Timeline for When is it true that "for a given velocity field, the curl represents a vector equal to twice the angular velocity vector"?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| May 22, 2021 at 17:18 | comment | added | Steven Thomas Hatton | He was explicitly addressing the fact that in a laminar flow none of the parcel trajectories are curved. I'm not claiming any kind of "vindication". I just found it interesting in the context of my question. | |
| May 21, 2021 at 10:43 | comment | added | J. Murray | @StevenThomasHatton Vorticity is a related concept, as I mentioned at the end of my answer. It is equal to (twice) the angular velocity of a local fluid parcel about its center of mass. | |
| May 21, 2021 at 5:08 | comment | added | Steven Thomas Hatton | I noticed that in one of those ancient videos the term "vorticity" was suggested to address my objection that nothing seems to actually be "rotating" in the case I presented. youtu.be/loCLkcYEWD4 | |
| May 19, 2021 at 0:10 | comment | added | Steven Thomas Hatton | This is an ancient and interesting demonstration of what rotation means in this context. youtu.be/pqWwHxn6LNo?t=1748 Deformation of Continuous Media | |
| Jul 15, 2020 at 17:49 | vote | accept | Steven Thomas Hatton | ||
| Jul 13, 2020 at 10:46 | comment | added | Steven Thomas Hatton | I guess one must consider the orientations of the diagonals of a square or cubic parcel as the frame which is rotated. | |
| Jul 12, 2020 at 19:49 | comment | added | J. Murray | @StevenThomasHatton That is not correct. The velocity gradient tensor is proportional to $\pmatrix{0& 0 \\1 & 0}= \pmatrix{0 & \frac{1}{2}\\ \frac{1}{2}&0} + \pmatrix{0 & -\frac{1}{2}\\ \frac{1}{2} & 0 } \equiv \mathbf D + \mathbf W$. $\mathbf W$ corresponds to the rate of rotation of a fluid parcel. | |
| Jul 12, 2020 at 1:11 | comment | added | Steven Thomas Hatton | The example of $\vec{v}=x\hat{j}$ results in $\vec{\omega}=\frac{1}{2}\hat{k}$ which does not give the velocity of a material point relative to the center of a parcel using $\vec{\omega }\times \vec{r}$. The instantaneous deformation of a parcel is a sheer without rotation. | |
| Jul 7, 2020 at 5:47 | history | answered | J. Murray | CC BY-SA 4.0 |