Convective derivative in cylindrical coordinate

Asked May 24 '20 at 05:58

Active May 28 '20 at 08:13

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My question is similar to this one about convective derivative. But how do I adapt it to the cylindrical coordinate? Simply changing Grad to cylindrical coordinate does not produce correct results, which can be found here, because we need to include the terms with the derivative of the unit vector too.

Here is the adapted code,

uVec = Through[{Subscript[u, r], Subscript[u, \[Theta]], 
     Subscript[u, z]}[r, \[Theta], z, t]];
dConvect[vec_] := 
 D[vec, t] + ((vec.Grad[#, {r, \[Theta], z}, "Cylindrical"]) & /@ 
    vec)
dConvect[uVec] // MatrixForm // TraditionalForm

which produces the result below.

edited May 27 '20 at 16:38

asked May 24 '20 at 05:58

iplasma

2

Something like formula 3 here? – J. M.'s missing motivation May 24 '20 at 06:05
yes, will post additional information soon. – iplasma May 27 '20 at 16:31
That's a good idea; if you add extra information, users might be persuaded to reopen your question. – J. M.'s missing motivation May 27 '20 at 16:32
with the added information, can this question be reopened? – iplasma May 27 '20 at 17:13

Convective derivative in cylindrical coordinate

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