# Kelvin and Rossby waves / 开尔文波与罗斯贝波

中英双语教学动画，无配音。用解析形状展示理想模型，不是观测或数值预报。
Bilingual on-screen teaching animation, without narration; illustrative analytic shapes, not observations or a forecast.

1. Coastal Kelvin: north is up, east right, land south. Northern Hemisphere eastward propagation leaves land on the right. The displayed oscillation amplitude decays offshore as exp(-d/R). Curves are amplitude sketches, not trajectories or a full map of sea-surface height.
2. Kelvin trapping: coastal R=c/|f|, equatorial L=sqrt(c/beta) for a Gaussian exp(-y²/(2L²)). c is modal speed. External shallow-water c=sqrt(gH); internal modes require their own speed. Cross-wave geostrophy does not imply along-wave geostrophic balance.
3. Rossby mechanism: ideal constant-thickness northward displacement conserves (f+zeta)/H, increasing f and decreasing relative vorticity. Clockwise rotation is shown schematically, not integrated from the governing equations.
4. Midlatitude Rossby dispersion: omega=-beta*k/(k²+l²+R^-2), no background flow. Westward phase does not force westward group velocity. This formula is not the full equatorial dispersion relation.
5. Equatorial comparison: moving dots represent signals, not parcels; their speed ratio is chosen for readability, not measured. Equatorial Kelvin is eastward. Large-scale equatorial Rossby signals can move westward. Boundary reflections are not modeled.

Sources:
- https://www.psl.noaa.gov/enso/glossary.html
- https://uhslc.soest.hawaii.edu/ocn620/notes/rossby-waves.html

Render: python -m manim -qm kelvin_rossby_animation.py OceanWaves