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Journal articles on the topic 'Linearized Driving Forces'
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1
Ye, Xiu Qian, Yi Bao Chen, Bih Sheng Hsu, and Yuh Chung Hu. "On the Dynamics of the Micro-Ring Driven by Traveling Bias Voltages." Advanced Materials Research 311-313 (August 2011): 1027–31. http://dx.doi.org/10.4028/www.scientific.net/amr.311-313.1027.
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There is no literature mentioned the modeling of the microstructures subjected to traveling electrostatic forces. This paper is the first time to present an analytical approach to investigate the dynamics of a micro-ring structure driven by the traveling bias voltage. The traveling electrostatic forces may come from the sequentially-actuated actuating electrodes arranged around the flexible ring. A linearized distributed model considering the electromechanical coupling effect is derived based on the small deflection assumption. According to the analytical results, the stiffness of the micro-ring will be softened periodically with the traveling speed of the driving voltage and the variation increases with the increasing of the voltage.
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Lee, Hyeongcheol, and Masayoshi Tomizuka. "Coordinated Longitudinal and Lateral Motion Control of Vehicles for IVHS." Journal of Dynamic Systems, Measurement, and Control 123, no. 3 (March 24, 1998): 535–43. http://dx.doi.org/10.1115/1.1386395.
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This paper presents a systematic design of the combined control of vehicle longitudinal and lateral motions for the Intelligent Vehicle Highway Systems (IVHS). A fully coordinated control of the steering and the accelerating/braking actions is presented to maximize the ability of distributing the traction forces in a desired way. This control method covers a broad range of driving condition by removing several conventional simplification on vehicle dynamics, such as the linearized lateral traction force assumption, the bicycle model assumption, and the non-slip assumption. The nominal traction force concept is also introduced to handle the unknown traction forces. Robust Adaptive Control (RAC) by backstepping for MIMO nonlinear systems is utilized to control the unmatched nonlinear vehicle dynamics, in the presence of parametric uncertainties and uncertain nonlinearities.
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Candioti, Lorenzo G., Thibault Duretz, Evangelos Moulas, and Stefan M. Schmalholz. "Buoyancy versus shear forces in building orogenic wedges." Solid Earth 12, no. 8 (August 10, 2021): 1749–75. http://dx.doi.org/10.5194/se-12-1749-2021.
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Abstract. The dynamics of growing collisional orogens are mainly controlled by buoyancy and shear forces. However, the relative importance of these forces, their temporal evolution and their impact on the tectonic style of orogenic wedges remain elusive. Here, we quantify buoyancy and shear forces during collisional orogeny and investigate their impact on orogenic wedge formation and exhumation of crustal rocks. We leverage two-dimensional petrological–thermomechanical numerical simulations of a long-term (ca. 170 Myr) lithosphere deformation cycle involving subsequent hyperextension, cooling, convergence, subduction and collision. Hyperextension generates a basin with exhumed continental mantle bounded by asymmetric passive margins. Before convergence, we replace the top few kilometres of the exhumed mantle with serpentinite to investigate its role during subduction and collision. We study the impact of three parameters: (1) shear resistance, or strength, of serpentinites, controlling the strength of the evolving subduction interface; (2) strength of the continental upper crust; and (3) density structure of the subducted material. Densities are determined by linearized equations of state or by petrological-phase equilibria calculations. The three parameters control the evolution of the ratio of upward-directed buoyancy force to horizontal driving force, FB/FD=ArF, which controls the mode of orogenic wedge formation: ArF≈0.5 causes thrust-sheet-dominated wedges, ArF≈0.75 causes minor wedge formation due to relamination of subducted crust below the upper plate, and ArF≈1 causes buoyancy-flow- or diapir-dominated wedges involving exhumation of crustal material from great depth (>80 km). Furthermore, employing phase equilibria density models reduces the average topography of wedges by several kilometres. We suggest that during the formation of the Pyrenees ArF⪅0.5 due to the absence of high-grade metamorphic rocks, whereas for the Alps ArF≈1 during exhumation of high-grade rocks and ArF⪅0.5 during the post-collisional stage. In the models, FD increases during wedge growth and subduction and eventually reaches magnitudes (≈18 TN m−1) which are required to initiate subduction. Such an increase in the horizontal force, required to continue driving subduction, might have “choked” the subduction of the European plate below the Adriatic one between 35 and 25 Ma and could have caused the reorganization of plate motion and subduction initiation of the Adriatic plate.
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Bell, Michael J., Adam T. Blaker, and Joël J. M. Hirschi. "Wind-Driven Oscillations in Meridional Overturning Circulations near the Equator. Part II: Idealized Simulations." Journal of Physical Oceanography 51, no. 3 (March 2021): 663–83. http://dx.doi.org/10.1175/jpo-d-19-0297.1.
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AbstractLarge-amplitude [±100 Sv (1 Sv ≡ 106 m3 s−1)], high-frequency oscillations in the Pacific Ocean’s meridional overturning circulation within 10° of the equator have been found in integrations of the NEMO ocean general circulation model. Part I of this paper showed that these oscillations are dominated by two bands of frequencies with periods close to 4 and 10 days and that they are driven by the winds within about 10° of the equator. This part shows that the oscillations can be well simulated by small-amplitude, wind-driven motions on a horizontally uniform, stably stratified state of rest. Its main novelty is that, by focusing on the zonally integrated linearized equations, it presents solutions for the motions in a basin with sloping side boundaries. The solutions are found using vertical normal modes and equatorial meridional modes representing Yanai and inertia–gravity waves. Simulations of 16-day-long segments of the time series for the Pacific of each of the first three meridional and vertical modes (nine modes in all) capture between 85% and 95% of the variance of matching time series segments diagnosed from the NEMO integrations. The best agreement is obtained by driving the solutions with the full wind forcing and the full pressure forces on the bathymetry. Similar results are obtained for the corresponding modes in the Atlantic and Indian Oceans. Slower variations in the same meridional and vertical modes of the MOC are also shown to be well simulated by a quasi-stationary solution driven by zonal wind and pressure forces.
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KACHURIN, Nikolai, Galina STAS, and Alexander KACHURIN. "DYNAMICS OF GAS EMISSION FROM EXPOSED SURFACE OF GAS-BEARING COAL SEAMS HAVING MEDIUM THICKNESS." Sustainable Development of Mountain Territories 13, no. 3 (September 30, 2021): 441–48. http://dx.doi.org/10.21177/1998-4502-2021-13-3-441-448.
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The goal of the research was to clarify the regularities of the dynamics of gas release from the surface of the outcrop of the developed coal seam. The main research methods were theoretical methods of mathematical physics and non-equilibrium thermodynamics. Gas-bearing coal seams are usually mined underground. When driving development workings, outcropping surfaces of gas-bearing coal seams appear and gases in the seams under excessive pressure are released into the atmosphere of the mine workings. Gas-bearing coal seams are usually mined underground. When driving preparatory workings, surfaces of outcropping of gas-bearing coal seams arise and gases that are in the seams under excessive pressure are released into the atmosphere of the mine workings. The most important gas-dynamic characteristic of this process is the rate of gas release, which represents the volume of gases released from a unit area of exposure of a coal seam per unit of time. A generalized law of resistance for gas filtration in a rock mass is recommended, and a fairly rigorous thermodynamic substantiation is given. It is shown that the densities of gas mass flows in accordance with the postulate of their linear relationship with the driving forces are determined by the Onsager relation. The results obtained and their discussion is presented. Mathematical models are proposed for engineering calculations of the dynamics of methane release from the outcropping surface of medium-thick coal seams. The error of the adopted approximations does not exceed 3%. The intensity of methane release is directly related to the planogram of work in the working face. Analysis of this dependence indicates that during the extraction cycle, methane release increases due to an increase in the area of the gas-release surface. The main conclusions are as follows: mathematical modeling of the processes of gas movement in a porous sorbing medium using approximate mathematical models representing linearized equations of mathematical physics; the regularities of the dynamics of the rate of gas release from the surface of the outcrop of a gas-bearing coal seam is the theoretical basis for the mathematical description of the process of gas release; the use of a linearized hyperbolic filtration equation most accurately describes the processes of methane release from the outcropping surface of mined coal seams.
