Wind component horizontal advection

The $u$-momentum flux-form horizontal advection term is expressed as

$$\nabla\cdot{\left( {\bf V}\mu u\right)}_{i,j} = \Big\lbrack {\ove... ...verline u^y}_{i,j+1} -{\overline V^x}_{i,j}{\overline u^y}_{i,j} \Big\rbrack /d$$ (129)

and the $u$-momentum flux terms are expressed as

$${\overline U^x}_{i,j} = \left( U_{i+1,j} + U_{i,j}\right)/2$$ (130)

$${\overline V^x}_{i,j} = \left( V_{i-1,j} + V_{i,j}\right)/2$$ (131)

where the horizontal velocity components are interpolated using

$${\overline u^x}_{i,j} = \left( u_{i,j} + u_{i+1,j} \right)/2$$ (132)

$${\overline u^y}_{i,j} = \left( u_{i,j} + u_{i,j-1} \right)/2$$ (133)

The $v$-momentum equation advection is written in finite difference form using the same method as above.