Problem: vertor a=(ar,aq,az) and vector b=(br,bq,bz) ar,aq,az represent the component in radial(r), circumferential(q) and axial(z) direction, respetively.

Delta is gradient operator in cylindrical coordinate

What is (a·Delta)b ?

I encounter it when I deal with a problem with linear stability analysis. I need a full form in r,q,z direction for coding.

Your help is highly appreciated.

Zeng

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(1). Take a look at the convection term first. You may be able to get the expanded form there. I mean the conservation equations.

Yes, I have checked the expended form of convection term in N-S equation, and derived the expended term of (a·Delta)b by myself, but I have no confidence on its correction, and I failed to find the expended form in the reference books.

Maybe the expended form of (a·Delta)b in cylindrical coodinate exist in reference, can you kindly help me to find them?

Thanks in advance.

Hi, Zeng,

The formulae you are looking for can be found in

G.K.Batchelor, An introduction to fluid dynamics, Cambridge University Press, 1970, Apendix 2.

or

G.A.Korn, T.M.Korn, Mathematical handbook for scientists and engineers, McGraw-Hill, 1961. Table 6.4.1 + Table 6.5.1

Rgds, Sergei