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Jang, Hyun M., and Nong M. Hwang. "Theory of the charged cluster formation in the low pressure synthesis of diamond: Part II. Free energy function and thermodynamic stability." Journal of Materials Research 13, no. 12 (December 1998): 3536–49. http://dx.doi.org/10.1557/jmr.1998.0482.
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To account for the dominant formation of diamond over graphite in the gas-activated chemical vapor deposition (CVD) process we have theoretically examined the free energy function of a small carbon-atom cluster as a function of the cluster size. The scalar potential around a charged spherical cluster was derived using the linearized Poisson–Boltzmann equation. It was shown that the repulsive electrostatic energy associated with the growth of the charged diamond cluster was proportional to the fifth power of the cluster size. This suggests the existence of a deep potential-energy-well for the cluster size larger than the critical size corresponding to the free energy barrier for the nucleation. Thus, the growing diamond cluster will be trapped in this potential well before it transforms to the thermodynamically stable graphite. Considering all the relevant thermodynamic driving forces, we have constructed the free energy function in terms of the cluster size. The numerical computation also supports the existence of the potential-energy-well. Therefore, the present theoretical model clearly explains why the charged diamond cluster does not transform to the neutral graphite cluster when the thermodynamic stability is reversed above a certain critical size during the growth.
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Alifov, Alishir. "Mixed forced, parametric, and self-oscillations with nonideal energy source and lagging forces." Izvestiya VUZ. Applied Nonlinear Dynamics 29, no. 5 (September 30, 2021): 739–50. http://dx.doi.org/10.18500/0869-6632-2021-29-5-739-750.
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The purpose of this study is to determine the effect of retarded forces in elasticity and damping on the dynamics of mixed forced, parametric, and self-oscillations in a system with limited excitation. A mechanical frictional self-oscillating system driven by a limited-power engine was used as a model. Methods. In this work, to solve the nonlinear differential equations of motion of the system under consideration, the method of direct linearization is used, which differs from the known methods of nonlinear mechanics in ease of use and very low labor and time costs. This is especially important from the point of view of calculations when designing real devices. Results. The characteristic of the friction force that causes self-oscillations, represented by a general polynomial function, is linearized using the method of direct linearization of nonlinearities. Using the same method, solutions of the differential equations of motion of the system are constructed, equations are obtained for determining the nonstationary values of the amplitude, phase of oscillations and the speed of the energy source. Stationary motions are considered, as well as their stability by means of the Routh–Hurwitz criteria. Performed calculations obtained information about the effect of delays on the dynamics of the system. Conclusion. Calculations have shown that delays shift the amplitude curves to the right and left, up and down on the amplitude–frequency plane, change their shape, and affect the stability of motion.
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VARDANYAN, A., and A. KTEYAN. "STOCHASTIC DYNAMICS OF DC AND AC DRIVEN DISLOCATION KINKS." International Journal of Modern Physics B 27, no. 04 (December 20, 2012): 1250206. http://dx.doi.org/10.1142/s0217979212502062.
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Dynamics of a pinned dislocation kink controlled by the acting DC and AC forces is studied analytically. The motion of the kink, described by sine-Gordon (sG) equation, is explored within the framework of McLaughlin–Scott perturbation theory. Assuming weakness of the acting AC force, the equation of motion of the dislocation kink in the pinning potential is linearized. Based on the equations derived, we study stochastic behavior of the kink, and determine the probability of its depinning. The dependencies of the depinning probability on DC and AC forces are analyzed in detail.
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de la Cruz, H., J. C. Jimenez, and J. P. Zubelli. "Locally Linearized methods for the simulation of stochastic oscillators driven by random forces." BIT Numerical Mathematics 57, no. 1 (May 30, 2016): 123–51. http://dx.doi.org/10.1007/s10543-016-0620-2.
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Perig, Alexander V., Alexander N. Stadnik, Alexander I. Deriglazov, and Sergey V. Podlesny. "3 DOF Spherical Pendulum Oscillations with a Uniform Slewing Pivot Center and a Small Angle Assumption." Shock and Vibration 2014 (2014): 1–32. http://dx.doi.org/10.1155/2014/203709.
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The present paper addresses the derivation of a 3 DOF mathematical model of a spherical pendulum attached to a crane boom tip for uniform slewing motion of the crane. The governing nonlinear DAE-based system for crane boom uniform slewing has been proposed, numerically solved, and experimentally verified. The proposed nonlinear and linearized models have been derived with an introduction of Cartesian coordinates. The linearized model with small angle assumption has an analytical solution. The relative and absolute payload trajectories have been derived. The amplitudes of load oscillations, which depend on computed initial conditions, have been estimated. The dependence of natural frequencies on the transport inertia forces and gravity forces has been computed. The conservative system, which contains first time derivatives of coordinates without oscillation damping, has been derived. The dynamic analogy between crane boom-driven payload swaying motion and Foucault’s pendulum motion has been grounded and outlined. For a small swaying angle, good agreement between theoretical and averaged experimental results was obtained.
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Witte, M. G., and G. J. Savonije. "Forced Nonradial Oscillations in Early-Type Rotating Stars." International Astronomical Union Colloquium 176 (2000): 376. http://dx.doi.org/10.1017/s0252921100058085.
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A method of calculating nonradial oscillations in rotating stars is presented. Using this method, we are able to calculate the spectrum of g-, f- and p-mode eigenfunctions of a star for different stellar rotation speeds, and also the spectrum of rotational r modes. Stability of the modes as a function of stellar rotation speed can be investigated. By regarding the response of a star which undergoes periodic deformations due to the gravitational force of an orbiting companion as a forced nonradial oscillation, the problem of determining the eigenfrequencies of the star becomes one of finding resonances with the forcing potential. Expanding the potential of the orbiting (point mass) companion in terms of the usual spherical functions, the response of the star to each tidal term , with l and m fixed, can be calculated separately. By varying the forcing frequency σ we are then able to calculate the stellar spectrum. To calculate the response of the star we numerically solve the fully non-adiabatic, but linearised hydrodynamical equations for the star, in which the Coriolis forces due to stellar rotation are fully taken into account. To this end we utilise an implicit 2D finite difference scheme which solves the equations on an (r, ϑ) grid. A calculated solution describes the steady state in which the power σT due to the external driving force is in equilibrium with the internal damping. For results and more references see Witte & Savonije (1999).
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Meng, Qingheng, Yuanlin Zhang, Jin Wei, Yuh-Chung Hu, Yan Shi, and Tao Yu. "Dynamic Characteristics of Microring Driven by the Symmetrically Distributed Electrostatic Force." Complexity 2021 (February 4, 2021): 1–12. http://dx.doi.org/10.1155/2021/1926052.
