Two-dimensional Disturbances Research Articles

Periodic surface disturbances in the concentration-stratified viscous fluid

The propagation of two-dimensional periodic capillary-gravitational periodic disturbances of a free surface in a viscous uniformly stratified liquid is investigated. Dispersion relations describing periodic surface flows of physical quantities are obtained. It is shown that there are additional flow components that are absent in the model of an ideal fluid. The obtained dispersion relations uniformly converge to the known expressions in the limit transitions.

Stability of a viscous liquid film flowing down an inclined plane with respect to three-dimensional disturbances

An analysis is presented for the stability of a viscous liquid film flowing down an inclined plane with respect to three-dimensional disturbances under the action of gravity and surface tension. Using momentum-integral method, the nonlinear free surface evolution equation is derived by introducing the self-similar semiparabolic velocity profiles along the flow (x- and y-axis) directions. A normal mode technique and the method of multiple scales are used to obtain the theoretical (linear and nonlinear stability) results of this flow problem, which conceive the physical parameters: Reynolds number Re, Weber number We, angle of inclination of the plane θ and the angle of propagation of the interfacial disturbances ϕ. The temporal growth rate ωi+ and second Landau constant J2, based on which various (explosive, supercritical, unconditional, subcritical) stability zones of this flow problem are categorized, contain the shape factors B and β owing to the non-zero steady basic flow along the y-axis direction. A novel result which emerges from the linear stability analysis is that for any given value of Re, We and θ, any stability that arises in two-dimensional disturbances (ϕ = 0) must also be present in three-dimensional disturbances. For ϕ = 0, there exists a second explosive unstable zone (instead of unconditional stable zone) after a certain value of Re (or θ) due to the involvement of B and β in the expression of J2. This explosive unstable zone vanishes after a certain value of ϕ depending upon the values of Re, We and θ, which confirms the stabilizing influence of ϕ on the thin film flow dynamics irrespective of the values of Re, We and θ.

Nonmodal stability analysis of Poiseuille flow through a porous medium

We unravel the nonmodal stability of a three-dimensional nonstratified Poiseuille flow in a saturated hyperporous medium constrained by impermeable rigid parallel plates. The primary objective is to broaden the scope of previous studies that conducted modal stability analysis for two-dimensional disturbances. Here, we explore both temporal and spatial transient disturbance energy growths for three-dimensional disturbances when the Reynolds number and porosity of the material are high, based on evolution equations with respect to time and space, respectively. Modal stability analysis reveals that the critical Reynolds number for the onset of shear mode instability increases as porosity increases. Moreover, the Darcy viscous drag term stabilizes shear mode instability, resulting in a delay in the transition from laminar flow to turbulence. In addition, it demonstrates the suppression of three-dimensional shear mode instability as the spanwise wavenumber increases, thereby confirming the statement of Squire’s theorem. By contrast, nonmodal stability analysis discloses that both temporal and spatial transient disturbance energy growths curtail as the effect of the Darcy viscous drag force intensifies. But their maximum values behave like O(Re2) for a fixed porous material, where Re is the Reynolds number. However, for different porous materials, the scalings for both temporal and spatial transient disturbance energy growths are different. Furthermore, increasing porosity also suppresses both temporal and spatial disturbance energy growths. Finally, we observe that temporal transient disturbance energy growth becomes larger for a spanwise perturbation, while spatial transient disturbance energy growth becomes larger for a steady perturbation when angular frequency vanishes. The initial disturbance that excites the largest temporal energy amplification generates two sets of alternating high-speed and low-speed elongated streaks in the streamwise direction.

Thermoelastic interactions in a micropolar poroelastic medium

The present problem investigates the two-dimensional disturbances in a homogeneous, isotropic, micropolar thermoelastic saturated porous medium under the purview of Green-Lindsay (GL) theory of thermoelasticity. The medium is assumed to be unstrained and unstressed initially and has uniform temperature. The formulation is subjected to a moving thermal shock. Normal mode technique is employed to obtain the exact expressions for the displacement components, stresses, pore pressure and temperature. Numerical computations have been carried out with the help of MATLAB software and the results are illustrated graphically. Comparisons are made to show the effects of time, velocity of the load, micropolar and porous parameters on the resulting quantities. The outcomes point out a strong impact of these parameters on the physical quantities and agree with the boundary conditions. Some particular cases of interest have been deducted from the current investigation to validate the results. The present work is useful and valuable for analysis of problems involving thermal shock, micropolar and poroelastic deformations.

