Mixing
is there a tornado-ish equation or vector 3D? [closed]
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up vote
3
down vote
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the formula
I've successfully found that $m = 2ln(x^2+y^2) $ look like a really static and not moving tornado.
But in the same time with vector equation I've found how to twist a cylinder.
$ r = sin(v+pi*u) $
$f(x,y,z) = (r * sin(pi*u),r * cos(pi*u), v) $
adding time to the vector
if we add $tau$ to $r$ the cylinder start moving like this
the goal
So my goal is to make $m$ rotate like a tornado-ish. maybe incorporating the vector to the equation is the way, but as of now i'm hitting a wall.
in short, the goal is the make the cylinder and $m$ look like a tornado, so it can spine like a bit like a tornado.
linear-algebra geometry differential-equations vector-spaces vectors
asked Aug 6 at 10:16
Maximilien Nowak
184
closed as unclear what you're asking by Ivan Neretin, Delta-u, Adrian Keister, Clayton, José Carlos Santos Aug 6 at 21:42
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |Â
up vote
3
down vote
favorite
the formula
I've successfully found that $m = 2ln(x^2+y^2) $ look like a really static and not moving tornado.
But in the same time with vector equation I've found how to twist a cylinder.
$ r = sin(v+pi*u) $
$f(x,y,z) = (r * sin(pi*u),r * cos(pi*u), v) $
adding time to the vector
if we add $tau$ to $r$ the cylinder start moving like this
the goal
So my goal is to make $m$ rotate like a tornado-ish. maybe incorporating the vector to the equation is the way, but as of now i'm hitting a wall.
in short, the goal is the make the cylinder and $m$ look like a tornado, so it can spine like a bit like a tornado.
linear-algebra geometry differential-equations vector-spaces vectors
asked Aug 6 at 10:16
Maximilien Nowak
184
closed as unclear what you're asking by Ivan Neretin, Delta-u, Adrian Keister, Clayton, José Carlos Santos Aug 6 at 21:42
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
A function of form $z = f(x, y, t)$ cannot describe a tornado with a twisty or (very) off-vertical condensation funnel like in the Wikipedia image associated with the tornado article, because the function is essentially a height map; the vertical distance from the "cloud top" down to the visible edge of the funnel at that planar point $(x, y)$ at time $t$. So, the "wall" is real, it is a limitation on the form you chose.
– Nominal Animal
Aug 6 at 15:01
It might be possible with an implicit surface, i.e. $f(x, y, z, t) = 0$, where $t$ is a time variable, and $f$ describes the shape of the funnel as a function of time. For wind direction and speed, you'd need a vector-valued function, $vecf(x, y, z, t)$, where the vector length divided by time unit yields the wind speed in the direction pointed by the vector at that point. But do note that I'd expect such a function to be pretty complex, not really worth the effort needed to construct one that is "convincing" (close enough to real world cases).
– Nominal Animal
Aug 6 at 15:08
I don't know anything about tornados and hurricanes and winds but... there shouldn't be a differential equation modelling such a phenomenon? And from the differential equation maybe you can get some solution.
– Dog_69
Aug 6 at 15:30
add a comment |Â
up vote
3
down vote
favorite
up vote
3
down vote
favorite
the formula
I've successfully found that $m = 2ln(x^2+y^2) $ look like a really static and not moving tornado.
But in the same time with vector equation I've found how to twist a cylinder.
$ r = sin(v+pi*u) $
$f(x,y,z) = (r * sin(pi*u),r * cos(pi*u), v) $
adding time to the vector
if we add $tau$ to $r$ the cylinder start moving like this
the goal
So my goal is to make $m$ rotate like a tornado-ish. maybe incorporating the vector to the equation is the way, but as of now i'm hitting a wall.
in short, the goal is the make the cylinder and $m$ look like a tornado, so it can spine like a bit like a tornado.
linear-algebra geometry differential-equations vector-spaces vectors
asked Aug 6 at 10:16
Maximilien Nowak
184
the formula
I've successfully found that $m = 2ln(x^2+y^2) $ look like a really static and not moving tornado.
But in the same time with vector equation I've found how to twist a cylinder.