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This paper aims at investigating the dynamic characteristics of a microring driven by dual arch electrodes because they are basic elements of microelectrostatic motors. The dual arch electrodes surround the periphery of the microring and are arranged symmetrically to the center of the ring. The electrodes are fixed while the microring is flexible. The electrostatic force will deform the microring, while the deflection of the microring changes the gap between the microring and the electrodes, thereby changing the electrostatic force. Therefore, this is an electromechanical coupling effect. The nonlinear partial-differential equation that governs the motion of the microring is derived based on thin shell theory. Then, based on the assumption of small deflection, the nonlinear governing equation is linearized by truncating the higher-order terms of the Taylor series expansion of the nonlinear electrostatic force. After that, the linearized governing equation is discretized into a set of ordinary differential equations using Galerkin method in which the mode shape functions of the ring are adopted. The influences of the structural damping of the microring and the span of the arch electrodes on the forced response and dynamical stabilities of the microring are investigated. The results show that the damping ratio has a great influence on the system instability during high-frequency excitation. The unstable region of the system can increase with the increase of the electrode span; the response amplitude can also be increased within a certain range.
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Jeong, Sumin, and Natalie Baddour. "Vibrations due to Flow-Driven Repeated Impacts." Mathematical Problems in Engineering 2013 (2013): 1–17. http://dx.doi.org/10.1155/2013/760939.
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We consider a two-degree-of-freedom model where the focus is on analyzing the vibrations of a fixed but flexible structure that is struck repeatedly by a second object. The repetitive impacts due to the second mass are driven by a flowing fluid. Morison’s equation is used to model the effect of the fluid on the properties of the structure. The model is developed based on both linearized and quadratic fluid drag forces, both of which are analyzed analytically and simulated numerically. Conservation of linear momentum and the coefficient of restitution are used to characterize the nature of the impacts between the two masses. A resonance condition of the model is analyzed with a Fourier transform. This model is proposed to explain the nature of ice-induced vibrations, without the need for a model of the ice-failure mechanism. The predictions of the model are compared to ice-induced vibrations data that are available in the open literature and found to be in good agreement. Therefore, the use of a repetitive impact model that does not require modeling the ice-failure mechanism can be used to explain some of the observed behavior of ice-induced vibrations.
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BERTOZZI, ANDREA L., ANDREAS MÜNCH, MICHAEL SHEARER, and KEVIN ZUMBRUN. "Stability of compressive and undercompressive thin film travelling waves." European Journal of Applied Mathematics 12, no. 3 (June 2001): 253–91. http://dx.doi.org/10.1017/s0956792501004466.
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Recent studies of liquid films driven by competing forces due to surface tension gradients and gravity reveal that undercompressive travelling waves play an important role in the dynamics when the competing forces are comparable. In this paper, we provide a theoretical framework for assessing the spectral stability of compressive and undercompressive travelling waves in thin film models. Associated with the linear stability problem is an Evans function which vanishes precisely at eigenvalues of the linearized operator. The structure of an index related to the Evans function explains computational results for stability of compressive waves. A new formula for the index in the undercompressive case yields results consistent with stability. In considering stability of undercompressive waves to transverse perturbations, there is an apparent inconsistency between long-wave asymptotics of the largest eigenvalue and its actual behaviour. We show that this paradox is due to the unusual structure of the eigenfunctions and we construct a revised long-wave asymptotics. We conclude with numerical computations of the largest eigenvalue, comparisons with the asymptotic results, and several open problems associated with our findings.
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Park, Kiwan, Myung Ki Cheoun, and Chang-Bae Kim. "Turbulent Magnetic Diffusivity β Effect in a Magnetically Forced System." Astrophysical Journal 944, no. 1 (February 1, 2023): 2. http://dx.doi.org/10.3847/1538-4357/ac9bf9.
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Abstract We have studied the large-scale dynamo forced with helical magnetic energy. Compared to the kinetic forcing process, the magnetic process is not clearly observed nor intuitive. However, it may represent the actual B field amplification in the stellar corona, accretion disk, plasma lab, or other magnetically dominated systems where the strong kinetic effect does not exist. The interaction between the magnetic field and the plasma is essentially nonlinear. However, when the plasma system is driven by helical energy, whether kinetic or magnetic, the nonlinear process can be linearized with pseudotensors a, β and the large-scale magnetic field B ¯ . Conventionally, the α effect is thought to be the main dynamo effect converting kinetic energy into magnetic energy and transferring it to the large-scale regime. In contrast, β effect has been thought to diffuse magnetic energy. However, these conclusions are not based on the exact definition of α and β. In this paper, instead of the analytic definition of α and β, we derive a semi-analytic equation and apply it to the simulation data. The half analytic and numerical result shows that the averaged α effect is not so important in amplifying the B ¯ field. Rather, it is the negative β effect combined with the Laplacian (∇2 → −k 2) that plays a key role in the dynamo process. Further, the negative magnetic diffusivity accounts for the attenuation of the plasma kinetic energy E ¯ V in large scales. We discuss this process using the theoretical method and the intuitive field structure model.
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Holt, Chris, Luis San Andre´s, Sunil Sahay, Peter Tang, Gerry La Rue, and Kostandin Gjika. "Test Response and Nonlinear Analysis of a Turbocharger Supported on Floating Ring Bearings." Journal of Vibration and Acoustics 127, no. 2 (April 1, 2005): 107–15. http://dx.doi.org/10.1115/1.1857922.
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Measurements of casing acceleration on an automotive turbocharger running to a top speed of 115 krpm and driven by ambient temperature pressurized air are reported. Waterfall acceleration spectra versus rotor speed show the effects of increasing lubricant inlet pressure and temperature on turbocharger rotordynamic response. A comprehensive analysis of the test data shows regimes of speed operation with two subsynchronous whirl motions (rotordynamic instabilities). Increasing the lubricant feed pressure delays the onset speed of instability for the most severe subsynchronous motion. However, increasing the lubricant feed pressure also produces larger synchronous displacements. The effect of lubricant feed temperature is minimal on the onset and end speeds of rotordynamic instability. Nevertheless, operation with a cold lubricant exhibits lower amplitudes of motion, synchronous and subsynchronous. The experimental results show the subsynchronous frequencies of motion do not lock (whip) at system natural frequencies but continuously track the rotor speed. No instabilities (subsynchronous whirl) remain for operating speeds above 90 krpm. Linear and nonlinear analysis results for the operation of a small automotive turbocharger supported on floating ring bearings are presented. A comprehensive fluid film bearing model predicting the forced response of floating ring bearings is also described. The linear rotordynamic model predicts well the rotor free–free modes and onset speed of instability using linearized bearing force coefficients. The nonlinear model incorporating instantaneous bearing reaction forces in the numerical integration of the rotor equations of motion predicts the limit cycle amplitudes with two fundamental subsynchronous whirl frequencies. Comparisons of both models to experimental results follow. The predictions evidence two unstable whirl ratios at approximately 12 ring speed and 12 ring speed plus 12 journal speed. The transient nonlinear responses reveal the importance of rotor imbalance in suppressing the subsynchronous instabilities at large rotor speeds as also observed in the experiments.
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Ortuño-Macías, José, Krzysztof Nalewajko, Dmitri A. Uzdensky, Mitchell C. Begelman, Gregory R. Werner, Alexander Y. Chen, and Bhupendra Mishra. "Kinetic Simulations of Instabilities and Particle Acceleration in Cylindrical Magnetized Relativistic Jets." Astrophysical Journal 931, no. 2 (June 1, 2022): 137. http://dx.doi.org/10.3847/1538-4357/ac6acd.
