Timeline for Linearized stream function
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 3, 2016 at 18:19 | history | bounty ended | charlestoncrabb | ||
| Feb 3, 2016 at 14:15 | comment | added | Willie Wong | some arbitrary function $f$ [e.g. the case of traveling solitons]. But if you expect wave like behaviour than it is natural to postulate that $f$ takes the form of $\exp i \alpha$ and see what happens.) | |
| Feb 3, 2016 at 14:13 | comment | added | Willie Wong | @charlestoncrabb: "why it works" is basically answered by "you plug it in and see what happens". The motivation behind the choice is that parallel shear flow can be imagined to be a flow between two plates, where the fluid is flowing in the $x$ direction with velocity depending on the $y$ direction only. If you add a perturbation, you sort of intuitively expect the perturbation to be carried down stream in a traveling wave. So a first order approximation is precisely of the form $\Psi(y) \exp (i \alpha (x - ct))$. (A traveling wave solution more generally should depend on $f(x-ct)$ for | |
| Feb 3, 2016 at 0:38 | comment | added | charlestoncrabb | Thank you very much for your thoughtful response. What you've said makes sense. I awarded the bounty, though I am still curious what the motivation behind choosing $\phi=\Psi(y)e^{ia(x-ct)}$. Is there a nice intuitive connection between this ansatz and why it works? | |
| Feb 3, 2016 at 0:36 | vote | accept | charlestoncrabb | ||
| Feb 1, 2016 at 15:36 | history | answered | Willie Wong | CC BY-SA 3.0 |