$ r = sin(v+pi*u) $
$f(x,y,z) = (r * sin(pi*u),r * cos(pi*u), v) $
adding time to the vector
if we add $tau$ to $r$ the cylinder start moving like this
the goal
So my goal is to make $m$ rotate like a tornado-ish. maybe incorporating the vector to the equation is the way, but as of now i'm hitting a wall.
in short, the goal is the make the cylinder and $m$ look like a tornado, so it can spine like a bit like a tornado.
linear-algebra geometry differential-equations vector-spaces vectors
asked Aug 6 at 10:16
Maximilien Nowak
184
edited Aug 7 at 8:18
asked Aug 6 at 10:16
Maximilien Nowak
184
asked Aug 6 at 10:16
Maximilien Nowak
184
asked Aug 6 at 10:16
Maximilien Nowak
184
184
closed as unclear what you're asking by Ivan Neretin, Delta-u, Adrian Keister, Clayton, José Carlos Santos Aug 6 at 21:42
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Ivan Neretin, Delta-u, Adrian Keister, Clayton, José Carlos Santos Aug 6 at 21:42
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
A function of form $z = f(x, y, t)$ cannot describe a tornado with a twisty or (very) off-vertical condensation funnel like in the Wikipedia image associated with the tornado article, because the function is essentially a height map; the vertical distance from the "cloud top" down to the visible edge of the funnel at that planar point $(x, y)$ at time $t$. So, the "wall" is real, it is a limitation on the form you chose.
– Nominal Animal
Aug 6 at 15:01
It might be possible with an implicit surface, i.e. $f(x, y, z, t) = 0$, where $t$ is a time variable, and $f$ describes the shape of the funnel as a function of time. For wind direction and speed, you'd need a vector-valued function, $vecf(x, y, z, t)$, where the vector length divided by time unit yields the wind speed in the direction pointed by the vector at that point. But do note that I'd expect such a function to be pretty complex, not really worth the effort needed to construct one that is "convincing" (close enough to real world cases).
– Nominal Animal
Aug 6 at 15:08
I don't know anything about tornados and hurricanes and winds but... there shouldn't be a differential equation modelling such a phenomenon? And from the differential equation maybe you can get some solution.
– Dog_69
Aug 6 at 15:30
add a comment |Â
A function of form $z = f(x, y, t)$ cannot describe a tornado with a twisty or (very) off-vertical condensation funnel like in the Wikipedia image associated with the tornado article, because the function is essentially a height map; the vertical distance from the "cloud top" down to the visible edge of the funnel at that planar point $(x, y)$ at time $t$. So, the "wall" is real, it is a limitation on the form you chose.
– Nominal Animal
Aug 6 at 15:01
It might be possible with an implicit surface, i.e. $f(x, y, z, t) = 0$, where $t$ is a time variable, and $f$ describes the shape of the funnel as a function of time. For wind direction and speed, you'd need a vector-valued function, $vecf(x, y, z, t)$, where the vector length divided by time unit yields the wind speed in the direction pointed by the vector at that point. But do note that I'd expect such a function to be pretty complex, not really worth the effort needed to construct one that is "convincing" (close enough to real world cases).
– Nominal Animal
Aug 6 at 15:08
I don't know anything about tornados and hurricanes and winds but... there shouldn't be a differential equation modelling such a phenomenon? And from the differential equation maybe you can get some solution.
– Dog_69
Aug 6 at 15:30
A function of form $z = f(x, y, t)$ cannot describe a tornado with a twisty or (very) off-vertical condensation funnel like in the Wikipedia image associated with the tornado article, because the function is essentially a height map; the vertical distance from the "cloud top" down to the visible edge of the funnel at that planar point $(x, y)$ at time $t$. So, the "wall" is real, it is a limitation on the form you chose.
– Nominal Animal
Aug 6 at 15:01
A function of form $z = f(x, y, t)$ cannot describe a tornado with a twisty or (very) off-vertical condensation funnel like in the Wikipedia image associated with the tornado article, because the function is essentially a height map; the vertical distance from the "cloud top" down to the visible edge of the funnel at that planar point $(x, y)$ at time $t$. So, the "wall" is real, it is a limitation on the form you chose.
– Nominal Animal
Aug 6 at 15:01
It might be possible with an implicit surface, i.e. $f(x, y, z, t) = 0$, where $t$ is a time variable, and $f$ describes the shape of the funnel as a function of time. For wind direction and speed, you'd need a vector-valued function, $vecf(x, y, z, t)$, where the vector length divided by time unit yields the wind speed in the direction pointed by the vector at that point. But do note that I'd expect such a function to be pretty complex, not really worth the effort needed to construct one that is "convincing" (close enough to real world cases).
– Nominal Animal
Aug 6 at 15:08
It might be possible with an implicit surface, i.e. $f(x, y, z, t) = 0$, where $t$ is a time variable, and $f$ describes the shape of the funnel as a function of time. For wind direction and speed, you'd need a vector-valued function, $vecf(x, y, z, t)$, where the vector length divided by time unit yields the wind speed in the direction pointed by the vector at that point. But do note that I'd expect such a function to be pretty complex, not really worth the effort needed to construct one that is "convincing" (close enough to real world cases).
