• Proceedings of the KSME Conference
• /
• 2001.06e
• /
• pp.27-32
• /
• 2001

A study has been made of the condition to maintaining Taylor-Proudman column flows in a compressible rotating fluid, which is driven by small mechanical and/or thermal perturbations imposing on the container wall in the basic state of isothermal rigid body rotation. The Rossby and system Ekman numbers are assumed to be very small. The Taylor-Proudman column flow can be produced when energy parameter, e, becomes constant on the whole flow region. Energy balance concept, related to energy parameter, and its physical interpretation are given with comprehensive discussions.

• Proceedings of the KSME Conference
• /
• 2002.08a
• /
• pp.341-344
• /
• 2002

A matched asymptotic analysis is conducted for a compressible rotating flow in a cylindrical container when a mechanical and/or a thermal disturbance is imposed on the wall. The system Ekman number is assumed to be very small. The conditions for the Taylor-Proudman column in the interior, which were also given in the companion paper Park & Hyun, 2002) by means of the energy balancing analysis, have been re-derived. The concept of the variable, the energy content $e[{\equiv}T+2 {\alpha}^2 {\gamma}{\nu}]$, is reformulated, and its effectiveness in characterizing the energy transport mechanism is delineated. It is seen that, under the condition of the Taylor-Proudman column, numerous admissible theoretical solutions for interior flow exist with an associated wail boundary condition. Some canonical examples are illustrated with comprehensive physical descriptions. The differential heating problem on the top and bottom endwall disks is revisited by using the concept of the energy content. The results are shown to be in line with the previous findings.

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

• Journal of the Korean Society of Visualization
• /
• v.21 no.2
• /
• pp.45-54
• /
• 2023

In the present study, we propose new type of a spinning disk reactor(SDR) with high performance and very convenient structure to make a large scale equipment from lab-scale than the conventional one. A split-disk experimental equipment, based on new type of spinning disk reactor, has been developed to generate an energy to break a bulk of injected gas into smaller gas bubble. Several cases of an experimental observation make it to confirm that a bulk of injecting gas could be continuously break into smaller bubbles. It shows the feasibility to make a scale-up of SDR by using the characteristic of Taylor-Proudman column in rotating flow. A theoretical study on single phase liquid flow is given to predict a liquid induced shear stress, which make the present study to be self-containment.

• Journal of the Korean earth science society
• /
• v.31 no.1
• /
• pp.88-94
• /
• 2010

A simple laboratory device and methodology are developed for deep understanding of the western boundary current (WBC). The apparatus consists of a rotating (count-clockwise) rectangular tank with a sloping bottom in order to simulate the beta effect, the variation of the Coriolis parameter with latitude. We also used a clockwise rotating disk at the surface water to mimic the wind stress forcing in mid-latitude oceans. Four experiments were carried out using some combination of a bottom type and a rotation of the tank. Experiment with the beta effect clearly demonstrated the WBClike flow as well as the Sverdrup interior. However, the water in a tank gave rise to an inertial motion under the influence of a constant Coriolis force alone. We also discussed a stiffening of the rotating fluid on the basis of the Taylor-Proudman effect. We believe that the apparatus and methods developed in this study help to understand the WBC due to the beta effect.

• Journal of Ocean Engineering and Technology
• /
• v.15 no.3
• /
• pp.9-19
• /
• 2001

In this paper we present the aspect of inertial oscillation typically observed in the spin-up of fluids at low Rossby numbers in a circular cylinder. Numerical computations for the quasi three-dimensional equation as well as one-dimensional equation are performed to estimate the predictability of the one-dimensional equation with Ekman pumping/suction models. It is assumed that the discrepancy between the two results may be attributed to the inertial oscillation The detailed analysis to the numerical results reveals that the axial plane is dominated by a comparatively strong oscillatory flows caused by the inertial oscillation. In view of the fact that the time-averaged flow field however agrees to the Taylor-Proudman theorem, it is recommended that further analysis is needed to obtain an improved one-dimensional model like the Reynolds-averaged Navier-Stokes equation for turbulent flows.