Talk:Upper-convected time derivative

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First eqn wrong?

Hi, I think the first equation in this article is wrong. I think it should be $\mathbf {A} ^{\nabla }={\frac {D}{Dt}}\mathbf {A} -\mathbf {A} \cdot (\nabla \mathbf {v} )^{T}-(\nabla \mathbf {v} )\cdot \mathbf {A}$
According to http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TJ2-4GGXW30-1&_user=1490772&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1063297362&_rerunOrigin=google&_acct=C000053052&_version=1&_urlVersion=0&_userid=1490772&md5=5e9ea275ceb48c057344987c2bb4173d —Preceding unsigned comment added by 78.128.196.118 (talk) 20:52, 25 October 2009 (UTC)[reply]

No, the definition is correct. It can be verified within Wikipedia by linking to Lie derivatives, which describe the transport of arbitrary tensor fields (and differential forms) in the flow of a vector field.

I suggest this article be redirected to the Tensor fields section of the main page "Lie derivative" and perhaps include one line there describing the upper convected time derivative as a special case, including its uses. Czigi (talk) 18:05, 14 May 2010 (UTC)[reply]

Nitpick

Nitpicky point: this discussion assumes that div {\bf v} = 0. If you look in Oldroyd's paper [Proc. R. Soc. Lond. A 1950 200, 523-541], Sect. 3(a), you will note that he also has the term "+div {\bf v} {\bf A}" on the right-hand side. This is the general upper-convected frame-indifferent derivate of Oldroyd. See also Aris's book "Vectors, Tensors, and the Basic Equations of Fluid Mechanics," Sect. 8.32. No reason to assume div {\bf v} = 0 when giving the general exposition. Evilmathninja (talk) 03:37, 7 January 2012 (UTC)[reply]

I agree! 208.59.64.68 (talk) 22:57, 12 October 2022 (UTC)[reply]