– Nominal Animal
Aug 6 at 15:08
I don't know anything about tornados and hurricanes and winds but... there shouldn't be a differential equation modelling such a phenomenon? And from the differential equation maybe you can get some solution.
– Dog_69
Aug 6 at 15:30
I don't know anything about tornados and hurricanes and winds but... there shouldn't be a differential equation modelling such a phenomenon? And from the differential equation maybe you can get some solution.
– Dog_69
Aug 6 at 15:30
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
5
down vote
accepted
I do not know what you are after, neither do I know anything about tornado’s, but perhaps something like an unstable spiral might be easier to describe such a shape. To be specific, I used a system of the form
beginalign
beginpmatrix
dotx_1\dotx_2\ dotx_3
endpmatrix= beginpmatrix a & b & 0\ -b & a & 0 \ 0 & 0 & c endpmatrixbeginpmatrix
x_1\x_2\ x_3
endpmatrix,quad b>a,a>0,c>0
endalign
to have a growing unstable spiral. In the image I used $a = 0.05,b = 2,c = 0.01$, with an added sine input on the first coordinate to create the distortion ($2*sin(t/10)$).
answered Aug 6 at 21:05
WalterJ
795611
can you explain bit more ? if i want to use this as a vector i need to select each row of the matrice for x, y and z ?
– Maximilien Nowak
Aug 7 at 14:24
1
Well, the 'tornado' you see in the picture is the solution for the given set of differential equations under a small non-zero initial condition. Using your favorite programming language you can probably solve this system and get back a timeseries of points $(x,y,z)$, or as I called them $(x_1,x_2,x_3)$. There is a lot to play with.
– WalterJ
Aug 7 at 19:42
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
5
down vote
accepted
I do not know what you are after, neither do I know anything about tornado’s, but perhaps something like an unstable spiral might be easier to describe such a shape. To be specific, I used a system of the form
beginalign
beginpmatrix
dotx_1\dotx_2\ dotx_3
endpmatrix= beginpmatrix a & b & 0\ -b & a & 0 \ 0 & 0 & c endpmatrixbeginpmatrix
x_1\x_2\ x_3
endpmatrix,quad b>a,a>0,c>0
endalign
to have a growing unstable spiral. In the image I used $a = 0.05,b = 2,c = 0.01$, with an added sine input on the first coordinate to create the distortion ($2*sin(t/10)$).
answered Aug 6 at 21:05
WalterJ
795611
can you explain bit more ? if i want to use this as a vector i need to select each row of the matrice for x, y and z ?
– Maximilien Nowak
Aug 7 at 14:24
1
Well, the 'tornado' you see in the picture is the solution for the given set of differential equations under a small non-zero initial condition. Using your favorite programming language you can probably solve this system and get back a timeseries of points $(x,y,z)$, or as I called them $(x_1,x_2,x_3)$. There is a lot to play with.
– WalterJ
Aug 7 at 19:42
add a comment |Â
up vote
5
down vote
accepted
I do not know what you are after, neither do I know anything about tornado’s, but perhaps something like an unstable spiral might be easier to describe such a shape. To be specific, I used a system of the form
beginalign
beginpmatrix
dotx_1\dotx_2\ dotx_3
endpmatrix= beginpmatrix a & b & 0\ -b & a & 0 \ 0 & 0 & c endpmatrixbeginpmatrix
x_1\x_2\ x_3
endpmatrix,quad b>a,a>0,c>0
endalign
to have a growing unstable spiral. In the image I used $a = 0.05,b = 2,c = 0.01$, with an added sine input on the first coordinate to create the distortion ($2*sin(t/10)$).
answered Aug 6 at 21:05
WalterJ
795611
can you explain bit more ? if i want to use this as a vector i need to select each row of the matrice for x, y and z ?
– Maximilien Nowak
Aug 7 at 14:24
1
Well, the 'tornado' you see in the picture is the solution for the given set of differential equations under a small non-zero initial condition. Using your favorite programming language you can probably solve this system and get back a timeseries of points $(x,y,z)$, or as I called them $(x_1,x_2,x_3)$. There is a lot to play with.
