Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.07446 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We present an analogy between natural oscillations of the standing wave type on a pool of liquid with an interface and a mechanical oscillator model. It is shown that the equations of motion governing both systems have qualitatively similar solutions - trivial as well as time-periodic with finite amplitude. The time-periodic solutions can be linearly unstable in both cases depending on the oscillation amplitude, thereby leading to interesting dynamics. Linear stability results of both systems are discussed in detail; a novel Mathieu-like equation is derived for the stability of the standing wave to a super-harmonic perturbation. This is obtained through a much simpler approach that yields linear stability results while also reinforcing the analogy. Analytical predictions are compared against numerical solutions to the full nonlinear governing equations for both systems. A good match is obtained in most cases with theory; mismatches are further analysed and the limitations of this analogy are also pointed out.