scholarly journals A non-hydrostatic two-layer staggered scheme for transient waves due to anti-symmetric seabed thrust

2018 ◽  
Author(s):  
Sri Redjeki Pudjaprasetya ◽  
Ikha Magdalena ◽  
Sugih Sudharma Tjandra
Keyword(s):  
Dispersion Relation ◽  
Numerical Scheme ◽  
Vertical Direction ◽  
Wave Number ◽  
Transient Waves ◽  
Good Balance ◽  
Wide Range ◽  
Staggered Scheme ◽  
Wave Trains ◽  
2004 Tsunami

The development of transient waves generated by bottom motion is studied numericallyin this work. A non-hydrostatic numerical scheme, based on solving the two dimensionalEuler equations using two-layer approximation for the vertical direction, is implemented.The dispersion relation of this scheme is shown to agree with the analytical dispersionrelation over a wide range of kd0, where k denotes the wave number and d0 the characteristic water depth. To ensure that a good balance between non-linearity and dispersion is accommodated by the scheme, the propagation of a solitary wave (undisturbed in shape) was simulated. Our next focus was on the simulation of transient waves generatedby bottom motion. After conducting a benchmark test against Hammack's experimentalresults for downward bottom motion, an anti-symmetric bottom thrust was considered.The resulting transient waves developed different behavior depending on the water depth.Finally, to mimic the December 2004 tsunami, a seabed motion was generated over Acehbathymetry. This simulation showed that a package of wave trains developed and propa-gated towards the Aceh coast, and exhibited inter alia the feature of shoreline withdrawaloften observed.

A Nonhydrostatic Two-Layer Staggered Scheme for Transient Waves due to Anti-Symmetric Seabed Thrust

2017 ◽  
Vol 11 (01) ◽  
pp. 1740002 ◽  
Author(s):  
S. R. Pudjaprasetya ◽  
I. Magdalena ◽  
S. S. Tjandra
Keyword(s):  
Dispersion Relation ◽  
Water Depth ◽  
Numerical Scheme ◽  
Vertical Direction ◽  
Wave Number ◽  
Transient Waves ◽  
Wide Range ◽  
Staggered Scheme ◽  
Wave Trains ◽  
2004 Tsunami

The development of transient waves generated by bottom motion is studied numerically in this work. A nonhydrostatic numerical scheme, based on solving the two-dimensional Euler equations using two-layer approximation for the vertical direction, is implemented. The dispersion relation of this scheme is shown to agree with the analytical dispersion relation over a wide range of [Formula: see text], where [Formula: see text] denotes the wave number and [Formula: see text] the characteristic water depth. To ensure that a good balance between nonlinearity and dispersion is accommodated by the scheme, the propagation of a solitary wave (undisturbed in shape) was simulated. Our next focus was on the simulation of transient waves generated by bottom motion. After conducting a benchmark test against Hammack’s experimental results for downward bottom motion, an anti-symmetric bottom thrust was considered. The resulting transient waves developed different behavior depending on the water depth. Finally, to mimic the December 2004 tsunami, a seabed motion was generated over Aceh bathymetry. This simulation showed that a package of wave trains developed and propagated towards the Aceh coast, and exhibited inter alia the feature of shoreline withdrawal often observed.

scholarly journals Porosity Effects on the Dispersion Relation of Water Waves through Dense Array of Vertical Cylinders

2020 ◽  
Vol 8 (12) ◽  
pp. 960
Author(s):  
Joffrey Jamain ◽  
Julien Touboul ◽  
Vincent Rey ◽  
Kostas Belibassakis
Keyword(s):  
Dispersion Relation ◽  
Water Waves ◽  
Environmental Flows ◽  
Numerical Study ◽  
Wave Number ◽  
Coastal Vegetation ◽  
The Finite Element Method ◽  
Dense Array ◽  
Wide Range ◽  
Vertical Cylinders