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Abstract Relativistic magnetized jets, such as those from AGN, GRBs, and XRBs, are susceptible to current- and pressure-driven MHD instabilities that can lead to particle acceleration and nonthermal radiation. Here, we investigate the development of these instabilities through 3D kinetic simulations of cylindrically symmetric equilibria involving toroidal magnetic fields with electron–positron pair plasma. Generalizing recent treatments by Alves et al. and Davelaar et al., we consider a range of initial structures in which the force due to toroidal magnetic field is balanced by a combination of forces due to axial magnetic field and gas pressure. We argue that the particle energy limit identified by Alves et al. is due to the finite duration of the fast magnetic dissipation phase. We find a rather minor role of electric fields parallel to the local magnetic fields in particle acceleration. In all investigated cases, a kink mode arises in the central core region with a growth timescale consistent with the predictions of linearized MHD models. In the case of a gas-pressure-balanced (Z-pinch) profile, we identify a weak local pinch mode well outside the jet core. We argue that pressure-driven modes are important for relativistic jets, in regions where sufficient gas pressure is produced by other dissipation mechanisms.
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McGregor, Shayne, Neil J. Holbrook, and Scott B. Power. "The Response of a Stochastically Forced ENSO Model to Observed Off-Equatorial Wind Stress Forcing." Journal of Climate 22, no. 10 (May 15, 2009): 2512–25. http://dx.doi.org/10.1175/2008jcli2387.1.
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Abstract This study investigates the response of a stochastically forced coupled atmosphere–ocean model of the equatorial Pacific to off-equatorial wind stress anomaly forcing. The intermediate-complexity coupled ENSO model comprises a linear, first baroclinic mode, ocean shallow water model with a steady-state, two–pressure level (250 and 750 mb) atmospheric component that has been linearized about a state of rest on the β plane. Estimates of observed equatorial region stochastic forcing are calculated from NCEP–NCAR reanalysis surface winds for the period 1950–2006 using singular value decomposition. The stochastic forcing is applied to the model both with and without off-equatorial region wind stress anomalies (i.e., poleward of 12.5° latitude). It is found that the multiyear changes in the equatorial Pacific thermocline depth “background state” induced by off-equatorial forcing can affect the amplitude of modeled sea surface temperature anomalies by up to 1°C. Moreover, off-equatorial wind stress anomalies increased the modeled amplitude of the two biggest El Niño events in the twentieth century (1982/83 and 1997/98) by more than 0.5°C, resulting in a more realistic modeled response. These equatorial changes driven by off-equatorial region wind stress anomalies are highly predictable to two years in advance and may be useful as a physical basis to enhance multiyear probabilistic predictions of ENSO indices.
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Mao, Sen, Changchuan Xie, Lan Yang, and Chao Yang. "Static Aeroelastic Characteristics of Morphing Trailing-Edge Wing Using Geometrically Exact Vortex Lattice Method." International Journal of Aerospace Engineering 2019 (November 16, 2019): 1–15. http://dx.doi.org/10.1155/2019/5847627.
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A morphing trailing-edge (TE) wing is an important morphing mode in aircraft design. In order to explore the static aeroelastic characteristics of a morphing TE wing, an efficient and feasible method for static aeroelastic analysis has been developed in this paper. A geometrically exact vortex lattice method (VLM) is applied to calculate the aerodynamic forces. Firstly, a typical model of a morphing TE wing is chosen and built which has an active morphing trailing edge driven by a piezoelectric patch. Then, the paper carries out the static aeroelastic analysis of the morphing TE wing and corresponding simulations were carried out. Finally, the analysis results are compared with those of a traditional wing with a rigid trailing edge using the traditional linearized VLM. The results indicate that the geometrically exact VLM can better describe the aerodynamic nonlinearity of a morphing TE wing in consideration of geometrical deformation in aeroelastic analysis. Moreover, out of consideration of the angle of attack, the deflection angle of the trailing edge, among others, the wing system does not show divergence but bifurcation. Consequently, the aeroelastic analysis method proposed in this paper is more applicable to the analysis and design of a morphing TE wing.
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Kimura, Y., and H. K. Moffatt. "Reconnection of skewed vortices." Journal of Fluid Mechanics 751 (June 20, 2014): 329–45. http://dx.doi.org/10.1017/jfm.2014.233.
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AbstractBased on experimental evidence that vortex reconnection commences with the approach of nearly antiparallel segments of vorticity, a linearised model is developed in which two Burgers-type vortices are driven together and stretched by an ambient irrotational strain field induced by more remote vorticity. When these Burgers vortices are exactly antiparallel, they are annihilated on the strain time-scale, independent of kinematic viscosity $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\nu $ in the limit $\nu \rightarrow 0$. When the vortices are skew to each other, they are annihilated under this action over a local extent that increases exponentially in the stretching direction, with clear evidence of reconnection on the same strain time-scale. The initial helicity associated with the skewed geometry is eliminated during the process of reconnection. The model applies equally to the reconnection of weak magnetic flux tubes under the action of a strain field, when Lorentz forces are negligible.
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Uhlhorn, Eric W., and Lynn K. Shay. "Loop Current Mixed Layer Energy Response to Hurricane Lili (2002). Part II: Idealized Numerical Simulations." Journal of Physical Oceanography 43, no. 6 (June 1, 2013): 1173–92. http://dx.doi.org/10.1175/jpo-d-12-0203.1.
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Abstract In this second part of a two-part study, details of the upper-ocean response within an idealized baroclinic current to a translating tropical cyclone are examined in a series of nonlinear, reduced-gravity numerical simulations. Based on observations obtained as part of a joint NOAA–National Science Foundation (NSF) experiment in Hurricane Lili (2002), the preexisting ocean mass and momentum fields are initialized with a Gulf of Mexico Loop Current–like jet, which is subsequently forced by a vortex whose wind stress field approximates that observed in the Lili experiments. Because of 1) favorable coupling between the wind stress and preexisting current vectors, and 2) wind-driven currents flowing across the large horizontal pressure gradient, wind energy transfer to the mixed layer can be more efficient in such a regime as compared to the case of an initially horizontally homogeneous ocean. However, nearly all energy is removed by advection and wave flux by two local inertial periods after storm passage, consistent with the observational results. Experiments are performed to quantify differences in one-dimensional and three-dimensional linearized approximations to the full model equations. In addition, sensitivity experiments to variations in the initial geostrophic current structure are performed to develop a parameter space over which a significant energy response could optimally be observed.
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Roos, Pieter C., Giordano Lipari, Chris Pitzalis, Koen R. G. Reef, Gerhardus H. P. Campmans, and Suzanne J. M. H. Hulscher. "Unsteady Linearisation of Bed Shear Stress for Idealised Storm Surge Modelling." Journal of Marine Science and Engineering 9, no. 11 (October 21, 2021): 1160. http://dx.doi.org/10.3390/jmse9111160.
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The modelling of time-varying shallow flows, such as tides and storm surges, is complicated by the nonlinear dependency of bed shear stress on flow speed. For tidal flows, Lorentz’s linearisation circumvents nonlinearity by specifying a (steady) friction coefficient r based on a tide-averaged criterion of energy equivalence. However, this approach is not suitable for phenomena with episodic and irregular forcings such as storm surges. Here, we studied the implications of applying Lorentz’s energy criterion in an instantaneous sense, so that an unsteady friction coefficient r(t) adjusts to the temporal development of natural wind-driven flows. This new bed-stress parametrisation was implemented in an idealised model of a single channel, forced by time-varying signals of wind stress (acting over the entire domain) and surface elevation (at the channel mouth). The solution method combines analytical solutions of the cross-sectionally averaged linearised shallow-water equations, obtained in the frequency domain, with an iterative procedure to determine r(t). Model results, compared with a reference finite-difference solution retaining the quadratic bed shear stress, show that this new approach accurately captures the qualitative and quantitative aspects of the surge dynamics (height and timing of surge peaks, sloshing, friction-induced tide-surge interaction) for both synthetic and realistic wind forcings.
