• 한국연소학회:학술대회논문집
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• 2001.11a
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• pp.125-135
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• 2001

Aiming at a direct, also more realistic, prediction of unstable waves evolving in the combustion chamber, present paper introduces a new analytical method. Instability equations are freshly formulated, and solve the time-integrated ODEs for amplification factors to find the transients of pressure and velocity fluctuations. Present numerical approach requires no separate treatments for nonlinearities. Preliminary numerical experiments for unstable waves in quasi-one-dimensional rocket combustor, show validity and applicability of present model, and promise for its practical use. Study for the complex models for physics, especially velocity- and pressure-coupled responses, and inclusion of multi dimensionality remains as future tasks.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.191-203
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• 2011

The interface between fluids of different densities is unstable under acceleration by a shock wave. A previous small amplitude linear theory for the compressible Euler equation failed to provide a quantitatively correct prediction for the growth rate of the unstable interface. In this paper, to include dominant nonlinear effects in a large amplitude regime, we present high-order perturbation equations of the Euler equation, and boundary conditions for the contact interface and shock waves.

• Journal of the Korean earth science society
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• v.38 no.3
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• pp.173-181
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• 2017

The stability of the steady Rossby-Haurwitz wave (R-H wave) in the nondivergent barotropic model (NBM) on the sphere was investigated with the normal mode method. The linearized NBM equation with respect to the R-H wave was formulated into the eigenvalue-eigenvector problem consisting of the huge sparse matrix by expanding the variables with the spherical harmonic functions. It was shown that the definite threshold R-H wave amplitude for instability could be obtained by the normal mode method. It was revealed that some unstable modes were stationary, which tend to amplify without the time change of the spatial structure. The maximum growth rate of the most unstable mode turned out to be in almost linear proportion to the R-H wave amplitude. As a whole, the growth rate of the unstable mode was found to increase with the zonal- and total-wavenumber. The most unstable mode turned out to consist of more-than-one zonal wavenumber, and in some cases, the mode exhibited a discontinuity over the local domain of weak or vanishing flow. The normal mode method developed here could be readily extended to the basic state comprised of multiple zonalwavenumber components as far as the same total wavenumber is given.

• Geomechanics and Engineering
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• v.14 no.1
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• pp.19-27
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• 2018

It follows from the basic principles of mechanics of deformable solids relating to the strength, stability and propagation of elastic waves that the Earth's inner core cannot exist in the form of a spherical structure in the assumed thermobaric conditions and calculation values of physico-mechanical parameters. Pressure level reaches a value that is significantly greater than the theoretical limit of medium strength in the model approximations at the surface of the sphere of the inner core. On the other hand, equilibrium state of the sphere is unstable on the geometric forming at much lower loads under the influence of the "dead" surface loads. In case of the action of "follower" loads, the assumed pressure value on the surface of the sphere is comparable with the value of the critical load of "internal" instability. In these cases, due to the instability of the equilibrium state, propagation of homogeneous deformations becomes uneven in the sphere. Moreover, the elastic waves with actual velocity cannot propagate in such conditions in solid medium. Violation of these fundamental conditions of mechanics required in determining the physical and mechanical properties of the medium should be taken into account in the integrated interpretations of seismic and laboratory (experimental) data. In this case, application of the linear theory of elasticity and elastic waves does not ensure the reliability of results on the structure and composition of the Earth's core despite compliance with the required integral conditions on the mass, moment of inertia and natural oscillations of the Earth.