There is growing interest for water-wave flows through arrangements of cylinders with application to the performance of porous marine structures and environmental flows in coastal vegetation. For specific few cases experimental data are available in the literature concerning the modification of the dispersion equation for waves through a dense array of vertical cylinders. This paper presents a numerical study of the porosity effects on the dispersion relation of water waves through such configurations. To this aim, the sloshing problem in a tank full of vertical cylinders intersecting the free surface is studied using the finite element method, and the influence of the porosity on the wave number is quantified. On the basis of numerical results, a new modification of a dispersion relation for porous medium is suggested based on a wide range of collected data. Moreover, the domain of validity of this new dispersion relation is examined considering the number of cylinders and the extrapolation to the infinite medium.

scholarly journals A modular microfluidic system based on a multilayered configuration to generate large-scale perfusable microvascular networks

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Tao Yue ◽  
Da Zhao ◽  
Duc T. T. Phan ◽  
Xiaolin Wang ◽  
Joshua Jonghyun Park ◽  
...  
Keyword(s):  
Large Scale ◽  
Circulatory System ◽  
Vertical Direction ◽  
Microfluidic System ◽  
Vital Role ◽  
Microvascular Networks ◽  
Biological Studies ◽  
Wide Range ◽  
High Flexibility

AbstractThe vascular network of the circulatory system plays a vital role in maintaining homeostasis in the human body. In this paper, a novel modular microfluidic system with a vertical two-layered configuration is developed to generate large-scale perfused microvascular networks in vitro. The two-layer polydimethylsiloxane (PDMS) configuration allows the tissue chambers and medium channels not only to be designed and fabricated independently but also to be aligned and bonded accordingly. This method can produce a modular microfluidic system that has high flexibility and scalability to design an integrated platform with multiple perfused vascularized tissues with high densities. The medium channel was designed with a rhombic shape and fabricated to be semiclosed to form a capillary burst valve in the vertical direction, serving as the interface between the medium channels and tissue chambers. Angiogenesis and anastomosis at the vertical interface were successfully achieved by using different combinations of tissue chambers and medium channels. Various large-scale microvascular networks were generated and quantified in terms of vessel length and density. Minimal leakage of the perfused 70-kDa FITC-dextran confirmed the lumenization of the microvascular networks and the formation of tight vertical interconnections between the microvascular networks and medium channels in different structural layers. This platform enables the culturing of interconnected, large-scale perfused vascularized tissue networks with high density and scalability for a wide range of multiorgan-on-a-chip applications, including basic biological studies and drug screening.

Dynamics and Performance of a Harmonically Excited Vertical Impact Damper

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Sanjiv Ramachandran ◽  
George Lesieutre
Keyword(s):  
Loss Factor ◽  
Vertical Direction ◽  
Theoretical Models ◽  
Coefficient Of Restitution ◽  
Numerical Continuation ◽  
Particle Impact ◽  
Impact Damper ◽  
High Loss ◽  
Wide Range ◽  
And Performance

Particle impact dampers (PIDs) have been shown to be effective in vibration damping. However, our understanding of such dampers is still limited, based on the theoretical models existing today. Predicting the performance of the PID is an important problem, which needs to be investigated more thoroughly. This research seeks to understand the dynamics of a PID as well as those parameters which govern its behavior. The system investigated is a particle impact damper with a ceiling, under the influence of gravity. The base is harmonically excited in the vertical direction. A two-dimensional discrete map is obtained, wherein the variables at one impact uniquely dictate the variables at the next impact. This map is solved using a numerical continuation procedure. Periodic impact motions and “irregular” motions are observed. The effects of various parameters such as the gap clearance, coefficient of restitution, and the base acceleration are analyzed. The dependence of the effective damping loss factor on these parameters is also studied. The loss factor results indicate peak damping for certain combinations of parameters. These combinations of parameters correspond to a region in parameter space where two-impacts-per-cycle motions are observed over a wide range of nondimensional base accelerations. The value of the nondimensional acceleration at which the onset of two-impacts-per-cycle solutions occurs depends on the nondimensional gap clearance and the coefficient of restitution. The range of nondimensional gap clearances over which two-impacts-per-cycle solutions are observed increases as the coefficient of restitution increases. In the regime of two-impacts-per-cycle solutions, the value of nondimensional base acceleration corresponding to onset of these solutions initially decreases and then increases with increasing nondimensional gap clearance. As the two-impacts-per-cycle solutions are associated with high loss factors that are relatively insensitive to changing conditions, they are of great interest to the designer.

