• The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
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• v.3 no.2
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• pp.53-58
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• 1998

Ekman layer equation with rough-bottom boundary condition has been solved to determine the effect of roughness on the magnitude of Ekman veering. The bottom boundary condition and the flow field were expanded in a power of roughness (h) which is always smaller than the Ekman layer thickness (${\delta}_E$). By changing the magnitude of roughness parameter (h/${\delta}_E$), the magnitude of the veering, which rotates counterclockwise from the interior geostrophic flow, has been computed. At a fixed depth within the Ekman layer, the magnitude of veering increases as the roughness parameter increases. However, the cross-isobar flux turns out to decrease with increasing roughness. To verify the analytic solution, laboratory experiments were carried out. Rough-bottom cylinderical container filled with homogeneous fluid was sit on a rotating table. The flow pattern during the period of steady spin-up shows that the degree of veering coincides well with the analytic results for various roughness parameters.

• 한국가시화정보학회:학술대회논문집
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• 2004.11a
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• pp.36-39
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• 2004

In this study, we present the theoretical, numerical and experimental results of the sink flow from a rotating, circular tank Strikingly enough, when the upper free surface was set with no-slip boundary conditions, the Ekman boundary-layer develops not only above the bottom surface but under the free surface. The sink fluid is coming from the two Ekman layers, and the mass transfer from the bulk, inviscid region is dependent on the rotational speed. It is also remarkable to see that all the fluid gathered along the axis flows through a rapidly rotating fluid column with almost the same size as the hole.

• Journal of the Korean Society of Visualization
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• v.2 no.2
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• pp.38-44
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• 2004

Theoretical and numerical studies are given to the sink flows within a rotating circular tank driven by the fluid withdrawal from a bottom circular hole. It was found that, when the upper free surface was set with no-slip boundary conditions, the Ekman boundary-layer develops not only above the bottom surface but under the top surface. The sink fluid is coming from the two Ekman layers, and the mass transfer from the bulk, inviscid region is dependent on the rotational speed. It is also remarkable to see that all the fluid gathered along the axis flows in a form of rapidly rotating fluid column haying almost the same diameter as the bottom hole.

• Proceedings of the Korean Statistical Society Conference
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• 2002.11a
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• pp.179-184
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• 2002

층화 추출법에서 층의 경계점을 정하는 문제는 추정의 효율에 직접적으로 영향을 미치기 때문에 매우 실제적이고 중요한 문제이다. 층화변수가 일변량 연속변수인 경우 널리 알려진 방법으로는 누적도수제곱근법과 Ekman법이 있는데 이 두 방법은 모두 나름의 약점을 지니고 있다. 본 논문에서는 Breiman 등(1984)이 제시한 CART 기법 중 회귀나무(regression tree)모형을 이용하여 층의 경계점을 정하는 방법을 소개한다. 그리고 통계청의 어업총조사 자료를 사용하여 층의 경계점을 정하는 여러 다른 방법들의 효율을 비교한다.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.9
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• pp.1192-1200
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• 1999

The present study investigates flow characteristics in a cavity with one rotating disk and co-rotating disks for application to HDD. The experiments are conducted for rotating Reynolds numbers of $5.5{\times}104$ to $1.10{\times}105$ and for gap ratios of 0.059 to 0.175 in a single rotating and 0.047 to 0.094 in co-rotating disk. Time-resolved velocity components and turbulence intensity on the rotating disks are obtained by using LDA measurements. Detailed Knowledge of the flow characteristics is essential to analyze flow vibration and heat transfer and to design head-arm assembly and hub height in HDD. The results indicate that the velocity field in HDD is changed largely by the rotating Reynolds numbers and hub height of the disk.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.628-633
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• 2003

An analysis on the steady-state has been made of flow of a compressible fluid rapidly-rotating in a pipe. The flow is induced by an small arbitrary azimuthally-varying thermal forcing added on the basic state of rigid body isothermal rotation. The system Ekman number is assumed to be very small value. Analytic solutions have been obtained for axisymmetric and non-axisymmetric types, in which the axisymmetric solution comes from the azimuthally-averaged wall boundary condition and the non-axisymmetric solution from fluctuating wall boundary condition.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.456-462
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• 2001

