• Title, Summary, Keyword: Ekman layer

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Development of a Nonlinear Ekman Pumping Model (비선형 Ekman 펌핑 모델의 개발)

  • Suh Yong-Kweon;Park Jae-Hyun
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.30 no.6
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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.

Large eddy simulation of turbulent boundary layer effects on stratified fluids in a rotating conical container

  • Lee, Sang-Ki;Bae, Jun-Hong;Hwang, Eyl-Seon;M. Sadasivam
    • Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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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.

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Non-Linear Ekman Pumping Model (비선형 에크만 분출 모델)

  • Park, Jae-Hyoun;Kim, Jung-Hwan;Kim, Dong-Kyun;Bae, Suk-Tae;Kim, Jung-Ryul
    • Proceedings of the Korean Society of Marine Engineers Conference
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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.

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Free Surface Vortex in a Rotating Barrel with Rods of Different Heights

  • Zhang, Xiaoyue;Zhang, Min;Chen, Wanyu;Yang, Fan;Guo, Xueyan
    • 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.

A Sink Flow from a Rotating Tank (회전원통으로부터의 싱크 유동)

  • Suh Yong Kweon;Yeo Chang Ho
    • 한국가시화정보학회:학술대회논문집
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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.

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Theoretical and Numerical Analysis of Sink Flows under a Background Rotation (배경회전이 있는 싱크 유동의 이론 및 수치해석)

  • Suh Yong Kweon;Yeo Chang Ho
    • 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.

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Characteristics of the Ekman Layer Flow over a Rough Bottom (거친 바닥 위의 에크만 경계층 내의 흐름의 특성)

  • Na, Jung-Yul;Kim, Tae-Yeon
    • The Sea
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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.

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Flow Near a Rotating Disk with Surface Roughness (표면조도를 갖는 회전판 주위의 유동)

  • Park, Jun-Sang;Yoon, Myung-Sup;Hyun, Jae-Min
    • Proceedings of the KSME Conference
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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.

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Energy transport analysis for the Taylor-Proudman column in la rapidly-rotating compressible fluid (압축성 회전 유동에서의 Taylor-Proudman 기둥의 에너지 전달에 관한 해석)

  • Park Jun Sang;Hyun Jae Min
    • Proceedings of the KSME Conference
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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.

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Modeling of Circulation for the East Sea Using Reduced Gravity Models (감쇠중력 모형을 이용한 동해의 순환모델링)

  • Choi, Byung-Ho;Wang, Ou
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.9 no.3
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    • pp.105-114
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    • 1997
  • Wind is one of the main forcing contributing the circulation of the East Sea. By using 1.5-layer and 2.5-layer reduced gravity models, circulation in the East Sea is simulated. The bifurcation of the Tsushima Warm Current (TWC), the separation of East Korea Warm Current (EKWC) from the east coast of Korea, the Nearshore Branch of TWC, and the cyclonic gyres stretched from the East Korea Bay to the northern half of the East Sea are compared well with the schematic map. The features of the upper and the lower layer are very similar except for those of the central region. The Polar Front is the separating line of two different features. The main feature of northern part of the East Sea, north of the Polar Front is cyclonic gyres, which are composed of three cyclonic gyres in most seasons. North Korean Cold Current (NKCC) and Liman Cold Current (LCC) are the nearshore part of these cyclonic gyres. In the south of the Polar Front the current systems of both layers are anticyclonic in most seasons, except that those of the upper layer in winter and spring are not anticyclonic. Along the coast of Korea and Russia, the velocity structure is barotropic, while that of the central region is baroclinic. The effects due to the seasonal variations of wind stress and local Ekman suction/pumping are studied by imposing the domain with modified wind stress. which is spatial mean with temporal variations and temporal mean with spatial variations. It is found that the local Ekman suction/pumping due to wind stress curl is important to the formation of the cyclonic gyres in the western and the northwestern region of the East Sea.

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