Talk:Material derivative

message: Probably not the correct place for this, but the swimmer description of this derivative wrt lake temperature was wonderful and *really* clarified this for me.  Thank you! 133.87.57.32 (talk) 13:06, 23 June 2012 (UTC)
thread_title:  Thank you 

message: Am I confused, or does this article change notation between the introduction and the proof?  Is D/Dt the same operator as d/dt? Tom Duff 19:19, 30 January 2006 (UTC)
replies: text: Yes I have fixed it.  d/dt is used in many texts but I think D/Dt makes it clear that we are discussing a property in a vector field. Rex the first talk | contribs 01:00, 27 February 2007 (UTC)
thread_title:  Notation consistancy 

message: Looks to me like this article ought to be rolled in with substantive derivative.    Linuxlad 14:19, 22 June 2006 (UTC)
thread_title: Two of a kind

message: Is there any special reason for the parentheses used on the RHS in the definitions?
—DIV (128.250.204.118 09:04, 6 April 2007 (UTC)
thread_title: Parentheses

message: The first section of this article claims to define the convective derivative.  The next section offers a proof.  How can a definition be proven?  I am confused.  Is the proof intended to show that the convective derivative is the partial derivative with respect to time in a frame that moves with material particles?  That requires some reasoning, I think, not just direct application of the chain rule.
155.37.79.216 14:27, 7 September 2007 (UTC)
thread_title:  What has been proven? 

message: :There is a subtlety that the proof has missed.  Consider the point \mathbf{r}=\mathbf{r}(t) and \phi(\mathbf{x},t)  for \mathbf{x} a position coordinate independent of t, then the total derivative d\phi(\mathbf{r}(t), t) / dt may be found
:\frac{d\phi(\mathbf{r}(t), t)}{dt} =  \left. \frac{\partial \phi(\mathbf{x},t)}{\partial t} \right|_{\mathbf{x}=\mathbf{r}} +  \frac{d \mathbf{r}}{dt}  \cdot  \left[\nabla \phi(\mathbf{x},t) \right]_{\mathbf{x}=\mathbf{r}} 
If and only if \mathbf{r} is a Lagrangian point, so d \mathbf{r}(t) / dt = \mathbf{u}, does the total time derivative equal the convective derivative.
139.80.48.19 (talk) 22:29, 19 March 2008 (UTC)
thread_title:  A subtlety 

message: I propose to rename this article to Material derivative, because:
#Convective derivative is ambiguous, since it is also used to denote only the spatial part, v•∇.
#Material derivative is more commonly used. A Google Books search for the exact phrase gives:
:
phrase                         	hits
material derivative            	837
substantial derivative         	693
convective derivative          	650 (incl. uses for only the spatial part)
Lagrangian derivative          	490
substantive derivative         	407
derivative following the motion	321
particle derivative            	177
hydrodynamic derivative        	162
Stokes derivative              	106
advective derivative           	77
Crowsnest (talk) 22:26, 23 June 2008 (UTC)
thread_title:  Rename to Material derivative 

message: According to Help:Section#Floating_the_TOC, the TOC is floated "when it is beneficial to the layout of the article, or when the default TOC gets in the way of other elements." In what way is the template here beneficial to the layout of the article? More than 99% of our mathematics articles have never used this template; many of them have identical layouts of a lede section, a TOC, and then several lower sections, without images or other floating elements. — Carl (CBM · talk) 18:13, 21 May 2010 (UTC)
replies: text: The TOC to the right is benificial for this article, to my opinion, because it directly reveals the alternate names (most of them redirecting to here) given in the section "Names", which otherwise are separated by the TOC. So the TOC on the right is used to minimise in the lay-out the distance between the lead and the "Names" section. This article is special in the sense that a lot of alternative names are used for the same operator, and the TOC on the right helps to directly have an overview (on the same screen) without need of scrolling. -- Crowsnest (talk) 17:50, 11 June 2010 (UTC)
thread_title:  TOC right 

message: I want to ask if the formula for the material derivative for vector fields is wrong: it does not seem to define an objective quantity. 
I would have strongly expected an additional corotational term $+\vec{\omega} \times \vec{A}$, where $\vec{\omega}$ is the local vorticity of the fluid, because a rotating flow should rotate any local vectorial quantity $\vec{A}$ associated with the material. 
In the literature, this material derivative for vectorial quantities (including the additional corrotation term) is sometimes referred to as Jaumann corotational derivative if I understand correctly. 
I would like to change the main article, but want to consult with the community first. 
Benjamin.friedrich (talk)  — Preceding undated comment added 09:09, 16 January 2021 (UTC)
replies: text: Dear Benjamin.friedrich, thanks for pointing this out. Please go ahead to improve the article. I did not look deeply into it, but a quick search on material derivative for vector fields seems to support your assessment. Please add some references endorsing the changed or new material, see WP:REF. -- Crowsnest (talk) 20:09, 24 January 2021 (UTC)

text: An important point regarding this co-rotational term seems to be whether the observation is made in a rotating frame of reference or not. -- Crowsnest (talk) 20:36, 24 January 2021 (UTC)
replies: text: See Upper-convected time derivative for the derivative in fluids with rotation. That article says that this is identical to the Lie derivative, which  would then tell you about the general case of coordinate systems with non-trivial metric tensors (e.g. hydrodynamics near a black hole). Anyway, this article should clarify such questions/issues. 67.198.37.16 (talk) 20:53, 21 March 2024 (UTC)
thread_title:  Formula wrong for vector fields?