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Straneo, Fiammetta. "On the Connection between Dense Water Formation, Overturning, and Poleward Heat Transport in a Convective Basin*." Journal of Physical Oceanography 36, no. 9 (September 1, 2006): 1822–40. http://dx.doi.org/10.1175/jpo2932.1.
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Abstract An isopycnal, two-layer, idealized model for a convective basin is proposed, consisting of a convecting, interior region and a surrounding boundary current (buoyancy and wind-driven). Parameterized eddy fluxes govern the exchange between the two. To balance the interior buoyancy loss, the boundary current becomes denser as it flows around the basin. Geostrophy imposes that this densification be accompanied by sinking in the boundary current and hence by an overturning circulation. The poleward heat transport, associated with convection in the basin, can thus be viewed as a result of both an overturning and a horizontal circulation. When adapted to the Labrador Sea, the model is able to reproduce the bulk features of the mean state, the seasonal cycle, and even the shutdown of convection from 1969 to 1972. According to the model, only 40% of the poleward heat (buoyancy) transport of the Labrador Sea is associated with the overturning circulation. An exact solution is presented for the linearized equations when changes in the boundary current are small. Numerical solutions are calculated for variations in the amount of convection and for changes in the remotely forced circulation around the basin. These results highlight how the overturning circulation is not simply related to the amount of dense water formed. A speeding up of the circulation around the basin due to wind forcing, for example, will decrease the intensity of the overturning circulation while the dense water formation remains unvaried. In general, it is shown that the fraction of poleward buoyancy (or heat) transport carried by the overturning circulation is not an intrinsic property of the basin but can vary as a result of a number of factors.
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LAC, ETIENNE, and J. D. SHERWOOD. "Streaming potential generated by a drop moving along the centreline of a capillary." Journal of Fluid Mechanics 640 (November 12, 2009): 55–77. http://dx.doi.org/10.1017/s002211200999156x.
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The electrical streaming potential generated by a two-phase pressure-driven Stokes flow in a cylindrical capillary is computed numerically. The potential difference ΔΦ between the two ends of the capillary, proportional to the pressure difference Δp for single-phase flow, is modified by the presence of a suspended drop on the centreline of the capillary. We determine the change in ΔΦ caused by the presence of an uncharged insulating neutrally buoyant drop at a small electric Hartmann number, i.e. when the perturbation to the flow field caused by electric stresses is negligible.The drop velocity and deformation, and the consequent changes in the pressure difference Δp and streaming potential ΔΦ, depend upon three independent parameters: the size a of the undeformed drop relative to the radius R of the capillary; the viscosity ratio λ between the drop phase and the continuous phase; and the capillary number Ca which measures the ratio of viscous to capillary forces. We investigate how the streaming potential depends on these parameters: purely hydrodynamic aspects of the problem are discussed by Lac & Sherwood (J. Fluid Mech., doi:10.1017/S0022112009991212).The potential on the capillary wall is assumed sufficiently small so that the electrical double layer is described by the linearized Poisson–Boltzmann equation. The Debye length characterizing the thickness of the charge cloud is taken to be small compared with all other length scales, including the width of the gap between the drop and the capillary wall. The electric potential satisfies Laplace's equation, which we solve by means of a boundary integral method. The presence of the drop increases |ΔΦ| when the drop is more viscous than the surrounding fluid (λ > 1), though the change in |ΔΦ| can take either sign for λ < 1. However, the difference between ΔΦ and Δp (suitably non-dimensionalized) is always positive. Asymptotic predictions for the streaming potential in the case of a vanishingly small spherical droplet, and for large drops at high capillary numbers, agree well with computations.
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HUNT, J. C. R., D. D. STRETCH, and S. E. BELCHER. "Viscous coupling of shear-free turbulence across nearly flat fluid interfaces." Journal of Fluid Mechanics 671 (February 24, 2011): 96–120. http://dx.doi.org/10.1017/s0022112010005525.
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The interactions between shear-free turbulence in two regions (denoted as + and − on either side of a nearly flat horizontal interface are shown here to be controlled by several mechanisms, which depend on the magnitudes of the ratios of the densities, ρ+/ρ−, and kinematic viscosities of the fluids, μ+/μ−, and the root mean square (r.m.s.) velocities of the turbulence, u0+/u0−, above and below the interface. This study focuses on gas–liquid interfaces so that ρ+/ρ− ≪ 1 and also on where turbulence is generated either above or below the interface so that u0+/u0− is either very large or very small. It is assumed that vertical buoyancy forces across the interface are much larger than internal forces so that the interface is nearly flat, and coupling between turbulence on either side of the interface is determined by viscous stresses. A formal linearized rapid-distortion analysis with viscous effects is developed by extending the previous study by Hunt & Graham (J. Fluid Mech., vol. 84, 1978, pp. 209–235) of shear-free turbulence near rigid plane boundaries. The physical processes accounted for in our model include both the blocking effect of the interface on normal components of the turbulence and the viscous coupling of the horizontal field across thin interfacial viscous boundary layers. The horizontal divergence in the perturbation velocity field in the viscous layer drives weak inviscid irrotational velocity fluctuations outside the viscous boundary layers in a mechanism analogous to Ekman pumping. The analysis shows the following. (i) The blocking effects are similar to those near rigid boundaries on each side of the interface, but through the action of the thin viscous layers above and below the interface, the horizontal and vertical velocity components differ from those near a rigid surface and are correlated or anti-correlated respectively. (ii) Because of the growth of the viscous layers on either side of the interface, the ratio uI/u0, where uI is the r.m.s. of the interfacial velocity fluctuations and u0 the r.m.s. of the homogeneous turbulence far from the interface, does not vary with time. If the turbulence is driven in the lower layer with ρ+/ρ− ≪ 1 and u0+/u0− ≪ 1, then uI/u0− ~ 1 when Re (=u0−L−/ν−) ≫ 1 and R = (ρ−/ρ+)(v−/v+)1/2 ≫ 1. If the turbulence is driven in the upper layer with ρ+/ρ− ≪ 1 and u0+/u0− ≫ 1, then uI/u0+ ~ 1/(1 + R). (iii) Nonlinear effects become significant over periods greater than Lagrangian time scales. When turbulence is generated in the lower layer, and the Reynolds number is high enough, motions in the upper viscous layer are turbulent. The horizontal vorticity tends to decrease, and the vertical vorticity of the eddies dominates their asymptotic structure. When turbulence is generated in the upper layer, and the Reynolds number is less than about 106–107, the fluctuations in the viscous layer do not become turbulent. Nonlinear processes at the interface increase the ratio uI/u0+ for sheared or shear-free turbulence in the gas above its linear value of uI/u0+ ~ 1/(1 + R) to (ρ+/ρ−)1/2 ~ 1/30 for air–water interfaces. This estimate agrees with the direct numerical simulation results from Lombardi, De Angelis & Bannerjee (Phys. Fluids, vol. 8, no. 6, 1996, pp. 1643–1665). Because the linear viscous–inertial coupling mechanism is still significant, the eddy motions on either side of the interface have a similar horizontal structure, although their vertical structure differs.
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Schnitzer, Ory, Itzchak Frankel, and Ehud Yariv. "Electrokinetic flows about conducting drops." Journal of Fluid Mechanics 722 (April 2, 2013): 394–423. http://dx.doi.org/10.1017/jfm.2013.102.