Analytical evaluation of track response in the vertical direction due to a moving load

2016 ◽  
Vol 23 (18) ◽  
pp. 2989-3006 ◽  
Author(s):  
Wlodzimierz Czyczula ◽  
Piotr Koziol ◽  
Dariusz Kudla ◽  
Sergiusz Lisowski
Keyword(s):  
Steady State ◽  
Moving Load ◽  
Vertical Direction ◽  
Vertical Displacement ◽  
Steady State Response ◽  
Concentrated Force ◽  
State Response ◽  
Weakly Coupled ◽  
Wide Range ◽  
Rail Deflection

In the literature, typical analytical track response models are composed of beams (which represent the rail) on viscoelastic or elastic foundations. The load is usually considered as a single concentrated force (constant or varying in time) moving with constant speed. Concentrated or distributed loads or multilayer track models have rarely been considered. One can find some interesting results concerning analysis of distributed loads and multilayer track structures that include both analytical and numerical approaches. However, there is a noticeable lack of sufficient comparison between track responses under concentrated or distributed load and between one and multilayer track models. One of the unique features of the present paper is a comparison of data obtained for a series of concentrated and distributed loads, which takes into account a wide range of track parameters and train speeds. One of the fundamental questions associated with the multilayer track model is the level of coupling between the rail and the vibrations of the sleepers. In this paper, it is proved that sleepers are weakly coupled with the rail if the track is without significant imperfections, and the steady-state response is analyzed for this case. In other words, sleeper vibrations do not influence the rail vibrations significantly. Therefore the track is analyzed by means of a two-stage model. The first step of this model determines rail vibration under a moving load, and then the sleeper vibration is calculated from previously obtained kinematic excitation. The model is verified by comparison of the obtained results with experimental data. Techniques based on Fourier series are applied to the solution of the steady-state track response. Another important problem associated with track response under moving loads arises from the analysis of the effect of longitudinal forces in rails on vertical displacement. It is shown that, in the case of the steady-state response, longitudinal forces do not influence rail displacements significantly and this observation remains correct for a wide range of track parameters and train speeds. The paper also analyzes the legitimacy of the statement that additional rail deflection between sleepers, compared to the continuous rail support, can be considered as a track imperfection.

scholarly journals Two-Dimensional Convection Induced by Gravity and Centrifugal Forces in a Rotating Porous Layer Far Away from the Axis of Rotation

1998 ◽  
Vol 4 (2) ◽  
pp. 73-90 ◽  
Author(s):  
Peter Vadasz ◽  
Saneshan Govender
Keyword(s):  
Rayleigh Number ◽  
Porous Layer ◽  
Temperature Fields ◽  
Wave Number ◽  
Marginal Stability ◽  
Two Dimensional ◽  
Wide Range ◽  
Gravity Driven ◽  
Gravity Driven Flow ◽  
The Stability

The stability and onset of two-dimensional convection in a rotating fluid saturated porous layer subject to gravity and centrifugal body forces is investigated analytically. The problem corresponding to a layer placed far away from the centre of rotation was identified as a distinct case and therefore justifying special attention. The stability of a basic gravity driven convection is analysed. The marginal stability criterion is established in terms of a critical centrifugal Rayleigh number and a critical wave number for different values of the gravity related Rayleigh number. For any given value of the gravity related Rayleigh number there is a transitional value of the wave number, beyond which the basic gravity driven flow is stable. The results provide the stability map for a wide range of values of the gravity related Rayleigh number, as well as the corresponding flow and temperature fields.