– WalterJ
Aug 7 at 19:42
add a comment |Â
up vote
5
down vote
accepted
up vote
5
down vote
accepted
I do not know what you are after, neither do I know anything about tornado’s, but perhaps something like an unstable spiral might be easier to describe such a shape. To be specific, I used a system of the form
beginalign
beginpmatrix
dotx_1\dotx_2\ dotx_3
endpmatrix= beginpmatrix a & b & 0\ -b & a & 0 \ 0 & 0 & c endpmatrixbeginpmatrix
x_1\x_2\ x_3
endpmatrix,quad b>a,a>0,c>0
endalign
to have a growing unstable spiral. In the image I used $a = 0.05,b = 2,c = 0.01$, with an added sine input on the first coordinate to create the distortion ($2*sin(t/10)$).
answered Aug 6 at 21:05
WalterJ
795611
I do not know what you are after, neither do I know anything about tornado’s, but perhaps something like an unstable spiral might be easier to describe such a shape. To be specific, I used a system of the form
beginalign
beginpmatrix
dotx_1\dotx_2\ dotx_3
endpmatrix= beginpmatrix a & b & 0\ -b & a & 0 \ 0 & 0 & c endpmatrixbeginpmatrix
x_1\x_2\ x_3
endpmatrix,quad b>a,a>0,c>0
endalign
to have a growing unstable spiral. In the image I used $a = 0.05,b = 2,c = 0.01$, with an added sine input on the first coordinate to create the distortion ($2*sin(t/10)$).
answered Aug 6 at 21:05
WalterJ
795611
answered Aug 6 at 21:05
WalterJ
795611
answered Aug 6 at 21:05
WalterJ
795611
answered Aug 6 at 21:05
WalterJ
795611
795611
can you explain bit more ? if i want to use this as a vector i need to select each row of the matrice for x, y and z ?
– Maximilien Nowak
Aug 7 at 14:24
1
Well, the 'tornado' you see in the picture is the solution for the given set of differential equations under a small non-zero initial condition. Using your favorite programming language you can probably solve this system and get back a timeseries of points $(x,y,z)$, or as I called them $(x_1,x_2,x_3)$. There is a lot to play with.
– WalterJ
Aug 7 at 19:42
add a comment |Â
can you explain bit more ? if i want to use this as a vector i need to select each row of the matrice for x, y and z ?
– Maximilien Nowak
Aug 7 at 14:24
1
Well, the 'tornado' you see in the picture is the solution for the given set of differential equations under a small non-zero initial condition. Using your favorite programming language you can probably solve this system and get back a timeseries of points $(x,y,z)$, or as I called them $(x_1,x_2,x_3)$. There is a lot to play with.
– WalterJ
Aug 7 at 19:42
can you explain bit more ? if i want to use this as a vector i need to select each row of the matrice for x, y and z ?
– Maximilien Nowak
Aug 7 at 14:24
can you explain bit more ? if i want to use this as a vector i need to select each row of the matrice for x, y and z ?
– Maximilien Nowak
Aug 7 at 14:24
1
1
Well, the 'tornado' you see in the picture is the solution for the given set of differential equations under a small non-zero initial condition. Using your favorite programming language you can probably solve this system and get back a timeseries of points $(x,y,z)$, or as I called them $(x_1,x_2,x_3)$. There is a lot to play with.
– WalterJ
Aug 7 at 19:42
Well, the 'tornado' you see in the picture is the solution for the given set of differential equations under a small non-zero initial condition. Using your favorite programming language you can probably solve this system and get back a timeseries of points $(x,y,z)$, or as I called them $(x_1,x_2,x_3)$. There is a lot to play with.
– WalterJ
Aug 7 at 19:42
add a comment |Â
A function of form $z = f(x, y, t)$ cannot describe a tornado with a twisty or (very) off-vertical condensation funnel like in the Wikipedia image associated with the tornado article, because the function is essentially a height map; the vertical distance from the "cloud top" down to the visible edge of the funnel at that planar point $(x, y)$ at time $t$. So, the "wall" is real, it is a limitation on the form you chose.
– Nominal Animal
Aug 6 at 15:01
It might be possible with an implicit surface, i.e. $f(x, y, z, t) = 0$, where $t$ is a time variable, and $f$ describes the shape of the funnel as a function of time. For wind direction and speed, you'd need a vector-valued function, $vecf(x, y, z, t)$, where the vector length divided by time unit yields the wind speed in the direction pointed by the vector at that point. But do note that I'd expect such a function to be pretty complex, not really worth the effort needed to construct one that is "convincing" (close enough to real world cases).
– Nominal Animal
Aug 6 at 15:08
I don't know anything about tornados and hurricanes and winds but... there shouldn't be a differential equation modelling such a phenomenon? And from the differential equation maybe you can get some solution.
– Dog_69
Aug 6 at 15:30