Characteristics of ionospheric disturbances during the 2021 Typhoon Chanthu based on GPS and GLONASS

Severe typhoons often result in substantial economic and human losses. Therefore, near-real-time monitoring and forecasting of severe typhoons have a significant importance. In this paper, characteristics of ionospheric disturbances during the 2021 Typhoon Chanthu are estimated and investigated from GPS and GLONASS measurements. We calculate high-precision de-trended and filtered ionospheric vertical total electron content (VTEC) data based on GPS and GLONASS data from intensive Global Navigation Satellite System (GNSS) observations at 30-second intervals in Taiwan. Based on the VTEC values, we analyze the characteristics of ionospheric disturbances caused by Typhoon Chanthu, such as the time of appearance of ionospheric disturbances, changes in the magnitude of these disturbances, alterations in two-dimensional disturbances, fluctuations in the speed of disturbance propagation, and shifts in the frequency spectrum. The results reveal that both GPS-TEC and GLONASS-TEC exhibit noticeable disturbances during the specified timeframe. These disturbances are accompanied by the occurrence of “N”-type anomalies in TEC. Notably, at the occurrence of the disturbance, the elevation angle of GPS PRN32 and GLONASS PRN1 satellites is approximately 50°-55°, and their respective distances from the typhoon eye are roughly 350 km and 150 km. The propagation velocity and center frequency of the ionospheric disturbances are located in the range of gravity waves. Specifically, the disturbances propagation speeds of GPS PRN32 and GLONASS PRN1 are approximately 129.36 m/s and 128.33 m/s, respectively, while the center frequencies are about 1.17 mHz and 1.43 mHz. The ionospheric perturbations observed by GPS and GLONASS exhibit certain similarities, which provide valuable insights into the relationship between typhoons and ionospheric disturbances.

Zero-Shot Learning-Based Recognition of Highlight Images of Echoes of Active Sonar

Reducing the impact of underwater disturbance targets and improving the ability to recognize real moving targets underwater are important directions of active sonar research. In this paper, the highlight model of underwater targets was improved and a method was proposed to acquire highlight images of the echoes of these targets. A classification convolutional neural network called HasNet-5 was designed to extract the global features and local highlight features of the echo highlight images of underwater targets, which achieved the true/false recognition of targets via multi-classification. Five types of target highlight models were used to generate simulation data to complete the training, validation and testing of the network. Tests were performed using experimental data. The results indicate that the proposed method achieves 92% accuracy in real target recognition and 94% accuracy in two-dimensional disturbance target recognition. This study provides a new approach for underwater target recognition using active sonar.

The Onset of Instability in A Magnetohydrodynamic Channel Flow through Porous Media of Casson Fluid

A detailed study is made on the stability of linear two-dimensional disturbances of Plane Poiseuille Flow (PPF) of Casson fluid through porous media in the presence of a vertical uniform magnetic field, B0 which is extremely useful in metals, mines, and fuels industries. Using the method of normal modes, the disturbance equations are derived. The resulting eigenvalue problem is then solved by the spectral collocation method using Chebyshev-based polynomials. The critical values of the triplets ( Rec, αc, cc ) are obtained for various values of the Casson parameter, η , Hartmann number, Ha , and porous parameter, σp. The stability of the system is discussed using the neutral stability curves for each value of the parameters present in the problem. It is found that the stability regions are enlarged for small values of η and large values of the porous parameter, σp and Hartmann number, Ha. It is also observed that the stability characteristics of plane Poiseuille flow in a porous medium are remarkably different from non-porous cases. The results obtained here contribute to the contemporary efforts to better understand the stability characteristics of PPF of Casson fluid flow through porous media in the presence of a uniform transverse magnetic field.

Influence of variable thermal conductivity and inclined load on a nonlocal photothermoelastic semiconducting medium with two temperatures

The current study explores two-dimensional disturbances in a nonlocal photothermoelastic semiconducting medium with two temperatures by implementing the Green Naghdi-II theory. The thermal conductivity of the medium is assumed to be varying with temperature changes. The formulation is subjected to an inclined mechanical load. A lot of research has been carried out in recent years on photothermoelastic medium, but not much attention has been given to study the dynamical interactions in a nonlocal photothermoelastic medium with two temperatures and variable thermal conductivity under the effect of inclined mechanical load. The analytical solutions of physical field variables such as temperatures, stresses, carrier density and displacement are obtained by using the normal mode analysis method. For a specific material, numerical computations are performed to illustrate the results. The results that were obtained through numerical analysis for the physical quantities are displayed graphically. The comparisons are made among the results obtained by taking into account the different values of time, inclination angle, two temperature parameter, nonlocal parameter, variable thermal conductivity and photothermal elastic constants. Some special cases of interest have been inferred from the present study for validation.

