• Title/Summary/Keyword: Dispersion equation

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Determination of Shear Wave Velocity Profiles of Natural Soils and Pavement Systems Using Surface Wave Technique (표면파 기법을 이용한 자연지반 및 포장지반의 전단파 속도 분포 추정에 관한 연구)

  • Woo, Je Yoon;Kim, Soo Il
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.8 no.4
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    • pp.49-57
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    • 1988
  • A new analytical inversion technique is developed to determine the shear wave velocity profiles of natural soils and pavement systems from the dispersion curves of Rayleigh waves. Haskell's theory on the dispersion of the surface waves in multi-layered elastic solids is utilized. A frequency-unlimited dispersion equation is developed by use of the delta matrix technique. Rigid halfspace is assumed at the depth of the one wavelength of Rayleigh waves. Computer program is coded and validity of the technique is verified through the numerical model tests.

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현장 규모 biobarrier의 수리학적 특성과 기초 설계

  • 최영화;오재일;왕수균;배범한
    • Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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    • 2003.09a
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    • pp.426-430
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    • 2003
  • Subsurface biobarrier technology has potential applications to contain contaminated groundwater and/or to degrade toxic pollutants in groundwater. Effective biobarrier formation is need to assess of hydrogeologic characteristics and to conduct practical operation strategies and design based on this prior to design biobarrier. Thus, in this study, we examined hydrogeologic characteristics in biobarrier construction site. Hydraulic conductivities which calculated from slug test data have shown difference with each well as 1.20$\times$10$^{-3}$ -6.00$\times$10$^{-5}$ cm/sec. Tracer test is a method in which concentration of tracer solution during withdrawal in each well by vacuum extraction system is measured with time. Tracer solution was continuously injected by constant head tank. Measured tracer concentration versus time data were fitted to analytical solution of convection dispersion equation (CDE). The fitting data of CDE to the measured data at each extraction well yielded were 0.61cm/min(pore velocity), 5.38$\textrm{cm}^2$/min(dispersion coefficient) for discharge rate of 0.47 1/min and 1.75cm/min(pore velocity), 36.34$\textrm{cm}^2$/min(dispersion coefficient) for discharge rate of 0.93 1/min. As a result, we acquired fundamental parameters which need to design biobarrier and operation strategies.

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Analysis of Airflow Pattern and Particle Dispersion in Enclosed Environment Using Traditional CFD and Lattice Boltzmann Methods

  • Inoguchi, Tomo;Ito, Kazuhide
    • International Journal of High-Rise Buildings
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    • v.1 no.2
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    • pp.87-97
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    • 2012
  • The indoor environments in high-rise buildings are generally well enclosed by defined boundary conditions. Here, a numerical simulation method based on the Lattice Boltzmann method (LBM), which aims to model and simulate the turbulent flow accurately in an enclosed environment, and its comparison with traditional computational fluid dynamics (CFD) results, are presented in this paper. CFD has become a powerful tool for predicting and evaluating enclosed airflows with the rapid advance in computer capacity and speed, and various types of CFD turbulence modeling and its application and validation have been reported. The LBM is a relatively new method; it involves solving of the discrete Boltzmann equation to simulate the fluid flow with a collision model instead of solving Navier-Stokes equations. In this study, the LBM-based scheme of flow pattern and particle dispersion analyses are validated using the benchmark test case of two- and three-dimensional and isothermal conditions (IEA/Annex 20 case); the prediction accuracy and advantages are also discussed by comparison with the results of CFD.

Ocean Outfall Modelling with the Particle Tracking Method (입자추적법을 이용한 해양방류구 모델링)

  • Jung, Yun-Chul
    • Journal of Navigation and Port Research
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    • v.26 no.5
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    • pp.563-569
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    • 2002
  • To overcome the weaknesses of conventional finite difference model in pollutant dispersion modelling, the particle tracking method is used. In this study, a three dimensional particle tracking model which can be used in Princeton Ocean Model was developed and verified through the various numerical tests. Usability of the model was also confirmed through the ocean outfall modelling in Tampa Bay, Florida. As it is expected, random walk model showed the less dispersion in a range compared to the conventional finite difference model and its reason is estimated due to an error from numerical diffusion which the conventional model holds. This newly developed model is expected to be used in various ocean dispersion modelling.

Analysis of Stem Wave due to Long Breakwaters at the Entrance Channel

  • Kwon, Seong-Min;Moon, Seung-Hyo;Lee, Sang-Heon;Yoo, Jae-Woong;Lee, Joong-Woo
    • Journal of Navigation and Port Research
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    • v.41 no.5
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    • pp.345-352
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    • 2017
  • Recently, a new port reserves deep water depth for safe navigation and mooring, following the trend of larger ship building. Larger port facilities include long and huge breakwaters, and mainly adopt vertical type considering low construction cost. A vertical breakwater creates stem waves combining inclined incident waves and reflected waves, and this causes maneuvering difficulty to the passing vessels, and erosion of shoreline with additional damages to berthing facilities. Thus, in this study, the researchers have investigated the response of stem waves at the vertical breakwater near the entrance channel and applied numerical models, which are commonly used for the analysis of wave response at the harbor design. The basic equation composing models here adopted both the linear parabolic approximation adding the nonlinear dispersion relationship and nonlinear parabolic approximation adding a linear dispersion relationship. To analyze the applicability of both models, the research compared the numerical results with the existing hydraulic model results. The gap of serial breakwaters and aligned angles caused more complicated stem wave generation and secondary stem wave was found through the breakwater gap. Those analyzed results should be applied to ship handling simulation studies at the approaching channels, along with the mooring test.

