Here y has length N + 2 and F has size ( N + 2 ) N . In general (not only in the Froude limit) Euler equations are expressible as: ∂ ∂ ∂ ∂ t ( ρ ρ ρ ρ u 0 ) + ∇ ∇ ⋅ ⋅ ( ρ ρ u ρ ρ u ⊗ ⊗ u + p I u ) = ( 0 ρ ρ g 0 )