Difference between revisions of "Nonlinear Shallow Water Waves"

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Conservation of momentum reads as follows
 
Conservation of momentum reads as follows
  
<math>\frac{D \vec{u}}{D t} (\vec{x} ,t) = \frac{-1}{\pho} \nabla p + g </math>
+
<math>\frac{D \vec{u}}{D t} (\vec{x} ,t) = \frac{D \rho}{\pho} \nabla p + g </math>
  
  
 
[[Category:789]]
 
[[Category:789]]

Revision as of 07:56, 14 October 2008

Introduction

We want to consider

[math]\displaystyle{ \frac{D \rho}{D t} (\vec{x} ,t) + \rho(\vec{x} ,t)\nabla \cdot u(\vec{x} ,t) = 0, x \in \Omega }[/math]

Since water is incompressible i.e. [math]\displaystyle{ \frac{D \rho}{D t} = 0 }[/math] and then [math]\displaystyle{ \nabla \cdot \vec{u} = 0 }[/math] i.e. the divergance of the velocity field is zero.

Conservation of momentum reads as follows

[math]\displaystyle{ \frac{D \vec{u}}{D t} (\vec{x} ,t) = \frac{D \rho}{\pho} \nabla p + g }[/math]