Talk:Upper-convected time derivative

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)

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)

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)

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