[tex](\vec A \cdot \nabla) [/tex](adsbygoogle = window.adsbygoogle || []).push({});

Is this operator well defined? It appears in many vector calculs identites, and it has an easy enough explicit formula in cartesian coordinates. But I've heard it cannot be written generally in the curvilinear coordinates. I assume this is because this operator can be applied to vectors or scalars, and has different forms depending on which. Is this the case? Why is this operator always glossed over in vector calculus classes? Why are explicit curvilinear formulas for it never given? Does it have a name?

For example:

[tex]( (\vec v \cdot \nabla) \vec v)_r \neq (\vec v \cdot \nabla) v_r [/tex]

although I was never told this, and still don't completely understand it.

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