Wave trains in an excitable FitzHugh-Nagumo model: Bistable dispersion relation and formation of isolas

2007 ◽  
Vol 75 (3) ◽  
Author(s):  
Georg Röder ◽  
Grigory Bordyugov ◽  
Harald Engel ◽  
Martin Falcke
Keyword(s):  
Dispersion Relation ◽  
Wave Trains

Note on magneto-hydrodynamic gravitational stability of a double fluids interface

2008 ◽  
Vol 86 (3) ◽  
pp. 477-485
Author(s):  
Ahmed E Radwan ◽  
Mourad F Dimian
Keyword(s):  
Dispersion Relation ◽  
Present Model ◽  
The Self ◽  
Wave Number ◽  
Symmetric Mode ◽  
Fluid Interface ◽  
Unperturbed State ◽  
Gravitational Stability ◽  
The Stability ◽  
Range Force

The magneto–gravitational stability of double-fluid interface is discussed. The pressure in the unperturbed state is not constant because the self-gravitating force is a long-range force. The dispersion relation is derived and discussed. The self-gravitating model is unstable in the symmetric mode m = 0 (m is the transverse wave number), while it is stable in all other states. The effects of the densities, the liquid-fluid radii ratios, and the electromagnetic force on the stability of the present model are identified for all wavelengths.PACS Nos.: 47.35.Tv, 47.65.–d, 04.40.–b

scholarly journals Thermodynamical Extension of a Symplectic Numerical Scheme with Half Space and Time Shifts Demonstrated on Rheological Waves in Solids

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 155 ◽  
Author(s):  
Tamás Fülöp ◽  
Róbert Kovács ◽  
Mátyás Szücs ◽  
Mohammad Fawaier
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Dispersion Relation ◽  
Half Space ◽  
Numerical Stability ◽  
Numerical Scheme ◽  
Nonlinear Dispersion ◽  
Finite Element Software ◽  
Space And Time ◽  
Nonlinear Dispersion Relation

On the example of the Poynting–Thomson–Zener rheological model for solids, which exhibits both dissipation and wave propagation, with nonlinear dispersion relation, we introduce and investigate a finite difference numerical scheme. Our goal is to demonstrate its properties and to ease the computations in later applications for continuum thermodynamical problems. The key element is the positioning of the discretized quantities with shifts by half space and time steps with respect to each other. The arrangement is chosen according to the spacetime properties of the quantities and of the equations governing them. Numerical stability, dissipative error, and dispersive error are analyzed in detail. With the best settings found, the scheme is capable of making precise and fast predictions. Finally, the proposed scheme is compared to a commercial finite element software, COMSOL, which demonstrates essential differences even on the simplest—elastic—level of modeling.

scholarly journals Magnetic Rayleigh–Taylor instability at a contact discontinuity with an oblique magnetic field

2020 ◽  
Vol 634 ◽  
pp. A96
Author(s):  
E. Vickers ◽  
I. Ballai ◽  
R. Erdélyi
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Contact Discontinuity ◽  
Homogeneous Magnetic Field ◽  
Taylor Instability ◽  
Wide Range ◽  
Rayleigh Taylor Instability ◽  
The Magnetic Field ◽  
Theoretical Results

Aims. We investigate the nature of the magnetic Rayleigh–Taylor instability at a density interface that is permeated by an oblique homogeneous magnetic field in an incompressible limit. Methods. Using the system of linearised ideal incompressible magnetohydrodynamics equations, we derive the dispersion relation for perturbations of the contact discontinuity by imposing the necessary continuity conditions at the interface. The imaginary part of the frequency describes the growth rate of waves due to instability. The growth rate of waves is studied by numerically solving the dispersion relation. Results. The critical wavenumber at which waves become unstable, which is present for a parallel magnetic field, disappears because the magnetic field is inclined. Instead, waves are shown to be unstable for all wavenumbers. Theoretical results are applied to diagnose the structure of the magnetic field in prominence threads. When we apply our theoretical results to observed waves in prominence plumes, we obtain a wide range of field inclination angles, from 0.5° up to 30°. These results highlight the diagnostic possibilities that our study offers.

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