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Engineering Mathematics
Review of Viscous Flows
Review of Computational Fluid Mechanics
Review of Turbulence and Turbulence Modeling

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ME 637 The National Science Foundation
 Viscous Flows
Navier-Stokes Equation, Vorticity, Stream Function | Exact Solutions | Drag on Spherical Particles | Creeping Flows | Nonspherical Particles

Creeping Flows

Point Force Solution

 Consider the response of the Stokes equation to a point force exerted at the origin. Equation (1) and (2) may be rewritten as

(5)

(6)

The general solution to (5) and (6) in an unbounded domain is given as

(7)

Here,  is referred to as the Oseen tensor. The solution in a two-dimensional flow is given by

(8)

Using the Green theorem, the velocity vector may be represented as

(9)

where

(10)

and

(11)

Equations (9) and (11) give the velocity and the pressure fields for arbitrary given distribution of stress and velocity on solid surface boundaries.

 For an unbounded flow and for a point force , from (9) and (11) it follows that

(12)

(13)

which is referred to as a Stokeslet.



Dr. Goodarz Ahmadi | Turbulence & Multiphase Fluid Flow Laboratory | Department of Mechanical & Aeronautical Engineering
Copyright © 2002-2005 Dr. Goodarz Ahmadi. All rights reserved.
Potsdam, New York, 13699
ahmadi@clarkson.edu