Modeling wave propagation in graphene sheets influenced by magnetic field via a refined trigonometric two-variable plate theory

  • Fardshad, R. Ebrahimi;Mohammadi, Y.;Ebrahimi, F.
    • Structural Engineering and Mechanics
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    • v.72 no.3
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    • pp.329-338
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    • 2019
  • In this paper, the magnetic field influence on the wave propagation characteristics of graphene nanosheets is examined within the frame work of a two-variable plate theory. The small-scale effect is taken into consideration based on the nonlocal strain gradient theory. For more accurate analysis of graphene sheets, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. A derivation of the differential equation is conducted, employing extended principle of Hamilton and solved my means of analytical solution. A refined trigonometric two-variable plate theory is employed in Kinematic relations. The scattering relation of wave propagation in solid bodies which captures the relation of wave number and the resultant frequency is also investigated. According to the numerical results, it is revealed that the proposed modeling can provide accurate wave dispersion results of the graphene nanosheets as compared to some cases in the literature. It is shown that the wave dispersion characteristics of graphene sheets are influenced by magnetic field, elastic foundation and nonlocal parameters. Numerical results are presented to serve as benchmarks for future analyses of graphene nanosheets.

Interpretation of Ground Wave Using Ray Method in Pekeris Waveguide (Pekeris 도파관에서 음선 접근법을 이용한 지면파 해석)

  • Choi, Jee-Woong
    • The Journal of the Acoustical Society of Korea
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    • v.28 no.3
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    • pp.208-212
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    • 2009
  • Ground wave is an acoustic wave propagating at a sediment sound speed in the case that sediment sound speed is constant with depth, which is explained by modal dispersion effects. In this paper, the ground wave in time domain is simulated using the ray-based approach, which is possible because the modal dispersion can be explained by the guiding of energy caused by reflection and refraction in the waveguide geometry. For a Pekeris waveguide, the ground wave can be interpreted as a sequence of head waves, called a head wave sequence [Choi and Dahl, J. Acoust. Soc. Am. 119, 3660-3668 (2006)]. The ground wave is simulated by convolution of the source signal with a channel impulse response of the head wave sequence, which is compared with simulated signals obtained via a Fourier synthesis of a complex parabolic equation (PE) field.

Study on the numerical models of turbulent dispersion of solid particles in a two-phase turbulent jet flow (이상난류제트 유동에서 고체입자 난류확산의 수치모델에 관한 연구)

  • 양선규;최영돈
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.11 no.1
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    • pp.1-18
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    • 1987
  • Prediction performances by Einstein's equation of diffusivity, Peskin's model, Three-Equation model, Four-Equation model and Algebraic Stress Model, have been compared by analyzing twophase (air-solid) turbulent jet flow. Turbulent kinetic energy equation of dispersed phase was solved to investigate effects of turbulent kinetic energy on turbulent diffusivity. Turbulent kinetic energy dissipation rate of particles has been considered by solving turbulent kinetic energy dissipation rate equation of dispesed phase and applying it to turbulent diffusivity of dispersed phase. Results show that turbulent diffusivity of dispersed phase can be expressed by turbulent kinetic energy ratio between phases and prediction of turbulent kinetic energy was improved by considering turbulent kinetic energy dissipation rate of dispersed phase for modelling turbulent diffusivity. This investigation also show that Algebraic Stress Model is the most promising method in analyzing gas-solid two phaes turbulent flow.

Mach Reflection of Sinusoidally- Modulated Nonlinear Stokes Waves by a Thin Wedge (쐐기에 의한 비선형파의 마하반사)

  • Hang-S. Choi;Won-S. Chee
    • Journal of the Society of Naval Architects of Korea
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    • v.28 no.1
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    • pp.53-59
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    • 1991
  • By employing multiple-scale expansion techniques, the diffraction of sinusoidally-modulated nonlinear Stokes waves by a stationary thin wedge has been studied within the framework of potential theory. It is found that the evolution of diffracted waves can be described by the Zakharov equation to the leading order and it can be replaced by the cubic $Schr\ddot{o}dinger$ equation with an additional linear term for stable modulations. Computations are made for the cubic $Schr\ddot{o}dinger$ equation with different values of nonlinear and dispersion parameters. Numerical results well reflect the experimental findings in the amplitude and width of generated stem waves. It is numerically confirmed that the nonlinearity dominates the wave field, while the dispersion hardly affects the wave evolution, and stem waves are likely to be formed for steep incident waves in the case of stable sinusoidal modulations.

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Analytical Comparison of Time-Dependent Mild-Slope Equations (시간의존 완경사방정식의 이론적 비교)

  • Lee, Chang-Hoon;James T. Kirby
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.6 no.4
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    • pp.389-396
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    • 1994
  • We analyze existing time-dependent mild-slope equations, which were developed by Smith and Sprinks (1975) (or, equivalently, Radder and Dingemans (1985)) and Kubo et al. (1992), in terms of the dispersion relation and energy transport. One-dimensionally in the horizontal direction, we compare the modulation of wave amplitudes for the time-dependent mild-slope equations against the linear Scrodinger equation. In view of the dispersion relation and modulation of wave amplitudes, Smith and Sprinks' model is more accurate in shallower water (kh$\leq$0.2$\pi$) and satisfies the linear Scrodinger equation in very shallow water (kh>0.2$\pi$) and satisfies the linear Scrodinger equation at a point of intermediate water depth (kh=0.3$\pi$). In view of the energy transport, Kubo et al.'s model is more accurate but yields singular solutions at some higher frequency range.

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