<Moderator's note: Moved from the homework forum.> 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.