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Engineering Mathematics
Review of Viscous Flows
Review of Computational Fluid Mechanics

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ME 437 The National Science Foundation
 Viscous Flows
Navier-Stokes Equation, Vorticity, Stream Function | Exact Solutions | Drag on Spherical Particles | Creeping Flows | Nonspherical Particles

Incompressible Viscous Flows

For an incompressible fluid, the continuity equation and the Navier-Stokes equation are given as

Using a vector identity, Equation (2) may be restated as

Define vorticity

and taking curl of (3) we find

Noting that curl of gradient is zero and

Equation (5) may be restated as

Equation (7) is the vorticity transport equation. It shows that in addition to being convected and diffused, vorticity is also generated by the first on the right hand side of Equation (7) by a vortex stretching mechanism.



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