Farvre平均

$ u=\overline{u}+u''

$ u=\tilde u+u'

性質

$ \tilde{\tilde{u}}=\tilde{\frac{\overline{\rho u}}{\overline{\rho}}}=\frac{\overline{\rho\frac{\overline{\rho u}}{\overline{\rho}}}}{\overline{\rho}}=\frac{\overline{\overline{\rho u}+\overline{\rho u}\frac{\rho''}{\overline\rho}}}{\overline\rho}=\tilde u+\tilde u\overline{\frac{p''}{\overline p}}=\tilde u

$ \tilde{u'}=\tilde{u}-\tilde{\tilde{u}}=0

$ \widetilde{\overline a}=\overline a

$ \overline{\widetilde a}=\widetilde a

$ \overline{a\widetilde b}=\overline a\widetilde b

$ \widetilde{a\overline b}=\widetilde a\overline b

$ \overline{\rho\widetilde b}=\overline{\rho b}

$ \overline{ab}=\overline a\overline b+\overline{a''b''}

$ \widetilde{ab}=\widetilde a\widetilde b+\widetilde{a'b'}

$ \overline{ab'}=\overline{ab}-\overline{a}\widetilde{b}=\overline a\overline{b'}+\overline{a''b''}

$ \overline{\rho b'}=0

$ \overline{ab''}=\overline{a''b''}

$ \widetilde{ab'}=\widetilde{a'b'}

$ {a'}''=a''

$ {a''}'=a'

$ \overline a=\widetilde a+\overline{a'}

$ \widetilde{a}=\overline{a}+\widetilde{a''}

$ \overline{a'}+\widetilde{a''}=0