A Free Surface Fluid with Two-Dimensional Periodic Disturbances in Various Models of the Fluid

A Free Surface Fluid with Two-Dimensional Periodic Disturbances in Various Models of the Fluid

Dynamic Disturbance Propagation Model of Pedestrian Panic Behaviors and Lyapunov-Based Crowd Stability Analysis

In public places, pedestrian panic behaviors have received increasing attention due to their dangerous impact on normal pedestrian flow. To address this issue, this study considered crowd panic behaviors as two-dimensional Gaussian disturbances quantitatively triggered by accidents and analyzed the stability of the pedestrian crowd based on Lyapunov criterion. First, this study established a two-dimensional static model for the disturbance pressure in a crowd. Then, a dynamic disturbance–propagation model (DPM) of crowd panic behaviors was proposed based on the conservation law of fluid dynamics. The anisotropy of the disturbance pressure propagation was proven with theoretical derivations and simulation experiments, which kept consistent with ground truth. Further, a stability criterion was proposed for pedestrian crowd flow under disturbances based on Lyapunov theory. To validate the proposed DPM, we simulated a disturbance scenario in the waiting hall of Shanghai Hongqiao Railway Station. Subsequently, the visual disturbance propagation dynamics and crowd state evolution due to a panic behavior disturbance in a pedestrian crowd were investigated; Finally, the experimental results demonstrated that disturbance pressures and pedestrian density fluctuated and diffused with the panic behavior outbreak point as the disturbance center, showing heterogeneous characteristics. This study shows how we can locate the high-risk areas affected by pedestrian panic behaviors in advance, and further help control crowd flow to keep a pedestrian crowd safe in public buildings.

Response of the Shock Wave/Boundary Layer Interaction to Disturbances Induced by the Plasma Discharge

The paper focuses on the investigation of unsteady effects in shock wave/boundary layer interaction. The study was carried out using a flat plate model subjected to a free stream Mach number of 1.43 and a unit Reynolds number (Re1) of 11.5 × 106 1/m. To generate two-dimensional disturbances in the laminar boundary layer upstream of the separation region, a dielectric barrier discharge was employed. The disturbances were generated within the frequency range of 500 to 1700 Hz. The Strouhal numbers based on the length of the separation bubble ranged from 0.04 to 0.13. The measurements were carried out using a hot-wire anemometer. Analysis of the data shows that disturbances in this frequency range mostly decay. The maximum amplitudes of perturbations were observed at frequencies of 1250 Hz and 1700 Hz.

Dynamic modeling and tracking control strategy for flexible telescopic space manipulator based on neural network compensation

Flexible telescopic space manipulator (FTSM) is playing an increasingly important role in assisting astronauts to accomplish space missions. The telescopic structure leads to time-varying dynamical parameters of the FTSM, thereby reducing the tracking control accuracy. At the same time, the lightweight and large length-diameter ratios are very likely to cause the vibration phenomenon of FTSM during the motion. To solve the above problems, in the dynamics modeling, this paper uses the assumed modal method (AMM) and Lagrange principle to establish the dynamics model considering two-dimensional deformation and disturbance torque. Furthermore, the dynamics models are simplified and derived by ignoring the nonlinear terms (INTs). Besides, the influence of the simplified dynamics models on the accuracy of FTSM’s deformation is analyzed by simulation. It is found that the INTs simplified dynamics model has higher modeling accuracy. Based on the INTs simplification model, the control law is designed. More importantly, the RBF neural network is used to identify and compensate for the time-varying terms and disturbance torque in the FTSM. Then the sliding mode control strategy is proposed by the hyperbolic tangent function as the approximation rate. Finally, the effectiveness of the RBF neural network compensated sliding mode control strategy is illustrated by simulation and ground control experiments of the FTSM.

Study on co-seismic ionospheric disturbance of Alaska earthquake on July 29, 2021 based on GPS TEC

With the rapid development of space geodetic information technology, the Global Positioning System (GPS) has been widely used in seismology and space environmental research. Typically, the occurrence of a large earthquake will lead to some changes in the ionosphere, this phenomenon is called coseismic ionospheric disturbances (CIDs). In this contribution, differential slant total electron content (dSTEC) is used to study the anomalous characteristics of the ionosphere. First, based on the ionospheric dSTEC time series and two-dimensional disturbance detection, the temporal and spatial characteristics of ionospheric disturbances can be accurately analysed. Secondly, using wavelet transform spectrum analysis and disturbance propagation velocity, it can be determined that the disturbance sources of this earthquake can be identified as acoustic wave, gravity wave and Rayleigh wave. Finally, in order to further clarify the direction of the earthquake disturbance, this study focuses on proposing an innovative method for the disturbance propagation direction, and determines that there are two directions of the propagation of the CIDs of the Alaski earthquake.

