Navier-stokes equation (fluid mechanics)

[alsey42147]

i'm revising for my exams, and i didn't go to many of my fluids lectures, now I'm well confused. in the navier-stokes equation for viscous fluid flow, there is a term:

v(del squared)u

where v is the kinematic viscosity and u is the velocity field of the fluid. at this point in my notes, the lecturer seems to start doing crazy things which don't make sense.

first of all, its (del squared)u, not (del squared)(dot)u. i thought (del squared)u only had any meaning if u is a scalar field, but its not, its a vector field. what does this mean?

 

[arildno]

$\nabla^{2}$ is a differential operator that perfectly well can be applied to a vector.

 

[Gokul43201]

http://mathworld.wolfram.com/VectorLaplacian.html

and to further generalize...

http://mathworld.wolfram.com/TensorLaplacian.html

 

[altruistic]

V.delV is convection accelaration term in NSE it is the major source for non-linearity of the equation

You can work it out by

(V.del)V or V.(del V) both methods are same

 

[HossamCFD]

V.delV is convection accelaration term in NSE it is the major source for non-linearity of the equation

You can work it out by

(V.del)V or V.(del V) both methods are same

I believe the OP was asking about the viscous dissipation term not the convective term.