▁and ▁the ▁other ▁two ▁represent ▁the ▁momentum ▁equations . ▁ ▁Taylor – Green ▁vor tex ▁solution ▁In ▁the ▁domain ▁, ▁the ▁solution ▁is ▁given ▁by ▁ ▁where ▁, ▁ ▁being ▁the ▁kin ematic ▁vis cos ity ▁of ▁the ▁fluid . ▁Following ▁the ▁analysis ▁of ▁Taylor ▁and ▁Green ▁for ▁the ▁two - dimensional ▁situation , ▁and ▁for ▁, ▁gives ▁agreement ▁with ▁this ▁exact ▁solution , ▁if ▁the ▁exponential ▁is ▁expanded ▁as ▁a ▁Taylor ▁series , ▁i . e . ▁. ▁ ▁The ▁pressure ▁field ▁ ▁can ▁be ▁obtained ▁by ▁subst itut ing ▁the ▁velocity ▁solution ▁in ▁the ▁momentum ▁equations ▁and ▁is ▁given ▁by ▁ ▁The ▁stream ▁function ▁of ▁the ▁Taylor – Green ▁vor tex ▁solution , ▁i . e . ▁which ▁satisfies ▁ ▁for ▁flow ▁velocity ▁, ▁is ▁ ▁Similarly , ▁the ▁v ort icity , ▁which ▁satisfies ▁, ▁is ▁given ▁by ▁ ▁The ▁Taylor – Green ▁vor tex ▁solution ▁may ▁be ▁used ▁for ▁testing ▁and ▁validation ▁of ▁temporal ▁accuracy ▁of ▁Nav ier – Sto kes ▁algorithms . ▁ ▁References ▁ ▁Category : Fl uid ▁dynamics ▁Category : Comput ational ▁fluid ▁dynamics <0x0A> </s> ▁Margaret ▁" P eg gy " ▁Mack all ▁Taylor ▁( née ▁Smith ; ▁September ▁ 2 1 , ▁ 1 7 8 8 ▁– ▁August ▁ 1 4 , ▁ 1 8 5 2 ) ▁was ▁the ▁wife ▁of ▁Zach ary ▁Taylor . ▁She ▁was ▁the ▁First ▁Lady ▁of ▁the ▁United ▁States ▁from ▁ 1 8 4 9 ▁to ▁ 1 8 5 0 . ▁ ▁Early ▁life ▁and ▁marriage