• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2000.04a
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• pp.75-80
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• 2000

We revisit the arrested Ekman boundary layer problem, using a fully non-linear numerical model with the subgrid dissipation modeled by the large eddy simulation method (LES). The main objective of this study is to find out whether the dynamic balance of the arrested Ekman boundary layer explained by MacCready and Rhines (1991) is valid for high Reynolds number. The model solution indicates that for high Reynolds number and low Richardson number flows, the density anomaly diffusion by near-wall turbulent action may become intense enough to homogenize completely the density structure within the boundary layer, in the direction perpendicular to the sloping wall. Then the buoyancy effect becomes negligible allowing a near-equilibrium Ekman boundary layer flow to persist for a long period.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.6 s.249
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• pp.568-577
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• 2006

Developed in this study is a nonlinear Ekman pumping model to be used in simulating the rotating flows with quasi-three-dimensional Navier-Stokes equations. In this model, the Ekman pumping velocity is given from the solution of the Ekman boundary-layer equations for the region adjacent to the bottom wall of the flow domain; the boundary-layer equations are solved in the momentum-integral form. The developed model is then applied to rotating flows in a rectangular container receiving a time-periodic forcing. By comparing our results with the DNS and experimental data we have validated the developed model. We also compared our results with those given from the classical Ekman pumping model. It was found that our model can predict the rotating flows more precisely than the classical linear model.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2006.06a
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• pp.305-306
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• 2006

Developed in this study is a nonlinear Ekman pumping model to be used in simulating the rotating flows with quasi-three-dimensional Navier-Stokes equations. In this model, the Ekman pumping velocity is given from the solution of the Ekman boundary-layer equations for the region adjacent to the bottom wall of the flow domain; the boundary-layer equations are solved in the momentum-integral form. The developed model is then applied to rotating flows in a rectangular container receiving a time-periodic forcing. By comparing our results with the DNS and experimental data we have validated the developed model. We also compared our results with those given from the classical Ekman pumping model. It was found that our model can predict tile rotating flows more precisely than the classical linear model.

• 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.

• International Journal of Fluid Machinery and Systems
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• v.9 no.4
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• pp.325-331
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• 2016

A bathtub vortex above the outlet of a rotating barrel is simulated. By analyzing the Ekman layer theory, it can be found that the main flow circulation is inversely proportional to the thickness of Ekman layer. The thicker the Ekman boundary layer, the weaker the rotational strength and the shorter of the length of gas core is. According to this law, models of barriers with rods of different heights are established. The reduction of air-core length in this air entrainment vortex and weakening the strength of rotation field were achieved.

• 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.

• 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.

• Journal of the korean society of oceanography
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• v.32 no.1
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• pp.8-16
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• 1997

The ventilation theory developed by Luyten, Pedlosky and Stommel (1983) is applied to the East Sea to understand the general circulation pattern of the Intermediate Water, especially the ventilated circulation beneath the Tsushima Warm Current. The original model is slightly modified such that it takes the inflow-outflow of the Tsushima Current into consideration. Results of the model indicate that for sufficiently strong Ekman pumping, the Intermediate Water circulates cyclonically by ventilation. The Intermediate Water subducts beneath the Tsushima Warm Water through the western boundary layer. Off the western boundary layer, it turns northward, outcrops to the north by passing the polar front and continues to flow northward until it finally is absorbed by the northern boundary layer. This result seems to be compatible with some recent observations. Over the ventilated area, the transport of the Tsushima Current is negligible and most transport occurs in the shadow area where the Intermediate layer is motionless indicating that, over the deep motionless layer, the two-layered vertical structure under consideration becomes substantially single-layered.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.329-332
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• 2002

A theoretical study is made of the steady flow of a compressible fluid in a rapidly rotating finite cylinder. Flow is generated by imposing mechanical and/or thermal disturbances at the rotating endwall disks. Both the Ekman and Rossby numbers are small. A detailed consideration is given to the energy budget for a control volume in the Ekman boundary layer. A combination of physical variables, which is termed the energy contents, consisting of temperature and modified angular momentum, emerges to be relevant. The distinguishing features of a compressible fluid, in contrast to those of an incompressible fluid, are noted. For the Taylor-Proudman column to be sustained, in the interior, it is shown that the net energy transport between the solid disk wall and the interior fluid should vanish. Physical rationalizations are facilitated by resorting to the concept of the afore-stated energy content.