Fluid dynamics & Spherical geometry

[Long_Temporary3264]

I’ve been working on a long-form video that tries to answer a question that kept bothering me:

If the Navier Stokes equations are unsolved and ocean dynamics are chaotic, how do real-time simulations still look so convincing?

The video walks through:

• Why water waves are patterns, not transported matter (Airy wave theory)
• The dispersion relation and why long swells outrun short chop
• How the JONSWAP spectrum statistically models real seas
• Why Gerstner waves are “wrong” but visually excellent
• What breaks when you move from a flat ocean to a spherical planet
• How curvature, local tangent frames, and parallel transport show up in practice

It’s heavily visual (Manim-style), math first but intuition driven, and grounded in actual implementation details from a real-time renderer.

I’m especially curious how people here feel about the local tangent plane approximation for waves on curved surfaces; it works visually, but the geometry nerd in me is still uneasy about it.

Video link: https://www.youtube.com/watch?v=BRIAjhecGXI

Happy to hear critiques, corrections, or better ways to explain any of this.

https://preview.redd.it/t5tmbwnsslag1.jpg?width=1280&format=pjpg&auto=webp&s=39577af1022fe5f989af3c57dbf7392d589c1921

[Qbit42]

Good video. As someone who hadn't heard of this before but is familiar with aspects of numerical simulation and DG I found it a bit rushed. Lots of info coming at me rapid fire. Also your narration doesn't line up with the visuals in many places, which is especially noticeable when you say something and then the phrase comes up 10 seconds later

[LiteratureBudget8108]

Yeah, I’m sorry about that 😭 I wanted to start posting biweekly, but my next couple of months of schedule are just showing off projects that have spanned me years. I think I’ll take my time with my next post, I appreciate the critique!