Numerical Study of Instability of Medium Interface During Thermonuclear Combustion of a Cylindrical Shelled Microtarget

The study is limited to two-dimensional disturbances of the interface between media. A computational technology based on the explicit interface separation in the form of one of the lines of a regular grid is used. A method for visualizing spontaneous disturbances at an early stage when they cannot yet be seen on the interface profile is proposed. It is shown that the computer rounding error plays an insignificant role in their formation. For the late stage of the disturbance development, a method for obtaining the profile of the local oscillation amplitude along the interface is proposed. The features of spontaneous disturbance at different stages of its development are studied. It is shown that the spontaneous disturbance tends to grid convergence, at least until the beginning of the process of formation of a quasi-stationary shockless combustion wave. It is shown that during the formation of a quasi-stationary wave and its subsequent motion, an additional spontaneous disturbance arises. The interaction of a specified sinusoidal disturbance having an initial amplitude of up to 0.1 of the wavelength with a quasi-stationary combustion wave is studied. It is shown that the Kelvin–Helmholtz instability is the main mechanism for the development of instability at the nonlinear stage. The combustion wave is not destroyed. The profiles of the oscillation amplitude of the given disturbance are obtained, from which it is possible to extract the universal time-independent part.

Ionospheric Disturbances Triggered by China's Long March 2D Rocket

Using the data of 382 ground global navigation satellite system (GNSS) network stations in Western China, we studied and analyzed the ionospheric disturbances triggered by the “Long March” 2D rocket launch in Jiuquan, China on December 3, 2017. As compared with previous research, a higher sampling resolution for GNSS data (with a frequency of 1 Hz) was used to obtain more accurate occurrence times and propagation velocities of ionospheric disturbances. By using a method based on a quadratic function of time to fit a raw total electron content (TEC) series, a filtered TEC series was calculated using carrier observations, and a two-dimensional disturbances map was drawn. A new method, which accounts for the flight time of the rocket, was used to calculate the velocity of the shock wave. Ionospheric depletions and the shock wave were observed after the launch of the rocket. The depletion was observed within 100 to 1000 km south of the launch site along the rocket trajectory, which had a maximum amplitude of ∼3.8 TEC units (TECU), reaching ∼56% of the background TEC. A shock wave of V-shaped disturbances with amplitudes of ∼0.67 TECU was detected on both sides of the rocket trajectory. The shock wave moved southeast at an average velocity of ∼1861 m/s at a location 2200 km away from the launch site. Ionospheric disturbances with distances of more than ∼3000 km from the launch site were also observed.

Effects of anisotropy on the stability of Giesekus fluid flow

In the present work, the stability of a viscoelastic fluid flow is studied by linear stability theory, and some results are verified by direct numerical simulation. The investigation considers the fluid flow between two parallel plates, modeled by the Giesekus constitutive equation. The results show the influence of the anisotropic tensorial correction parameter αG on this model, showing a stabilizing influence for two-dimensional disturbances for small values of αG. However, as αG increases, a reduction in the critical Reynolds number values is observed, possibly hastening the transition to turbulence. Low values for αG for three-dimensional disturbances cause more significant variations for the critical Reynolds number. This variation decreases as the value of this parameter increases. The results also show that low values of αG increase the instability of three-dimensional disturbances and confirm that Squire's theorem is not valid for this model. As for the two-dimensional disturbances, the anisotropic term on the Giesekus model lowers the critical Reynolds number for higher quantities of polymer viscosity in the mixture and high values for the Weissenberg number.

