Vector Calculus

[taitae25]

Hi,

I have a rather, very simple question which I can't find the answer to in many of my math text book simply because I forgot what the operation is called.

Symbols: v_ = vector v
. = dot operator
del = the nabla or del operator

The operation is the following.

( v_ . del)v_

I wish I can show you the actual equation but this is the best I can do.
I'm studying MHD right now and it's a crucial mathematical operation that I must know to proceed any further :?

I basically don't know what the above operation looks like in the expanded form.

The actual equation I am looking at is the rate chage of magnetic field w/r/t time.

dB_/dt = (w_ . del) B_ + partial B/partial t

it's the (w_ . del) B_ part that is making me scratch my head.

where w = partical velocity, B = magnetic field, t = time.

Thank you.

will[/tex]

 

[pka]

I cannot read your question enough to know what it is asking. It would be to your advantage to learn some LaTeX if you need to use this type of forum.

Here are some comments that may help.
\(\displaystyle \L\left( {v \cdot \nabla } \right)\) is a scalar, being a dot product. Moreover, is has the value 0 if v is a constant vector because nabla is partial operator: \(\displaystyle \L\nabla = i\frac{\partial }{{\partial x}} + j\frac{\partial }{{\partial y}} + k\frac{\partial }{{\partial z}}\)

So if v is a vector function of x, y, & z then \(\displaystyle \L\left( {v \cdot \nabla } \right)v\) is just a scalar multiple of v.

If you quote my message you will see some LaTeX code. You may use it to try to explain the problem.

 

[taitae25]

pka,

Thank you. Your hint pretty much solved my question. So after the operation in the bracket is operated on the vector outside the bracket, I basically have a total of 9 spatial derivative of the vector. I can't belive I couldn't figure that out.

Thank you very much.

Will