Navier-Stokes equations: Difference between revisions

Latest revision as of 15:42, 17 June 2011

The incompressible Navier-Stokes equations are
$\rho {\frac {D\mathbf {u} }{Dt}}=-\nabla p+\rho \mathbf {g} +\mu \nabla ^{2}\mathbf {u} \,,$
$\nabla \cdot \mathbf {u} =0\,,$
for an adiabatic fluid. A prognostic equation for density is
${\frac {D\rho }{Dt}}=\kappa \nabla ^{2}\rho \,.$

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 The incompressible Navier-Stokes equations are <br>
 <math>
-\rho  \frac{D \mathbf{u}}{D t}  = - \nabla p -\rho g \hat{\mathbf{k}} + \mu \nabla^2 \mathbf{u} \, ,</math><br>
+\rho  \frac{D \mathbf{u}}{D t}  = - \nabla p + \rho \mathbf{g} + \mu \nabla^2 \mathbf{u} \, ,</math><br>
 <math>
 \nabla \cdot \mathbf{u} = 0 \,, </math><br>
-for an adiabatic fluid, a prognostic equation for density is<br>
+for an adiabatic fluid. A prognostic equation for density is<br>
 <math>
-\frac{D \rho}{D t} = \kappa \nabla^2 \rho \, ,
+\frac{D \rho}{D t} = \kappa \nabla^2 \rho \, .
 </math> <br>
-where diffusion (the right hand side) is typically neglected.

Navier-Stokes equations: Difference between revisions

Latest revision as of 15:42, 17 June 2011

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