed to extract local motion states and capture spatio-temporal dependencies. Additionally, the model incorporates a multi-scale feature fusion module, which effectively combines features of various scales through a series of fusion techniques to obtain a comprehensive representation, enabling automatic and accurate travel mode identification. Experiments on real-world datasets, including the GeoLife Trajectories dataset and the Sussex-Huawei Locomotion-Transportation (SHL) dataset, demonstrate the effectiveness of the MSAF model, achieving a competitive accuracy of 95.16% and 91.70%. This represents an improvement of 2.50% to 7.95% and 0.8% to 6.62% over several state-of-the-art baselines, effectively addressing sample imbalance challenges. Moreover, the experiments demonstrate the significant role of multiscale feature fusion in improving model performance.

Coordination control strategy of motion stability and tire slip for electric vehicle driven by in-wheel-motors

The Direct Yaw Moment Control (DYC) is a widely utilized technique for electric vehicles equipped with In-Wheel Motors (IWMs) to ensure yaw stability. However, most existing DYC studies calculate the additional control yaw moment solely based on the torque differences among the four IWMs, disregarding the nonlinear tire characteristics and wheel rotational movements. When road conditions are poor or torque changes are intense, the tire may slip, preventing it from generating the required longitudinal tire force for the desired direct yaw moment. To address this challenge, this study introduces a coordination control strategy for motion stability and tire slip in electric vehicles (EV) driven by IWMs. To enhance control performance, the nonlinear tire characteristics and wheel rotational movements are integrated into the modeling process when calculating tire forces. Additionally, a state and parameter coupling estimation algorithm is utilized to obtain feedback on tire parameters and vehicle motion states. Using these estimation results as a foundation, a coordination strategy is developed to achieve reference motion state tracking and tire slip ratio control. The Model Predictive Control (MPC) algorithm is employed to solve the control problem with constraints on both control inputs and outputs, and the estimation results are utilized to update the control model as well as provide states feedback. Simulations and experiments are conducted to validate the feasibility and effectiveness of the proposed control strategy. The results demonstrate that our proposed control strategy effectively improves vehicle stability by coordinating vehicle motion and tire slip control.

Dynamic characteristics of suspended particles influenced by cavitation bubble in a free field

This study investigates the dynamic characteristics of suspended particles in a free field under the influence of a single cavitation bubble. The phenomenon of suspended particles being influenced by cavitation bubbles of comparable size reflects the dynamic characteristics of particles, a common occurrence in both hydraulic machinery and biopharmaceutical fields. A high-speed camera captures the process of a single cavitation bubble interacting with suspended particles. Combined with three-dimensional numerical simulations, the motion states of suspended particles as the cavitation bubble expands and contracts are analyzed. Observations reveal that at various initial distances between suspended particles and the cavitation bubble, suspended particle motion is consistently influenced by the expansion and contraction of the same cavitation bubble during the initial four processes. The particle motion direction is parallel to the propagation direction of the radiation force produced during the expansion and collapse of the cavitation bubble, consistent with the characteristics of motion under longitudinal wave effects. The initial distance between suspended particles and the cavitation bubble dictates the ultimate displacement direction of suspended particles, with the influence of the cavitation bubble on suspended particle velocity weakening as their distance increases. Under conditions where particle size closely matches that of the bubble, the jet produced by the cavitation bubble does not significantly accelerate particles, and the influence of the jet on suspended particle motion states could be disregarded. The investigation reveals that the suspended particles are primarily influenced by the radiation force, drag force, and virtual mass force exerted by the cavitation bubble.

Locomotion and strike damage of fish passing through a fish friendly tubular pump using computational fluid dynamics and discrete element coupling method

The tubular pump is a typical water transfer apparatus designed for extremely low heads and large flow rates. It serves as the core equipment in pumping stations situated at lakes, rivers, and canals. An adverse effect on the ecological environment stems from fish injury and mortality primarily caused by blade strikes. The present work combines computational fluid dynamics and the discrete element method to simulate the dynamics of fish passing through a simplified blade, allowing us to establish a safe margin of the strike force to further assess fish damage in a more complex tubular pump system. The results indicated that strikes on fish alter their motion state in terms of direction and magnitude, inducing chaotic movements that heighten the risk of subsequent strikes with downstream components. Fish tend to align their velocities with the surrounding fluid due to flow-induced drag after multiple contacts with solid structures. The knife-shaped leading edge, and particularly the blade tip side, emerged as the primary factor in creating strike damage, and the adoption of a slanted and blunt leading edge can effectively reduce fish damage. In addition, decreasing the shaft speed, increasing the flow rate, and restricting the fish size were identified as measures conducive to fish survival in running pumps. The study further suggested that using fewer but larger pumps operating at lower shaft speeds would contribute to better fish friendliness, which can also ensure a sufficient delivery head and mass flow rate.

