Question: Problem 5: Using material derivative formulation on Eulerian coordinate:a=deludelt+graduu(a) Show that:curl(a)=DDt-(gradu)+(gradu)Hintscurl(a)=curl(deludelt+graduu)=delcurl(u)delt+curl(graduu)ME1,Eq.37:graduu=grad(12|u|2)+(curl(u))ucurl(graduu)=ubrace(curl(grad(12|u|2))ubrace)?=0+curl(u)Using ME1Eq.43(a):curl(u)=div(u-u)div(ab)=(grada)b+adiv(b)div(u)=(grad)u+div(u)div(u)=(gradu)+brace(div()ubrace)?=0=>curl(a)=deldelt+(grad)u+div(u)-(gradu)Note:curl(DuDt)DDt

Problem 5: Using material derivative formulation on Eulerian coordinate:a=deludelt+gradu*u(a) Show that:curl(a)=DDt-(gradu)*+(grad*u)Hintscurl(a)=curl(deludelt+gradu*u)=delcurl(u)delt+curl(gradu*u)ME1,Eq.37:gradu*u=grad(12|u|2)+(curl(u))ucurl(gradu*u)=ubrace(curl(grad(12|u|2))ubrace)?=0+curl(u)Using ME1Eq.43(a):curl(u)=div(u-u)div(ab)=(grada)*b+adiv(b)div(u)=(grad)*u+div(u)div(u)=(gradu)*+brace(div()ubrace)?=0=>curl(a)=deldelt+(grad)*u+div(u)-(gradu)*Note:curl(DuDt)DDt

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