Study on the spin-up of fluid in a rectangular container using Ekman pumping models

Abstract

Spin-up in a rectangular container with a free surface is investigated numerically and experimentally. In the formulation of two-dimensional numerical computation, we use a potential-like function in addition to the stream function to deal with the first-order Ekman pumping model. It is shown that our numerical results are in good agreement with those obtained by the experiment when either the leading-order or first-order pumping model is used. On the other hand, when no pumping effect is considered the numerical results show, except in the initial development, a considerable discrepancy from those of the experiment. Our attention in this study is focused on clarifying the physical mechanism of cyclonic vortex merging. At low Reynolds numbers and/or liquid depths the Ekman pumping damps the vortical flows fast, resulting in non-merging. At moderate Reynolds numbers, it enhances merging because the cyclonic vortices expand due to the Ekman pumping. We discuss the influence of various parameters, including Reynolds number, Rossby number, and dimensionless liquid depth, on the evolution of the vortical flows.

Numerical study on the motion of azimuthal vortices in axisymmetric rotating flows

“…Hart 1995Hart , 2000Zavala Sanson and van Heijst 2000;Suh and Choi 2002). The proposed models compare well with experimental results even in the non-axisymmetric container such as a rectangle.…”

“…The above solutions are firstly derived by Wedemeyer (1964), and later by Maas (1993) and van de Konijnenberg and van Heijst (1995).…”

“…In Section 2, the problem is formulated and the numerical methods are described. To verify the two-dimensional numerical code, we also employed one-dimensional equations by using the Ekman pumping models developed by Suh and Choi (2002). The Wedemeyer's solution is also presented in this section for further verification of the two-dimensional code.…”

Finite volume method with zonal-embedded grids for cylindrical coordinates

“…It is well known that when the ratio = , called the Rossby number and denoted as in this paper, is small enough the axial ow ( ow along the axis of rotation) is inhibited and the ow tends to be basically two dimensional [22]. The Ekman-pumping velocity W E shown in Table I is given by the linear Ekman-pumping law [23]…”

Review on open-problems of spin-up flow of an incompressible fluid

“…Since the 1990's, different aspects of spin-up, somewhat modified from the classical models, were investigated. Examples include spin-up in a non-axisymmetric container [Heijst (17); Suh & Choi (18)]. Also, spin-up flows were delineated when the shapes of the solid walls of the container were deformed.…”