Normally, people apply plane-wave analyses even in a curved geometry, often irrespective of wavelengths. It is mostly encountered in the area of astrophysics and space sciences, even without considering any inter-dependency between the perturbation wavelength and the radius of curvature. What is the main justification?
Can I get some references on the planar-nonplanar wave connectivity and inter-transitional behaviour?
In many cases boundary conditions are not known, or not important for the specific problem. For example in a big enough but finite piece of metal, for the electron inside it the exact boundary shape is unimportant and an infinite uniform assumption is appropriate, allowing to decompose the electron wave function in plane waves.
In astrophysics, curvature would generally apply in two situations, gravitational lensing dues to galaxies and clusters and in the overall curvature of the universe. For the former case, the wavelengths involved are much smaller than the radius of curvature because we cannot observe signals with wavelengths many light years long. In the latter case, curvature is taken into account in considering for example luminosity distance in a non-flat universe.
George: There are many more situations in astrophysics where geometrical curvature may be locally neglected. For a start think about describing small volumes of the atmosphere or the interior of stars and planets, or local regions in galactic, proto-planetary of circum-black-hole disks.
I am grateful to you all for answers and references.
Hope this discussion to continue.
The main reason to employ planar-analysis of wave is just to make mathematics easier, otherwise there is no valid physical justification.
Actually, the valid analysis of the wave with non-planar or curve morphology is Laguerre-Gaussian type.
For more details check the listed references;
Kashif Arshad, M. Lazar and S. Poedts (2017), "Quasi-electrostatic twisted waves in Lorentzian dusty plasmas", Planetary and Space Science 156, 139-146.
Kashif Arshad, M. Lazar, S. Mahmood, Aman-ur-Rehman and S. Poedts (2017), "Kinetic study of electrostatic twisted waves instability in nonthermal dusty plasmas", Physics of Plasmas 24, 033701.
- Badges
- Science topic
- Similar topics
- Geoscience
- Cartography
- Mapping