An Exact Solution of Oscillatory Couette Flow in a Rotating System

1991 ◽  
Vol 58 (4) ◽  
pp. 1104-1107 ◽  
Author(s):  
B. S. Mazumder
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Unsteady Flow ◽  
Couette Flow ◽  
Coriolis Force ◽  
Boundary Layer Flow ◽  
Shear Stresses ◽  
Flat Plates ◽  
Rotating System ◽  
Layer Flow

An exact solution of oscillatory Ekman boundary layer flow bounded by two horizontal flat plates, one of which is oscillating in its own plane and other at rest, is obtained. The effect of coriolis force on the resultant velocities and shear stresses for steady and unsteady flow has been studied.

A Note on Oscillatory Couette Flow in a Rotating System

1994 ◽  
Vol 61 (1) ◽  
pp. 208-209 ◽  
Author(s):  
R. Ganapathy
Keyword(s):  
Boundary Layer ◽  
Couette Flow ◽  
Relative Motion ◽  
Boundary Layer Flow ◽  
Alternative Solution ◽  
Parallel Plates ◽  
Rotating System ◽  
Rotating Systems ◽  
Ekman Boundary Layer ◽  
Layer Flow

An alternative solution is proposed for the oscillatory Ekman boundary layer flow bounded by two parallel plates in relative motion (Muzumder, 1991). The solution brings out among other things, the phenomenon of resonance which is of importance in rotating systems.

The effects of Coriolis force and radial stretch on the convective instability characteristics of the Bödewadt flow

2021 ◽  
pp. 095440622110071
Author(s):  
Dip Mukherjee ◽  
Bikash Sahoo
Keyword(s):  
Boundary Layer ◽  
Coriolis Force ◽  
Boundary Layer Flow ◽  
Convective Instability ◽  
Type I ◽  
Similarity Transformations ◽  
Instability Modes ◽  
Neutral Curves ◽  
Lower Disk ◽  
Layer Flow

The Bödewadt boundary-layer flow is induced by the rotation of a viscous fluid rotating with a constant angular velocity over a stationary disk. In this paper, the Bödewadt boundary-layer flow has been studied in the presence of the Coriolis force to observe the effect of radial stretch of the lower disk on the flow. For the first time in the literature, a numerical investigation of the effects of both stretching mechanism and the Coriolis force on the flow behaviour and on the convective instability characteristics of the above flow has been carried out. In this paper, the Kármán similarity transformations have been considered in order to convert the system of PDEs representing the momentum equations of the flow into a system of highly non-linear coupled ODEs and solved numerically to obtain the velocity profiles of the Bödewadt flow. Then, a convective instability analysis has been performed by using the Chebyshev collocation method in order to obtain the neutral curves. From the neutral curves it is observed that radial stretch has a globally stabilising effect on both the inviscid Type-I and the viscous Type-II instability modes. This underlying physical phenomena has been verified by performing an energy analysis of the flow. The results obtained excellently supports the previous works and will be prominently treated as a benchmark for our future studies.

Experimental Investigation of the Laminar Boundary Layer Flow on a Rotating Wavy Disk

2016 ◽  
Author(s):  
Christian Helcig ◽  
Christian Teigeler ◽  
Stefan aus der Wiesche
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Laminar Flow ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Similar Solution ◽  
Surface Shape ◽  
Self Similar Solution ◽  
Self Similar ◽  
Layer Flow

Since nearly one century, the flow on a flat rotating disk has provided the paradigm for studying rotating flows. For the laminar flow regime, a self-similar solution was obtained by von Kármán [6] in 1921, and a rather special feature of his exact solution of the Navier-Stokes equation is a constant boundary layer thickness not depending on the radial coordinate. A substantial modification of this canonical configuration is given by a wavy disk with a sinusoidal surface shape. Although axis-symmetric, no exact solution for the laminar flow on a wavy disk is known so far. In this study, detailed measurements of the velocity profiles were performed within the laminar boundary layer flow on a wavy disk. Based upon the experimental data, the potential of a self-similar solution approach for describing the resulting flow field was assessed. It was found that such an approach is useful for approximating the far-field solution but systematic deviations were observed in the vicinity of the disk origin.

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