• Bulletin of the Korean Space Science Society
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• 2009.10a
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• pp.44.1-44.1
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• 2009

Identification of wave characteristics during current disruption events in the near-Earth geomagnetic tail region (~ 10 RE) is important to understand the substorm onset mechanism. In this paper, linear stability analysis in the ion-cyclotron grequency range, considering temperature anisotropy and cross-field flow is presented. It is found that the ion-cyclotron drift waves propagating in a quasi-perpendicular direction with respect to the ambient magnetic field are characterized by low frequencies ($\omega$ < $0.5{\Omega}ci$), while quasi-parallel waves have frequencies close to the ion-cyclotron frequency ($\omega{\sim}{\Omega}ci$). This finding is consistent with the observation by THEMIS spacecraft of a current disruption event in which a similar high- and low-frequency band structure is also present [A. T. Y. Lui, et al., J. Geophys. Res. 113, A00C06 (2008)]. It is also found that the quasi-perpendicular mode is excited by the ion cross-field flow.

• The Bulletin of The Korean Astronomical Society
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• v.36 no.2
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• pp.111.2-111.2
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• 2011

While many astrophysical disks are vertically stratified and obey a polytropic equation of state, most studies on gravitational instability (GI) of flattened systems consider isothermal, razor-thin disks by taking vertical averages of disk properties. We investigate local GI of rotating pressure-confined polytropic disks with resolved vertical stratification by performing linear stability analysis. We find that the GI of vertically-stratified disks is in general a combination of conventional razor-thin Jeans modes and incompressible modes. The incompressible modes that dominate in the limit of the maximal disk compression require surface distortion and are an unstable version of terrestrial water waves. Disks with a steeper equation of state are found to be more Jeans unstable because they tend to have a smaller vertical scale height as well as a steeper temperature gradient corresponding to lower pressure support. GI depends more sensitively on the vertical temperature than density distribution. The density-weighted, harmonic mean, rather than the simple mean, of the adiabatic sound speed well describes the dispersion relation of horizontal modes, and thus is appropriate in the expression for Toomre Q stability parameter of razor-thin disks. We generalize Q into vertically-stratified disks, and discuss astrophysical application of our work.

• International Journal of Naval Architecture and Ocean Engineering
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• v.12 no.1
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• pp.297-313
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• 2020

An Arctic Spar is characterized by its conical shape near the waterline. In this case, the nonlinear effects from its irregular hull shape would be significant if there is either a large amplitude floater motion or steep wave conditions. Therefore, in this paper, the nonlinear effects of an Arctic Spar are numerically investigated by introducing a weakly nonlinear time-domain model that considers the time dependent hydrostatic restoring stiffness and Froude-Krylov forces. Through numerical simulations under multiple regular and irregular wave conditions, the nonlinear behavior of the Arctic Spar is clearly observed, but it is not shown in the linear analysis. In particular, it is found that the nonlinear Froude-Krylov force plays an important role when the wave frequency is close to the heave natural frequency. In addition, the nonlinear hydrostatic restoring stiffness causes the structure's unstable motion at a half of heave natural period.

• 한국해양학회지
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• v.25 no.2
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• pp.62-73
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• 1990

An experimental study is performed in order to catch the characteristics of the flow field at arrested salt wedge, using a rectangular open channel. Arrested salt wedge is generally so stable that the observations are easy, but velocities and interfacial waves are measured with the aid of visualization method, by injection of fluorescent dyes. The density interface, which is defined as the zone of maximum density variation with depth, exists in about 0.5 cm below the visual interface, and vertical density profile is quite well satisfied with Homeborn model. Interfacial layer has high turbulent intensity and its thickness decreases as the overall Richardson number increases and has magnitude of roughly 17% of upper layer. Cross-sectional velocity distribution just shows the influence of a side-wall friction and in the upper layer vertical velocity profile also becomes uniformly as Reynolds number increases, but in the lower layer it shows nearly parabolic type. Supposes that we divide salt wedge into three domains, that is, river mouth, intermediate and tip zone, entertainment coefficient is small at the intermediate zone and large at the river mouth and the tip zone. River mouth or intermediate zone has comparatively stable interface and capillary wave therefore s produced and propagated downstream. On the other hand, tip zone is very unstable, cusping ripple or bursting ripple is then produced incessantly. Arrested salt wedge form is nearly linear and has no relation to densimetric Froude number and Reynolds number.