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AbstractWe consider electrokinetic flows about a freely suspended liquid drop, deriving a macroscale description in the thin-double-layer limit where the ratio $\delta $ between Debye width and drop size is asymptotically small. In this description, the electrokinetic transport occurring within the diffuse part of the double layer (the ‘Debye layer’) is represented by effective boundary conditions governing the pertinent fields in the electro-neutral bulk, wherein the generally non-uniform distribution of $\zeta $, the dimensionless zeta potential, is a priori unknown. We focus upon highly conducting drops. Since the tangential electric field vanishes at the drop surface, the viscous stress associated with Debye-scale shear, driven by Coulomb body forces, cannot be balanced locally by Maxwell stresses. The requirement of microscale stress continuity therefore brings about a unique velocity scaling, where the standard electrokinetic scale is amplified by a ${\delta }^{- 1} $ factor. This reflects a transition from slip-driven electro-osmotic flows to shear-induced motion. The macroscale boundary conditions display distinct features reflecting this unique scaling. The effective shear-continuity condition introduces a Lippmann-type stress jump, appearing as a product of the local charge density and electric field. This term, representing the excess Debye-layer shear, follows here from a systematic coarse-graining procedure starting from the exact microscale description, rather than from thermodynamic considerations. The Neumann condition governing the bulk electric field is inhomogeneous, representing asymptotic matching with transverse ionic fluxes emanating from the Debye layer; these fluxes, in turn, are associated with non-uniform tangential ‘surface’ currents within this layer. Their appearance at leading order is a manifestation of dominant advection associated with the large velocity scale. For weak fields, the linearized macroscale equations admit an analytic solution, yielding a closed-form expression for the electrophoretic velocity. When scaled by Smoluchowski’s speed, it reads $${\delta }^{- 1} \frac{\sinh ( \overline{\zeta } / 2)/ \overline{\zeta } }{1+ { \textstyle\frac{3}{2} }\mu + 2\alpha {\mathop{\sinh }\nolimits }^{2} ( \overline{\zeta } / 2)} ,$$ wherein $ \overline{\zeta } $, the ‘drop zeta potential’, is the uniform value of $\zeta $ in the absence of an applied field, $\mu $ the ratio of drop to electrolyte viscosities, and $\alpha $ the ionic drag coefficient. The difference from solid-particle electrophoresis is manifested in two key features: the ${\delta }^{- 1} $ scaling, and the effect of ionic advection, as represented by the appearance of $\alpha $. Remarkably, our result differs from the small-$\delta $ limit of the mobility expression predicted by the weak-field model of Ohshima, Healy & White (J. Chem. Soc. Faraday Trans. 2, vol. 80, 1984, pp. 1643–1667). This discrepancy is related to the dominance of advection on the bulk scale, even for weak fields, which feature cannot be captured by a linear theory. The order of the respective limits of thin double layers and weak applied fields is not interchangeable.
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Eggers, Torben, Hye Rim Kim, Simon Bittner, Jens Friedrichs, and Joerg R. Seume. "Aerodynamic and Aeroelastic Effects of Design-Based Geometry Variations on a Low-Pressure Compressor." International Journal of Turbomachinery, Propulsion and Power 5, no. 4 (September 24, 2020): 26. http://dx.doi.org/10.3390/ijtpp5040026.
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In modern aircraft engines, the low-pressure compressor (LPC) is subjected to a flow characterized by strong wakes and secondary flows from the upstream fan. This concerns ultra-high bypass ratio (UHBR) turbofan engines, in particular. This paper presents the aerodynamic and aeroelastic sensitivities of parametric variations on the LPC, driven by the design considerations in the upstream fan. The goal of this investigation was to determine the influence of design-based geometry parameter variations on the LPC performance under realistic inlet flow distributions and the presence of an s-duct. Aerodynamic simulations are conducted at the design and off-design operating points with the fan outflow as the inlet boundary conditions. Based on the aerodynamic results, time-linearized unsteady simulations are conducted to evaluate the vibration amplitude at the resonance operating points. First, the bypass ratio is varied by reducing the channel height of the LPC. The LPC efficiency decreases by up to 1.7% due to the increase in blockage of the core flow. The forced response amplitude of the rotor decreases with increasing bypass ratio due to increased aerodynamic damping. Secondly, the fan cavity leakage flow is considered as it directly affects the near hub fan flow and thus the inflow of the LPC. This results in an increased total-pressure loss for the s-duct due to mixing losses. The additional mixing redistributes the flow at the s-duct exit leading to a total-pressure loss reduction of 4.3% in the first rotor at design point. This effect is altered at off-design conditions. The vibration amplitude at low speed resonance points is increased by 19% for the first torsion and 26% for second bending. Thirdly, sweep and lean are applied to the inlet guide vane (IGV) upstream of the LPC. Despite the s-duct and the variable inlet guide vane (VIGV) affecting the flow, the three-dimensional blade design achieves aerodynamic and aeroelastic improvements of rotor 1 at off-design. The total-pressure loss reduces by up to 18% and the resonance amplitude more than 10%. Only negligible improvements for rotor 1 are present at the design point. In a fourth step, the influence of axial gap size between the stator and the rotor rows in the LPC is examined in the range of small variations which shows no distinct aerodynamic and aeroelastic sensitivities. This finding not only supports previous studies, but it also suggests a correlation between mode shapes and locally increased excitaion with increasing axial gap size. As a result, potential design improvements in future fan-compressor design are suggested.
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Lerczak, James A., W. Rockwell Geyer, and David K. Ralston. "The Temporal Response of the Length of a Partially Stratified Estuary to Changes in River Flow and Tidal Amplitude." Journal of Physical Oceanography 39, no. 4 (April 1, 2009): 915–33. http://dx.doi.org/10.1175/2008jpo3933.1.
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Abstract The temporal response of the length of a partially mixed estuary to changes in freshwater discharge Qf and tidal amplitude UT is studied using a 108-day time series collected along the length of the Hudson River estuary in the spring and summer of 2004 and a long-term (13.4 yr) record of Qf , UT, and near-surface salinity. When Qf was moderately high, the tidally averaged length of the estuary L5, here defined as the distance from the mouth to the up-estuary location where the vertically averaged salinity is 5 psu, fluctuated by more than 47 km over the spring–neap cycle, ranging from 28 to >75 km. During low flow periods, L5 varied very little over the spring–neap cycle and approached a steady length. The response is quantified and compared to predictions of a linearized model derived from the global estuarine salt balance. The model is forced by fluctuations in Qf and UT relative to average discharge Qo and tidal amplitude UTo and predicts the linear response time scale τ and the steady-state length Lo for average forcing. Two vertical mixing schemes are considered, in which 1) mixing is proportional to UT and 2) dependence of mixing on stratification is also parameterized. Based on least squares fits between L5 and estuary length predicted by the model, estimated τ varied by an order of magnitude from a period of high average discharge (Qo = 750 m3 s−1, τ = 4.2 days) to a period of low discharge (Qo = 170 m3 s−1, τ = 40.4 days). Over the range of observed discharge, Lo ∝ Qo−0.30±0.03, consistent with the theoretical scaling for an estuary whose landward salt flux is driven by vertical estuarine exchange circulation. Estimated τ was proportional to the discharge advection time scale (LoA/Qo, where A is the cross-sectional area of the estuary). However, τ was 3–4 times larger than the theoretical prediction. The model with stratification-dependent mixing predicted variations in L5 with higher skill than the model with mixing proportional to UT. This model provides insight into the time-dependent response of a partially stratified estuary to changes in forcing and explains the strong dependence of the amplitude of the spring–neap response on freshwater discharge. However, the utility of the linear model is limited because it assumes a uniform channel, and because the underlying dynamics are nonlinear, and the forcing Qf and UT can undergo large amplitude variations. River discharge, in particular, can vary by over an order of magnitude over time scales comparable to or shorter than the response time scale of the estuary.