Economic plantwide control of a hybrid solid oxide fuel cell - gas turbine system

This study presents a novel approach for hybrid solid oxide fuel cell (SOFC) - gas turbine (GT) system control. The approach is based on a plantwide top-down strategy which leads to a proper selection of the control structure. As a result, while maintaining the system stability and dynamic performance during transients, the system operation is also kept at optimal conditions using simple PI controllers. The optimization cost function is defined to be the unit price of the net produced electricity. The system inlet fuel flow and the power drawn from the SOFC are considered as the main system disturbances. The two-dimensional disturbance space is discretized. Rigorous optimization problems are performed in each disturbance node and variation of system efficiency and constraint values are evaluated. Three different operating regions, with different sets of active constraints, are characterized. Equivalent to the identified operating regions, an efficiency map is also provided which illustrates the achievable system efficiencies in presence of disturbances. Based on the optimization outcomes, the identification of appropriate controlled variables is accomplished in each region. It revealed that to keep near-optimal operation under various operating conditions; the combustion chamber outlet temperature should be treated as a key controlled variable. Finally, dynamic simulations are performed and the proficiency of the proposed control structure is justified. According to the results, maximum SOFC temperature transients in all regions would be less than 2 K.min-1 while variations on the hybrid system output power are kept below 3 % and efficiency loss is restricted to 2 %.

On the validity of Squire’s theorem for viscoelastic fluid flows

This work presents a practical methodology to verify the validity of Squire’s theorem for viscoelastic fluid flow stability analysis. Squire’s theorem presents a relationship between two-dimensional and three-dimensional disturbances. The theorem shows that the critical Reynolds number for two-dimensional disturbances is smaller than any value for which unstable three-dimensional disturbances exist. This conclusion simplifies the stability analysis for fluid flows which satisfies this theorem by becoming sufficient for the stability analysis to look only for the two-dimensional disturbances to find the most dangerous condition. In the present investigation, the validity of Squire’s theorem is accessed for viscoelastic fluid flows considering the Upper-Convected Maxwell, Oldroyd-B, Giesekus, LPTT and FENE-type models. The mass, momentum, and viscoelastic constitutive equations are manipulated to arrive at the equivalent two-dimensional equations required for Squire’s Theorem validity. It was verified that Squire’s theorem is valid for the Upper-Convected Maxwell and the Oldroyd-B isotropic models as already known in the literature, showing that the proposed methodology is consistent with previous results. However, for the Giesekus, the LPTT and the FENE-type anisotropic models, the analysis shows that Squire’s theorem is not valid, indicating the relation between the isotropic behavior of the fluids and the validity of Squire’s theorem.

The onset of instability in a hydromagnetic channel flow of Casson fluid: the accurate solutions

We study the temporal stability of linear two-dimensional disturbances of plane Poiseuille flow of a Casson fluid in a rigid parallel channel under the influence of a uniform magnetic field. When the disturbance is taken in normal mode it transforms the perturbed equations to a fourth-order eigenvalue problem which is then solved by the spectral method. We first obtain sufficient conditions for the hydrodynamic stability in the channel by analyzing the nature of the growth rate and the Reynolds number. For the chosen set of parameters, the eigenspectra of the flow exhibit the familiar Y-shaped structure with three distinct modes depending on the phase speed approach. The eigenfunctions corresponding to the least stable and most unstable eigenmodes have the symmetric and antisymmetric modes. For a certain range of Casson parameter β and the magnetic number M, instability always appears on the wall mode for which the eigenfunction is antisymmetric about the channel center-line. The neutral stability curves that correspond to various values of β and M are found to be an extension of the continuation of the Tollmien-Schlichting instability that is noticed for a Newtonian channel flow. The regions of stability are enlarged for small β and large M.

Non-modal growth of finite-amplitude disturbances in oscillatory boundary layer

The essence of sub-critical transition of oscillatory boundary-layer flows is the non-modal growth of finite-amplitude disturbances. The current understanding of the mechanisms of the orderly and bypass transitions of oscillatory boundary-layer flows is limited. The present study adopts optimisation approaches to predict the maximum energy amplification of two- and three-dimensional perturbations in response to the optimal initial disturbance with or without external forcing. A series of direct numerical simulations are also performed to compare with the results obtained from the stability analyses. In particular, the optimal initial perturbation similar to a Tollmien–Schlichting (T–S) wave yields the largest transient growth under the combined effects of the Orr mechanism and inflectional point instability. With a considerable level of two-dimensional disturbance, the vortex tube nonlinearly develops from the T–S-like wave, and then either deforms into a $\varLambda$ -vortex in the near-wall region or rolls up to the free shear region. The further burst of turbulence can follow the first pathway as K-type transition or the second one as vortex tube breakdown due to the elliptical instability. Additionally, non-modal growth can initiate the inception of streaky structures by favourable three-dimensional initial perturbations and/or forcing. The secondary instabilities responsible for the streak breakdown are classified as the varicose (symmetric) and sinuous (anti-symmetric) modes. Under a sufficiently high level of three-dimensional disturbance, the bypass transition is predominantly characterised by the formation of the sinuous mode and turbulent spots, which leads to the suppression of inflection point instability.