Comprehensive numerical computations are made of a homogenous spin-up in a cylindrical cavity with a time-dependent rotation rate. Numerical solutions are acquired to the governing axisymmetric cylindrical Navier-Stokes equation. A rotation rate formula is ${\Omega}_f={\Omega}_i+{\Delta}{\Omega}(1-{\exp}(-t/t_c))$. If $t_c$ is large, it implies that a rotation change rate is small. The Ekman number, E, is set to $10^{-4}$ and the aspect ratio, R/H, fixed to I. For a linear spin-up(${\epsilon}<<$), the major contributor to spin-up in the interior is not viscous-diffusion term but inviscid term, especially Coriolis term, though $t_c$ is very large. The viscous-diffusion term only works near sidewall. But for spin-up from rest, when $t_c$ is very large, viscous-diffusion term affects interior area as well as sidewall, initially. So azimuthal velocity of interior for large $t_c$ appears faster than that of interior for relatively small $t_c$. However, the viscous-diffusion term of interior decreases as time increases. Instead, inviscid term appears in the interior.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.634-639
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• 2003

It has been studied the flow near a rotating disk with surface topography. The system Ekman number is assumed very small, i.e., $E[{\equiv}\frac{\nu}{{\Omega}^{\ast}L^{\ast2}}]<<1$ in which $L^{\ast}$ denotes a disk radius, ${\nu}$ kinematic viscosity of the fluid and ${\Omega}^{\ast}$ angular velocity of the basic state. Disk surface has a sinusoidal topographic variation along radial coordinate, i.e., $z={\delta}cos(2{\pi}{\omega}r)$, where ${\delta}$ and ${\omega}$ are, respectively, nondimensional amplitude and wave number of the disk surface. Analytic solutions, being useful over the parametric ranges of ${\delta}{\sim}O$( $E^{1/2}$ ) and ${\omega}{\leq}O$ ( $E^{1/2}$ ), are secured in a series-function form of Fourier-Bessel type. An asymptotic behavior, when $E{\rightarrow}0$, is clarified as : for a disk with surface roughness, in contrast to the case of a flat disk, the azimuthal velocity increases in magnitude, together with the thickening boundary layer. The radial velocity, however, decreases in magnitude as the amplitude of surface waviness increases. Consequently, the overall Ekman pumping at the edge of the boundary layer remains unchanged, maintaining the constant value equal to that of the flat disk.

• 한국전산유체공학회:학술대회논문집
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• 2008.03b
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• pp.487-490
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• 2008

A theoretical study is made of the flow in a confined cylindrical container with differential rotating top and bottom disks. Two kinds of theoretical solution for the azimuthal velocity were obtained: one is an exact solution of Bessel function type and the other is an approximate solution of exponential function type which comes from WKB approximation. Both theoretical solutions are shown to be self consistent with each other as well as a good agreement with previous studies. Moreover, in a range of relatively low Reynolds number, the obtained solution of Bessel function type shows better result than previous solutions.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.683-686
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• 2002

The hydrodynamic instability of the three-dimensional boundary-layer over a rotating disk has been numerically investigated for three cases flows using linear stability theory (i.e. Rossby number, Ro = -1, 0, and 1). Detailed numerical values of the disturbance wave number, wave frequency, azimuth angle, radius (Reynolds number, Re) and other characteristics have been calculated for $K{\acute{a}}rm{\acute{a}}n$, Ekman and $B{\"{o}}ewadt$ boundary-layer flows. Neutral curves for these flows are presented. Presented are the neutral stability results concerning the two instability modes (Type I and Type II) by using a two-point boundary value problem code COLUEW that was based upon the adaptive orthogonal collocation method using B-spline. The prediction from the present results on both instability modes among the three cases agrees with the previously known numerical and experimental data well.