レイノルズ平均ナビエ-ストークス方程式
∂ u i ̄ ∂ t + u ′ j ∂ u ′ i ∂ x j ̄ = f i ̄ − 1 ρ ∂ p ̄ ∂ x i + ν ∂ 2 u i ̄ ∂ x j ∂ x j {\displaystyle {\frac {\partial {\bar {u_{i}}}}{\partial t}}+{\overline {{{u^{\prime }}_{j}}{\frac {\partial {u^{\prime }}_{i}}{\partial x_{j}}}}}={\bar {f_{i}}}-{\frac {1}{\rho }}{\frac {\partial {\bar {p}}}{\partial x_{i}}}+\nu {\frac {\partial ^{2}{\bar {u_{i}}}}{\partial x_{j}\partial x_{j}}}}
連続式 : ∂ u i ∂ x i = ∂ u i ̄ ∂ x i + ∂ u i ′ ∂ x i = 0 {\displaystyle {\frac {\partial u_{i}}{\partial x_{i}}}={\frac {\partial {\bar {u_{i}}}}{\partial x_{i}}}+{\frac {\partial u_{i}^{\prime }}{\partial x_{i}}}=0} から運動方程式は以下のように変形できる。