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Shi, Yanlong, and Jim Fuller. "Viscous and centrifugal instabilities of massive stars." Monthly Notices of the Royal Astronomical Society, April 11, 2022. http://dx.doi.org/10.1093/mnras/stac986.
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Abstract Massive stars exhibit a variety of instabilities, many of which are poorly understood. We explore instabilities induced by centrifugal forces and angular momentum transport in massive rotating stars. First, we derive and numerically solve linearized oscillation equations for adiabatic radial modes in polytropic stellar models. In the presence of differential rotation, we show that centrifugal and Coriolis forces combined with viscous angular momentum transport can excite stellar pulsation modes, under both low- or high-viscosity conditions. In the low-viscosity limit, which is common in real stars, we demonstrate how to compute mode growth/damping rates via a work integral. Finally, we build realistic rotating 30 M⊙ star models and show that overstable (growing) radial modes are predicted to exist for most of the star’s life, in the absence of non-adiabatic effects. Peak growth rates are predicted to occur while the star is crossing the Hertzsprung-Russell gap, though non-adiabatic damping may dominate over viscous driving, depending on the effective viscosity produced by convective and/or magnetic torques. Viscous instability could be a new mechanism to drive massive star pulsations and is possibly related to instabilities of luminous blue variable stars.
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Sacco, Riccardo, Fabio Manganini, and Joseph W. Jerome. "Modeling and Simulation of Thermo-Fluid-Electrochemical Ion Flow in Biological Channels." Computational and Mathematical Biophysics 3, no. 1 (October 7, 2015). http://dx.doi.org/10.1515/mlbmb-2015-0006.
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AbstractIn this articlewe address the study of ion charge transport in the biological channels separating the intra and extracellular regions of a cell. The focus of the investigation is devoted to including thermal driving forces in the well-known velocity-extended Poisson-Nernst-Planck (vPNP) electrodiffusion model. Two extensions of the vPNP system are proposed: the velocity-extended Thermo-Hydrodynamic model (vTHD) and the velocity-extended Electro-Thermal model (vET). Both formulations are based on the principles of conservation of mass, momentum and energy, and collapse into the vPNP model under thermodynamical equilibrium conditions. Upon introducing a suitable one-dimensional geometrical representation of the channel,we discuss appropriate boundary conditions that depend only on effectively accessible measurable quantities. Then, we describe the novel models, the solution map used to iteratively solve them, and the mixed-hybrid flux-conservative stabilized finite element scheme used to discretize the linearized equations. Finally,we successfully apply our computational algorithms to the simulation of two different realistic biological channels: 1) the Gramicidin-A channel considered in [12]; and 2) the bipolar nanofluidic diode considered in [45].
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Moitra, Upamanyu, Sunil Kumar Sake, and Sandip P. Trivedi. "Near-extremal fluid mechanics." Journal of High Energy Physics 2021, no. 2 (February 2021). http://dx.doi.org/10.1007/jhep02(2021)021.
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Abstract We analyse near-extremal black brane configurations in asymptotically AdS4 spacetime with the temperature T, chemical potential μ, and three-velocity uν, varying slowly. We consider a low-temperature limit where the rate of variation is much slower than μ, but much bigger than T. This limit is different from the one considered for conventional fluid-mechanics in which the rate of variation is much smaller than both T, μ. We find that in our limit, as well, the Einstein-Maxwell equations can be solved in a systematic perturbative expansion. At first order, in the rate of variation, the resulting constitutive relations for the stress tensor and charge current are local in the boundary theory and can be easily calculated. At higher orders, we show that these relations become non-local in time but the perturbative expansion is still valid. We find that there are four linearised modes in this limit; these are similar to the hydrodynamic modes found in conventional fluid mechanics with the same dispersion relations. We also study some linearised time independent perturbations exhibiting attractor behaviour at the horizon — these arise in the presence of external driving forces in the boundary theory.
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Zhai, Yaoguang, Ronnie Bladh, and Göran Dyverfeldt. "Aeroelastic Stability Assessment of an Industrial Compressor Blade Including Mistuning Effects." Journal of Turbomachinery 134, no. 6 (September 19, 2012). http://dx.doi.org/10.1115/1.4007210.
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This paper presents a comprehensive investigation into the aeroelastic stability behavior of a transonic front blade in an industrial compressor when operating outside its normal range of service parameters. The evolution of the airfoil’s aeroelastic stability in the first flexural mode is studied as the front blade operation progresses towards choked flow conditions. First, linearized 3D flutter computations representing today’s industry standard are performed. The linearized calculations indicate a significant, shock-driven flutter risk at these off-design flow conditions. To further explore the aeroelastic behavior of the rotor and to find a viable solution toward flutter risk elimination, two parallel investigations are undertaken: (i) flow perturbation nonlinearity effects and potential presence of limit-cycle oscillation, and (ii) effects of blade mistuning and flutter mitigation potential of intentional mistuning, including its impact on forced response behavior. The nonlinear harmonic analyses show that the minimum aerodynamic damping increases rapidly and essentially linearly with blade oscillation amplitude beyond the linear regime. Thus, a state of safe limit-cycle oscillation is predicted for the fully tuned blade. Additionally, it is found that intentional, realizable blade frequency offsets in an alternating pattern efficiently stabilize the blade. Finally, it is verified that alternating mistuning has a beneficial effect versus the inevitable random mistuning also in the forced response.
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Abootorabi, Seyedalireza, and Armin Zare. "Model-based spectral coherence analysis." Journal of Fluid Mechanics 958 (March 1, 2023). http://dx.doi.org/10.1017/jfm.2023.82.
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Recent data-driven efforts have utilized spectral decomposition techniques to uncover the geometric self-similarity of dominant motions in the logarithmic layer, and thereby validate the attached eddy model. In this paper, we evaluate the predictive capability of the stochastically forced linearized Navier–Stokes equations in capturing such structural features in turbulent channel flow at $Re_\tau =2003$ . We use the linear coherence spectrum to quantify the wall-normal coherence within the velocity field generated by the linearized dynamics. In addition to the linearized Navier–Stokes equations around the turbulent mean velocity profile, we consider an enhanced variant in which molecular viscosity is augmented with turbulent eddy-viscosity. We use judiciously shaped white- and coloured-in-time stochastic forcing to generate a statistical response with energetic attributes that are consistent with the results of direct numerical simulation (DNS). Specifically, white-in-time forcing is scaled to ensure that the two-dimensional energy spectrum is reproduced and coloured-in-time forcing is shaped to match normal and shear stress profiles. We show that the addition of eddy-viscosity significantly strengthens the self-similar attributes of the resulting stochastic velocity field within the logarithmic layer and leads to an inner-scaled coherence spectrum. We use this coherence spectrum to extract the energetic signature of self-similar motions that actively contribute to momentum transfer and are responsible for producing Reynolds shear stress. Our findings support the use of coloured-in-time forcing in conjunction with the dynamic damping afforded by turbulent eddy-viscosity in improving predictions of the scaling trends associated with such active motions in accordance with DNS-based spectral decomposition.
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Zhang, Xueliang, Zhenmin Li, Wenchao Hu, and Bangchun Wen. "Synchronization and Stability of a Nonlinear Vibrating Mechanical System Characterized by Asymmetrical Piecewise Linearity." Chinese Journal of Mechanical Engineering 35, no. 1 (December 2022). http://dx.doi.org/10.1186/s10033-022-00822-0.
