Vector calculus operations on flux fields
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Given the following flux fields: $$ u(x,y,t) = -fracUL^3x^2y sinbig(frac2pi ULt big) \v(x,y,t) = fracUL^3xy^2 sinbig(frac2pi ULt big) \ phi(x,y,t) = phi_0 expbig(-fracx^2 + y^2L^2big) $$
Where $u$ and $v$ are components of the field $vec V = uvec i + v vec j$
Find:
1) $frac partial vec Vpartial t $
2) $big (vec V cdot nabla big )phi$
3) $big (vec V cdot nabla big )vec V$
4) $nabla times vec V$
I find the problem confusing because $u$ and $v$ are functions of $x,y,t$. For 1) I assume its straight forward just differentiating $u$ and $v$ with respect to $t$ and adding them. I have no idea how to compute the rest of the problems though.
multivariable-calculus derivatives vector-analysis
asked Aug 28 at 12:09
Pame
34217
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up vote
-1
down vote
favorite
Given the following flux fields: $$ u(x,y,t) = -fracUL^3x^2y sinbig(frac2pi ULt big) \v(x,y,t) = fracUL^3xy^2 sinbig(frac2pi ULt big) \ phi(x,y,t) = phi_0 expbig(-fracx^2 + y^2L^2big) $$
Where $u$ and $v$ are components of the field $vec V = uvec i + v vec j$
Find:
1) $frac partial vec Vpartial t $
2) $big (vec V cdot nabla big )phi$
3) $big (vec V cdot nabla big )vec V$
4) $nabla times vec V$
I find the problem confusing because $u$ and $v$ are functions of $x,y,t$. For 1) I assume its straight forward just differentiating $u$ and $v$ with respect to $t$ and adding them. I have no idea how to compute the rest of the problems though.
multivariable-calculus derivatives vector-analysis
asked Aug 28 at 12:09
Pame
34217
add a comment |Â
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
Given the following flux fields: $$ u(x,y,t) = -fracUL^3x^2y sinbig(frac2pi ULt big) \v(x,y,t) = fracUL^3xy^2 sinbig(frac2pi ULt big) \ phi(x,y,t) = phi_0 expbig(-fracx^2 + y^2L^2big) $$
Where $u$ and $v$ are components of the field $vec V = uvec i + v vec j$
Find:
1) $frac partial vec Vpartial t $
2) $big (vec V cdot nabla big )phi$
3) $big (vec V cdot nabla big )vec V$
4) $nabla times vec V$
I find the problem confusing because $u$ and $v$ are functions of $x,y,t$. For 1) I assume its straight forward just differentiating $u$ and $v$ with respect to $t$ and adding them. I have no idea how to compute the rest of the problems though.
multivariable-calculus derivatives vector-analysis
asked Aug 28 at 12:09
Pame
34217
Given the following flux fields: $$ u(x,y,t) = -fracUL^3x^2y sinbig(frac2pi ULt big) \v(x,y,t) = fracUL^3xy^2 sinbig(frac2pi ULt big) \ phi(x,y,t) = phi_0 expbig(-fracx^2 + y^2L^2big) $$
Where $u$ and $v$ are components of the field $vec V = uvec i + v vec j$
Find:
1) $frac partial vec Vpartial t $
2) $big (vec V cdot nabla big )phi$
3) $big (vec V cdot nabla big )vec V$
4) $nabla times vec V$
I find the problem confusing because $u$ and $v$ are functions of $x,y,t$. For 1) I assume its straight forward just differentiating $u$ and $v$ with respect to $t$ and adding them. I have no idea how to compute the rest of the problems though.
multivariable-calculus derivatives vector-analysis
asked Aug 28 at 12:09
Pame
34217
asked Aug 28 at 12:09
Pame
34217
asked Aug 28 at 12:09
Pame
34217
asked Aug 28 at 12:09
Pame
34217
34217
add a comment |Â
add a comment |Â
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