Recent notes

Water waves, mathematics & computation

Bing-Hai Lei’s notes on theoretical fluid mechanics, numerical methods, and the mathematics behind them—derivations, reading trails, and reusable calculations.

LID-DRIVEN CAVITYRe 100

U 0.50 ν 0.0050

About this flow

Precomputed 2D steady solutions, Re 10–400. U and ν use model units with L = 1. Intermediate states are interpolated; the smooth transition is visual, not a transient CFD solution. Tracers play at 2× model time. Colors show normalized vorticity with a fixed, symmetric asinh scale, clipped at ±18. Tiny corner eddies may be below this preview’s resolution.

Preparing flow…

Fourier Multipliers as Operators

Fourier Multipliers as Operators Fourier analysis is especially useful for linear, translation-invariant operators. In physical space, such an operator may involve derivatives…

2026-08-23

Index Notation and Embedded Surfaces

Index Notation and Embedded Surfaces Index notation and differential geometry provide compact ways to describe vectors, tensors, and curved surfaces. This short note collects a…

2026-08-23

Kelvin WedgeReading NoteIn Progress

What does $x^{\prime}$ mean in a Green’s function? — a linear algebra and operator view

In a Green's function $G(x,x')$, the primed variable $x'$ marks the source point — the location of a unit impulse — while $x$ is the field point where the response is…

2026-04-30

人应该怎样度过一生一

浓雾氤氲的森林，分不清是清晨还是黄昏，天边应该是有丝丝破碎的晨曦亦或是夕阳，还未走进你眼眸，便融化进了昏霭，染成一片模糊的光晕。你的思绪也仿若虚无之地，白茫茫一片，犹豫，抬起脚，犹豫，犹豫，犹豫，向前？向后？是追忆还是邂逅迷茫？

2026-03-25

Kelvin WedgeReading NoteIn Progress

From the Spectral Dirichlet-Neumann Symbol to the Physical-Space Operator Identity

We show how the spectral relation ∑ Formula implies the physical-space operator identity ∑ Formula, by inverse Fourier transform and the commutation of $\partial_z$ with the hori…

2026-02-05

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