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AbstractIn previous studies about the synchronization of vibrators, the restoring forces of springs are mainly treated as linear directly, whereas the nonlinear features are rarely considered in vibrating systems. To make up this drawback, a dynamical model of a nonlinear vibrating mechanical system with double rigid frames (RFs), driven by two vibrators, is proposed to explore the synchronization and stability of the system. In this paper, the nonlinearity is reflected in nonlinear restoring forces of springs characterized by asymmetrical piecewise linear, where the nonlinear stiffness of springs is linearized equivalently using the asymptotic method. Based on the average method and Hamilton’s principle, the theory conditions to achieve synchronization and stability of two vibrators are deduced. After the theory analyses, some numerical qualitative analyses are given to reveal the coupling dynamical characteristics of the system and the relative motion properties between two RFs. Besides, some experiments are carried out to examine the validity of the theoretical results and the correctness of the numerical analyses results. Based on the comparisons of the theory, numeric and experiment, the ideal working regions of the system are suggested. Based on the present work, some new types of vibrating equipment, such as vibrating discharging centrifugal dehydrators/conveyers/screens, can be designed.
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Hofmeister, Thomas, and Thomas Sattelmayer. "Amplitude-Dependent Damping and Driving Rates of High-Frequency Thermoacoustic Oscillations in a Lab-Scale Lean-Premixed Gas Turbine Combustor." Journal of Engineering for Gas Turbines and Power, August 3, 2021. http://dx.doi.org/10.1115/1.4051990.
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Abstract This paper presents numerical investigations of the amplitude-dependent stability behavior of thermoacoustic oscillations at screech level frequencies in a lean-premixed, swirl-stabilized, lab-scale gas turbine combustor. A hybrid Computational Fluid Dynamics / Computational AeroAcoustics (CFD / CAA) approach is applied to individually compute thermoacoustic damping and driving rates for various acoustic amplitude levels at the combustors' first transversal (T1) eigenfrequency. Forced CFD simulations with the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations mimic the real combustor's rotating T1 eigenmode. An increase of the forcing amplitude over time allows observation of the amplitude-dependent flow field and flame evolution. In accordance with measured OH*-chemiluminescence images, a pulsation amplitude-dependent flame contraction is reproduced in the CFD simulations. At several amplitude levels, period-averaged flow fields are then denoted as reference states, which serve as inputs for the CAA part. There, eigenfrequency simulations with linearized flow equations are performed with the Finite Element Method (FEM). The outcomes are damping and driving rates as a response to the amplitude-dependency of the mean flow field. It is found that driving due to flame-acoustics interactions governs a weak amplitude-dependency, which agrees with experimentally based studies at the authors' institute. This disqualifies the perception of heat release saturation as the root-cause for limit-cycle oscillations in this high-frequency thermoacoustic system. Instead, significantly increased dissipation due to the interaction of acoustically induced vorticity perturbations with the mean flow is identified, which may explain the formation of a limit-cycle.
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Hudson, Thomas, and Filip Rindler. "Elasto-plastic evolution of single crystals driven by dislocation flow." Mathematical Models and Methods in Applied Sciences, April 12, 2022, 1–60. http://dx.doi.org/10.1142/s0218202522500191.
Full textAbstract:
This work introduces a model for large-strain, geometrically nonlinear elasto-plastic dynamics in single crystals. The key feature of our model is that the plastic dynamics are entirely driven by the movement of dislocations, that is, [Formula: see text]-dimensional topological defects in the crystal lattice. It is well known that glide motion of dislocations is the dominant microscopic mechanism for plastic deformation in many crystalline materials, most notably in metals. We propose a novel geometric language, built on the concepts of space-time “slip trajectories” and the “crystal scaffold” to describe the movement of (discrete) dislocations and to couple this movement to plastic flow. The energetics and dissipation relationships in our model are derived from first principles drawing on the theories of crystal modeling, elasticity, and thermodynamics. The resulting force balances involve a new configurational stress tensor describing the forces acting against slip. In order to place our model into context, we further show that it recovers several laws that were known in special cases before, most notably the equation for the Peach–Koehler force (linearized configurational force) and the fact that the combination of all dislocations yields the curl of the plastic distortion field. Finally, we also include a brief discussion on how a number of other effects, such as hardening, softening, dislocation climb, and coarse-graining, could be incorporated into our model.
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Haller, George, Bálint Kaszás, Aihui Liu, and Joar Axås. "Nonlinear model reduction to fractional and mixed-mode spectral submanifolds." Chaos: An Interdisciplinary Journal of Nonlinear Science 33, no. 6 (June 1, 2023). http://dx.doi.org/10.1063/5.0143936.
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A primary spectral submanifold (SSM) is the unique smoothest nonlinear continuation of a nonresonant spectral subspace E of a dynamical system linearized at a fixed point. Passing from the full nonlinear dynamics to the flow on an attracting primary SSM provides a mathematically precise reduction of the full system dynamics to a very low-dimensional, smooth model in polynomial form. A limitation of this model reduction approach has been, however, that the spectral subspace yielding the SSM must be spanned by eigenvectors of the same stability type. A further limitation has been that in some problems, the nonlinear behavior of interest may be far away from the smoothest nonlinear continuation of the invariant subspace E. Here, we remove both of these limitations by constructing a significantly extended class of SSMs that also contains invariant manifolds with mixed internal stability types and of lower smoothness class arising from fractional powers in their parametrization. We show on examples how fractional and mixed-mode SSMs extend the power of data-driven SSM reduction to transitions in shear flows, dynamic buckling of beams, and periodically forced nonlinear oscillatory systems. More generally, our results reveal the general function library that should be used beyond integer-powered polynomials in fitting nonlinear reduced-order models to data.
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Kashinath, Karthik, Santosh Hemchandra, and Matthew P. Juniper. "Nonlinear Phenomena in Thermoacoustic Systems With Premixed Flames." Journal of Engineering for Gas Turbines and Power 135, no. 6 (May 20, 2013). http://dx.doi.org/10.1115/1.4023305.
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Nonlinear analysis of thermoacoustic instability is essential for the prediction of the frequencies, amplitudes, and stability of limit cycles. Limit cycles in thermoacoustic systems are reached when the energy input from driving processes and energy losses from damping processes balance each other over a cycle of the oscillation. In this paper, an integral relation for the rate of change of energy of a thermoacoustic system is derived. This relation is analogous to the well-known Rayleigh criterion in thermoacoustics, however, it can be used to calculate the amplitudes of limit cycles and their stability. The relation is applied to a thermoacoustic system of a ducted slot-stabilized 2-D premixed flame. The flame is modeled using a nonlinear kinematic model based on the G-equation, while the acoustics of planar waves in the tube are governed by linearized momentum and energy equations. Using open-loop forced simulations, the flame describing function (FDF) is calculated. The gain and phase information from the FDF is used with the integral relation to construct a cyclic integral rate of change of energy (CIRCE) diagram that indicates the amplitude and stability of limit cycles. This diagram is also used to identify the types of bifurcation the system exhibits and to find the minimum amplitude of excitation needed to reach a stable limit cycle from another linearly stable state for single-mode thermoacoustic systems. Furthermore, this diagram shows precisely how the choice of velocity model and the amplitude-dependence of the gain and the phase of the FDF influence the nonlinear dynamics of the system. Time domain simulations of the coupled thermoacoustic system are performed with a Galerkin discretization for acoustic pressure and velocity. Limit cycle calculations using a single mode, along with twenty modes, are compared against predictions from the CIRCE diagram. For the single mode system, the time domain calculations agree well with the frequency domain predictions. The heat release rate is highly nonlinear but, because there is only a single acoustic mode, this does not affect the limit cycle amplitude. For the twenty-mode system, however, the higher harmonics of the heat release rate and acoustic velocity interact, resulting in a larger limit cycle amplitude. Multimode simulations show that, in some situations, the contribution from higher harmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems.