Journal of Applied Mathematics and Physics

Volume 2, Issue 10 (September 2014)

ISSN Print: 2327-4352   ISSN Online: 2327-4379

Google-based Impact Factor: 0.63  Citations  

Analysis of the Navier-Stokes Equations

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DOI: 10.4236/jamp.2014.210106    4,728 Downloads   6,054 Views  
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ABSTRACT

The Navier-Stokes equations for incompressible fluid flows with impervious boundary and free surface are analyzed by means of a perturbation procedure involving dimensionless variables and a dimensionless perturbation parameter which is composed of kinematic viscosity of fluid, the acceleration of gravity and a characteristic length. The new dimensionless variables are introduced into the equation system. In addition, the perturbation parameter is introduced into terms for deriving approximations systems of different orders. Such systems are obtained by equating coefficients of like powers of perturbation parameter for the successive coefficients in the series. In these systems several terms are analyzed with regards to size and significance. Based on those systems, suitable solutions of NS equations can be found for different boundary conditions. For example, a relation for stationary channel flow is obtained as approximation to the NS equations of the lowest order after transformation back to dimensional variables.

Cite this paper

Martin, H. (2014) Analysis of the Navier-Stokes Equations. Journal of Applied Mathematics and Physics, 2, 938-947. doi: 10.4236/jamp.2014.210106.

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