Mixing
Non-dimensionalisation and Taylor expansion
$begingroup$
I need to expand an equation, of the form
$$dot{r} = gamma(a,mu) F_1 + g(mu,ell,h,R) F_2$$
in powers of $epsilon = a/ell$.
So I thoughts I would non-dimensionalize it first.
I know that $$gamma(a,mu) = 6pi a mu,$$ with $mu$ a dynamic viscosity, $a$ a length scale. $g$ is a complicated function of $mu$ and $ell,h,R$ which are also length scales. The $F_{1,2}$ are forces, $dot{r}$ is a velocity.
I would like to measure lengths in units of $ell$, and times in units of $Omega^{-1}$, where $Omega$ is a frequency.
It is not clear to me how can I get to a position where I can perform an expansion in $epsilon$.
taylor-expansion dimensional-analysis
asked Jan 22 at 15:49
usumdelphiniusumdelphini
323111
$endgroup$
add a comment |
$begingroup$
I need to expand an equation, of the form
$$dot{r} = gamma(a,mu) F_1 + g(mu,ell,h,R) F_2$$
in powers of $epsilon = a/ell$.
So I thoughts I would non-dimensionalize it first.
I know that $$gamma(a,mu) = 6pi a mu,$$ with $mu$ a dynamic viscosity, $a$ a length scale. $g$ is a complicated function of $mu$ and $ell,h,R$ which are also length scales. The $F_{1,2}$ are forces, $dot{r}$ is a velocity.
I would like to measure lengths in units of $ell$, and times in units of $Omega^{-1}$, where $Omega$ is a frequency.
It is not clear to me how can I get to a position where I can perform an expansion in $epsilon$.
taylor-expansion dimensional-analysis
asked Jan 22 at 15:49
usumdelphiniusumdelphini
323111
$endgroup$
add a comment |
$begingroup$
I need to expand an equation, of the form
$$dot{r} = gamma(a,mu) F_1 + g(mu,ell,h,R) F_2$$
in powers of $epsilon = a/ell$.
So I thoughts I would non-dimensionalize it first.
I know that $$gamma(a,mu) = 6pi a mu,$$ with $mu$ a dynamic viscosity, $a$ a length scale. $g$ is a complicated function of $mu$ and $ell,h,R$ which are also length scales. The $F_{1,2}$ are forces, $dot{r}$ is a velocity.
I would like to measure lengths in units of $ell$, and times in units of $Omega^{-1}$, where $Omega$ is a frequency.
It is not clear to me how can I get to a position where I can perform an expansion in $epsilon$.
taylor-expansion dimensional-analysis
asked Jan 22 at 15:49
usumdelphiniusumdelphini
323111
$endgroup$
I need to expand an equation, of the form
$$dot{r} = gamma(a,mu) F_1 + g(mu,ell,h,R) F_2$$
in powers of $epsilon = a/ell$.
So I thoughts I would non-dimensionalize it first.
I know that $$gamma(a,mu) = 6pi a mu,$$ with $mu$ a dynamic viscosity, $a$ a length scale. $g$ is a complicated function of $mu$ and $ell,h,R$ which are also length scales. The $F_{1,2}$ are forces, $dot{r}$ is a velocity.
I would like to measure lengths in units of $ell$, and times in units of $Omega^{-1}$, where $Omega$ is a frequency.
It is not clear to me how can I get to a position where I can perform an expansion in $epsilon$.
taylor-expansion dimensional-analysis
taylor-expansion dimensional-analysis
asked Jan 22 at 15:49
usumdelphiniusumdelphini
323111
asked Jan 22 at 15:49
usumdelphiniusumdelphini
323111
edited Jan 24 at 8:54
usumdelphini
asked Jan 22 at 15:49
usumdelphiniusumdelphini
323111
asked Jan 22 at 15:49
usumdelphiniusumdelphini
323111
asked Jan 22 at 15:49
usumdelphiniusumdelphini
323111
323111
add a comment |
add a comment |
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