<Moderator's note: Moved from the homework forum.>(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

The following equation is one of a few equations that describe a plasma model. The left hand side is the part I am having trouble with in that I can't seem to visualise what (V dot delV) actually does. My physics teacher has described the situation in comparison to a flowing river. He said to imagine a frozen snap shot in time so that as you look further and further up the river, the velocity will change depending on location, not time. eg a section of the river with a waterfall with have large velocity whilst a flat section of the river will have low velocity. This helps describe how there is a velocity gradient (not acceleration) but then how does the dot product with velocity work to create this scenario?

I am also confused as to the order of operations within the brackets as the gradient of v is a vector and then the dot product of v with the gradient of v would produce a scalar. OR if you choose the other order, the divergence of v is a scalar and then multiplied with the vector v, the result is a vector. Obviously something I have just said is wrong but I am unsure what.

Thanks for your help!

2. Relevant equations

3. The attempt at a solution

There is no real solution to my question, I just need to find a way to imagine the above mentioned section of this equation and to understand which order to use so that I can better understand what it is actually doing.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Interpretation of spatially dependent convective derivative

Tags:

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**