Displacement versus velocity memory effects from a gravitational plane wave

This article demonstrates that additionally to the well-known velocity memory effect, a vacuum gravitational plane wave can also induce a displacement memory on a couple of test particles. A complete classification of the conditions under which a velocity or a displacement memory effect occur is established. These conditions depend both the initial conditions of the relative motion and on the wave profile. The two cases where the wave admits a pulse or a step profile are treated. Our analytical expressions are then compared to numerical integrations to exhibit either a velocity or a displacement memory, in the case of these two families of profiles. Additionally to this classification, the existence of a new symmetry of polarized vacuum gravitational plane wave under Möbius reparametrization of the null time is demonstrated. Finally, we discuss the resolution of the geodesic deviation equation by means of the underlying symmetries of vacuum gravitational plane wave.

Study on debris flow discharge characteristics of check dam spillway

After a check dam is filled with sediment, the debris flow will flow out from the spillway. Insufficient discharge capacity of the spillway can lead to debris flow scouring the dam's shoulder and foundation. Therefore, it is necessary to study the discharge capacity of the spillway. It is of great importance for further optimizing the structural design of the check dam. This article analyzes discharge characteristics of debris flow of a spillway through a series of flume experiments. According to the motion states, it can be divided into five stages: contact stage of the spillway, flushing and climbing stage, increasing and reflux stage, stable discharge stage, and final discharge stage. We analyzed the influencing factors of the discharge capacity, including the type of spillway, bulk density of debris flow, scale of debris flow, flume gradient, and effective opening width of the spillway. Furthermore, we derived a calculation formula of discharge for the spillway based on Bernoulli's principle. Finally, we considered the influence of the ratio of flow area and Froude number to the discharge coefficient and established a calculation method of discharge. Consequently, we compared the calculated results with the measured results and found them to be in good agreement. Our research results provide a quantitative calculation method for the design of spillways and energy dissipation and erosion prevention projects under check dams, which is beneficial for improving engineering value and for better serving disaster prevention and reduction efforts.

Extended Kalman filter-based robust roll angle estimation method for spinning vehicles

Attitude measurement is a basic technique for monitoring vehicle motion states and safety. The spin motion of a vehicle couples the attitude angles with each other, which has an impact on the navigation and control of the vehicle. Global navigation satellite system (GNSS) signals-based roll angle measurement methods are important for vehicle attitude measurement. Most of existing studies use continuous signal power, but the case of loop lock loss leading to discontinuous power reception has not been considered. A robust estimation method for the roll angle based on the Tukey weight function is proposed to improve the measurement accuracy in cases of discontinuous reception. The characteristics of the GNSS signals, the geometric relationship between the signal power and roll angle of the vehicle are discussed. By installing a GNSS receiver with a single patched antenna on a rotating platform with a controllable rolling speed, the proposed method was verified by experiments. The robust estimation errors of different weight functions are analyzed. According to the characteristics of the gross measurement errors, a robust estimation method of multisatellite power observations is proposed to obtain a high-precision and stable estimation of the vehicle roll angle. The results show that the proposed algorithm can improve the accuracy of roll angle estimation even with gross measurement errors. As a result of the experiments, the estimation errors of the algorithm are 6.57° at a confidence level of 68 % and 15.49°at the confidence level of 95 %. In contrast, they are 11.38° and 37.31° for the traditional LS method. Moreover, the estimation accuracy of the algorithm is not significantly correlated with the vehicle rotational speed. Therefore, the vehicle roll angle can be estimated with high accuracy under a variety of rotational speeds.

Конвективные режимы псевдопластической жидкости в квадратной полости при воздействии высокочастотных вибраций в условиях пониженной гравитации

In this paper, we investigate convective modes of pseudoplastic fluid in a square cavity with solid perfectly heat-conducting boundaries under reduced gravity. The cavity performs vertical linearly polarized high-frequency vibrations. Between the vertical walls of the cavity a temperature drop is prescribed in the direction perpendicular to vibrations and the field of gravity. The fluid rheology is described using the Williamson model. The problem is solved based on the averaged thermovibration convection equations for nonlinear viscous fluids. The vibration intensity is determined by the vibration parameter V, which is proportional to the ratio of the amplitude of the vibration acceleration to the free-fall acceleration and does not depend on the temperature difference. The problem is found to have two types of solutions, which we call Newtonian and non-Newtonian modes. These solutions correspond to different convective structures, for which the dependences of the maximum of the stream function and the Nusselt number on the Grashof number are derived. We use these dependences for determining at different values of rheological parameters the threshold values of the Grasgof numbers, corresponding to the change in the modes of stationary averaged convection and the critical Grasgof numbers, corresponding to the loss of stability of stationary averaged flow and the occurrence of oscillatory modes of averaged convection. The structures of different modes of averaged stationary and oscillatory convection are studied. The results obtained for the Newtonian mode have shown that at small values of the Grasgoff number, a slow one-vortex stationary convective flow is realized in the cavity. With increasing the Grasgoff number it transforms into a three-vortex flow. A further increase in the Grasgoff number results in the appearance of a four-vortex convective flow, which eventually transforms again into a three-vortex motion. At even greater Gr, the stationary averaged motion becomes unstable and the oscillatory modes appear in the cavity. For the non-Newtonian mode, a stationary convective flow is the basic flow pattern detected in the cavity; the oscillatory modes are not observed in the whole investigated range of the Grasgoff numbers.